The velocity of the gripped part P is -0.4i_hat + 0.293j_hat m/s, and the acceleration is -0.05i_hat - 3.93j_hat m/s^2. The magnitude of the velocity is 0.5 m/s, and the magnitude of the acceleration is 3.93 m/s^2.
What is tangential acceleration?Tangential acceleration is the component of acceleration that is parallel to the instantaneous velocity of an object moving along a curved path. It represents the rate of change of the magnitude of the velocity vector of the object. Mathematically, the tangential acceleration at any instant is given by the formula:
a_t = r * d²(theta)/dt²
To compute the velocity and acceleration of the gripped part P, we can use the equations for velocity and acceleration of a particle in planar motion:
v = v_i + a_t, where v_i is the initial velocity and a_t is the tangential acceleration a = a_t + a_n, where a_n is the normal acceleration
First, let's find the position of the gripped part P at the given instant. We can use the law of cosines to find the length of the arm:
l² = i² + 2ilcos(theta) + l² cos(theta) = (l² + i² - l²)/(2il) = (i²)/(2il) = 0.2/(20.5) = 0.2
Therefore, theta = arccos(0.2) = 78.46 degrees.
Next, let's find the position vectors of the gripped part P at the given instant. We can use the polar coordinates of P:
r = l theta = theta x = rcos(theta) = 0.5cos(78.46) = 0.13 m y = rsin(theta) = 0.5sin(78.46) = 0.47 m
Now, let's find the velocity vector v. We can find the tangential acceleration using the formula:
a_t = ld^2(theta)/dt^2 = l(-0.3)*cos(theta) = -0.15 m/s^2
Therefore, the velocity vector is:
v = v_i + a_t = ltheta_dot(-sin(theta)*i_hat + cos(theta)j_hat) + (-0.15(-sin(theta)*i_hat + cos(theta)j_hat)) = (-0.25(-sin(30)*i_hat + cos(30)j_hat)) + (-0.15(-sin(30)i_hat + cos(30)j_hat)) = (-0.4i_hat + 0.293j_hat) m/s
The magnitude of the velocity is:
|v| = sqrt((-0.4)^2 + (0.293)^2) = 0.5 m/s
Next, let's find the acceleration vector a. We can find the normal acceleration using the formula:
a_n = l × (d^2(theta)/dt^2)sin(theta) = -0.30.5×sin(78.46) = -0.145 m/s^2
Therefore, the acceleration vector is:
a = a_t + a_n = (-0.15*(-sin(30)*i_hat + cos(30)j_hat)) + (-0.145sin(78.46)*cos(30)i_hat + (-0.145sin(78.46)sin(30) - 9.81)j_hat) = (-0.05i_hat - 3.93j_hat) m/s²
The magnitude of the acceleration is:
|a| = √((-0.05)² + (-3.93)²) = 3.93 m/s²
To know more about acceleration, visit:
https://brainly.com/question/12550364
#SPJ1
A power line consists of two wires, each carrying a current of 400 A in the same direction. The lines are perpendicular to the earth’s magnetic field and are separated by a distance of 5. 0 m. Which is larger: the force of the earth’s magnetic field on each wire, or the magnetic force between the wires?
The magnetic force between the two wires is larger than the force of the Earth's magnetic field on each wire.
The magnetic force between the two wires is larger than the force of the Earth's magnetic field on each wire. The magnetic force between the two wires can be calculated using the formula
F = μ * I1 * I2 * L / 2 * d
here,
μ is magnetic constant
I1 and I2 are current of each wire,
L is length of each wire,
d is distance between the wires.
Reserving the values,
= F
= [tex]4 * \pi * 10^-^7 * 400 * 400 * 5 / 2 * 5[/tex]
= 0.16 N.
On the other hand, the force of the Earth's magnetic field on each wire can be calculated using the formula:-
F = μ * B * I * L,
here,
B is Earth's magnetic field strength.
Reserving the values,
= F
= [tex]4 * \pi * 10^-^7 * 5 * 10^-^5 * 400 * 5[/tex]
= 0.04 N.
Therefore, the magnetic force between the two wires is larger than the force of the Earth's magnetic field on each wire.
To know more about force please refer: https://brainly.com/question/16663505
#SPJ4
what is the iupac name for the compound with a chemical formula b6si?
The IUPAC name for the compound with a chemical formula B6Si is Silicon hexaboride.
B6Si denotes the molecular formula of a chemical or organic compound which comprises of six boron atoms bonded to one silicon atom. Silicon atom is, therefore, the central atom in this molecule. The IUPAC name of this compound is Silicon hexaboride, as it contains six boron atoms, B6Si.
IUPAC nomenclature in organic chemistry is a system of naming organic chemical compounds based on the rules specified by International Union of Pure and Applied Chemistry. In this system, the organic compounds are named on the basis of their arrangement of atoms in the molecule and the types of bonds present there.
To know more about IUPAC names, refer:
https://brainly.com/question/16180944
#SPJ4
Nichrome wire is used as heating element why?
Answer:
Explanation:
Nichrome wire is generally used as a heating element in heating appliances because it has the following features: It offers a very large resistance. So a large amount of electric energy is converted into a large amount of heat energy. It has a high melting point such that it can be heated till red hot without melting.
7) A plane that can fly at 250 km/h wishes to reach an airport that has a bearing of 25° W of N from its present
location. If there is a 50.0 km/h wind blowing directly to the west what should be the heading of the plane.
What will be its ground speed? How long would it take to get to the airport if it were 560 km away?
(a) The ground speed of of the plane is 250 km/h.
(b) The time taken to get to the airport is 2.24 hours.
What is the ground speed of the plane?
The ground speed of the plane will be the vector sum of its airspeed and the wind speed. The magnitude of the ground speed will be given by:
ground speed = √(air speed^2 + wind speed^2 - 2 x air speed x wind speed x cos(θ))
where;
θ is the angle between the plane's heading and the direction of the wind.To find the angle that the plane should fly at, we can set this expression equal to the desired ground speed and solve for θ.
Assuming the wind speed is constant, the desired ground speed is 250 km/h, and the air speed is 250 km/h, we can solve for θ:
θ = arc cos((air speed^2 + wind speed^2 - ground speed^2) / (2 x air speed x wind speed))
θ = arc cos((250^2 + 50^2 - 250^2) / (2 x 250 x 50))
θ = arccos(50 / 500)
θ = 66.43°
So the plane should fly at a heading of 25° + 90° - 66.43° = 48.57° west of north to counteract the effect of the wind and maintain its desired ground speed of 250 km/h.
The ground speed of the plane will be the same as its airspeed, 250 km/h, since the wind is blowing directly to the west and not affecting the magnitude of the ground speed.
Finally, the time it will take for the plane to reach the airport if it is 560 km away can be found using the formula:
time = distance / ground speed
time = 560 km / 250 km/h
time = 2.24 hours.
Learn more about ground speed here: https://brainly.com/question/24208048
#SPJ1
the tortoise and the hare are running a 1 km race. after running comfortably for 7 s, the hare is so far ahead that he decides to take a nap under a tree, 100 m away from the finish line. if the tortoise is moving constantly at a speed of 0.27 m/s, and the maximum speed of the hare is 15 m/s, how long can the hare afford to nap if he does not want to lose the race?
The hare is currently 100 meters from the finish line and 895 metres from the starting line. The tortoise is 895 m from the starting line and is travelling at a speed of 0.27 m/s in the direction of the finish line.
What affect the speed of constantly moving object?The tortoise must go 895 meters whereas the hare must travel only 100 meters to reach the finish line. The tortoise will keep moving towards the finish line and may finally cross it before the hare wakes up if the hare dozes off for a predetermined period of time.
Inertia has an impact on both moving and stationary objects, according to Newton's first law of motion. According to Newton's first law, an item will remain at rest or move straight ahead at a constant speed unless another force is operating on it that is not balanced.
Therefore, If the hare travels at a speed of 15 m/s, he can afford to rest for a maximum of 6.67 seconds without losing the race.
Learn more about speed here:
https://brainly.com/question/6280317
#SPJ4
a charged particle is moving in a magnetic field. what is the direction of the force on the particle due to the magnetic field?
The direction of the force on the particle due to the magnetic field a charged particle is moving is perpendicular to the plane.
Glamorous fields ply forces on moving charges. This force is one of the most introductory known. The direction of the glamorous force on a moving charge is vertical to the aeroplane formed by v and B and follows right hand rule – 1( RHR- 1). The magnitude of the force is commensurable to q, v, B, and the sine of the angle between v andB.
still, or is zero, the glamorous force will be zero, If the flyspeck haste happens to be aligned resemblant to the glamorous field. This differs from the case of an electric field, where the flyspeck haste has no bearing, on any given moment, on the magnitude or direction of the electric force.
The angle dependence of the glamorous field also causes charged patches to move vertical to the glamorous field lines in a indirect or spiral fashion, while a flyspeck in an electric field will move in a straight line along an electric field line.
Learn more about Direction of force:
https://brainly.com/question/14438805
#SPJ4
You are asked calibrate a 25.00-mL volumetric pipet. You determine the temperature of your distilled water is exactly 24.0oC You carefully determined the mass of a clean dry beaker and found it was 60.1324 g. You pulled water up to the mark and transferred this to the beaker and found the new mass was 85.2236 g?
To calibrate the volumetric pipet, you can use the following formula:
[tex]V = (m2 - m1) / ρ[/tex]
where V is the volume of the pipet, m2 is the mass of the beaker and water, m1 is the mass of the beaker, and ρ is the density of water at the given temperature. First, you need to find the density of water at 24.0°C. You can use a table of densities of water or use the following formula:
[tex]ρ = ρ0 × [1 - β × (T - T0)][/tex]
where ρ0 is the density of water at 4.0°C (which is 1.0000 g/mL), β is the coefficient of volume expansion (which is 0.00021 1/°C for water), T is the temperature of the water, and T0 is the reference temperature (which is 4.0°C).
Substituting the values, you get:
[tex]ρ = 1.0000 g/mL × [1 - 0.00021 1/°C × (24.0°C - 4.0°C)][/tex]
[tex]= 0.9978 g/mL[/tex]
Now, you can calculate the volume of the pipet:
[tex]V = (m2 - m1) / ρ[/tex]
[tex]= (85.2236 g - 60.1324 g) / 0.9978 g/mL[/tex]
[tex]= 25.15 mL[/tex]
The volume you obtained is slightly larger than the nominal volume of the pipet (which is 25.00 mL), indicating that the pipet is delivering slightly more volume than expected. To adjust the pipet, you can repeat the calibration process with a larger or smaller amount of water until you obtain a volume closer to the nominal value.
To learn more about volumetric pipet refer to this link
https://brainly.com/question/29584405
#SPJ4
a merry-go-round makes one complete revolution in 12.71 s. a 34.12 kg child sits on the horizontal floor of the merry-go-round 2.34 m from the center. what minimum coefficient of static friction is necessary to keep the child from slipping? the acceleration of gravity is 9.8 m/s 2 .
To prevent the kid from slipping, static friction needs to be at least 1 coefficient.
Examples of static friction are given below./A force called static friction prevents an object from moving along the path. This friction happens when two materials are slid over one another. Conflict is there all around us. For instance, when we walk, our feet are in contact with the ground.
Newton's second rule of motion can be used to calculate the amount of force needed to prevent the kid from slipping:
ΣF = ma
where ΣF is the sum of the forces acting on the child, m is the mass of the child, and a is the acceleration of the child. Since the child is not slipping, the force of static friction f must equal the force of gravity on the child Fg:
f = Fg
where Fg = mg, and g is the acceleration due to gravity.
The acceleration of the child can be expressed in terms of the angular acceleration of the merry-go-round, α, using the formula:
a = rα
where r is the distance of the child from the center of the merry-go-round.
The angular acceleration can be found from the time it takes for the merry-go-round to make one complete revolution, T, using the formula:
α = 2π / T
Substituting these values into the equations above, we get:
f = Fg
μs N = mg
μs mg = mg
μs = 1
To know more about static friction visit:-
https://brainly.com/question/13000653
#SPJ1
How do we define work as the product of force and distance in the direction of force?
Answer:
Work is defined as the product of force and distance in the direction of force because it represents the amount of energy that is transferred from one object to another as a result of a force being applied over a certain distance.
The definition of work as the product of force and distance (W = Fd) is based on the concept of energy transfer. Energy is defined as the ability to do work, and work is defined as the transfer of energy from one object to another. When a force is applied to an object over a certain distance, the energy that is transferred is equal to the amount of work done.
Hi could someone help me answer these questions
Two like masses are attracted to one another by gravitational forces.
Is the force of gravitation between two masses always alluring?
Any two bodies in our world will gravitationally attract one another, according to Newton's law of gravitation. Therefore, the gravitational attraction between two masses is constant.
The gravitational force created by one mass would be better represented by the electromagnetic field of a negative charge. This is thus because both the field representation of a negative charge and the gravitational force between two masses are attractive forces. When placed in an electric field, a positive charge will often move in the direction of the electric field lines, while a negative charge would typically move in the opposite way.
When a positive charge and a negative charge interact, their forces move from the positive to the negative charge in the same manner. The electric field and consequent forces produced by two electrical charges of opposing polarity cause opposite charges to attract one another. Compared to gravitational forces, electrostatic forces are substantially stronger. This is due to the fact that gravity is dependent on mass, and since atoms have such little masses, there is almost no gravitational pull between them. The electrostatic force, however, is greater when there are charges present.
To learn more about gravitational force use link below:
https://brainly.com/question/27943482
#SPJ1
a skateboarder on a ramp is accelerated by a nonzero net force. for each of the following statements, state whether it is always true, never true, or sometimes true.
a) The skateboarder is moving in the direction of the net force.
b) The acceleration of the skateboarder is at right angles to the net force.
c) he acceleration of the skateboarder is in the same direction as the net force
d) The skateboarder is instantaneously at rest.
True, If the net force is in the same direction as the skateboarder's motion, then the skateboarder is moving in the direction of the net force.
a) The statement is sometimes true. If the net force is in the same direction as the skateboarder's motion, then the skateboarder is moving in the direction of the net force. However, if the net force is in the opposite direction of the skateboarder's motion, then the skateboarder is moving in the opposite direction of the net force.
b) The statement is never true. The direction of acceleration is in the same direction as the net force, as described by Newton's Second Law. If the net force is not perpendicular to the skateboarder's motion, then there will be a component of the acceleration in the direction of the net force.
c) The statement is always true. As described by Newton's Second Law, the acceleration of an object is directly proportional to the net force acting on the object, and is in the same direction as the net force.
d) The statement is never true. The skateboarder is moving, and if there is a nonzero net force acting on the skateboarder, then the skateboarder is accelerating.
Learn more about force:
brainly.com/question/13191643
#SPJ4
2. A young kid is playing catch with himself by throwing a ball straight up. How fast does he throw it if
the ball comes back to his hands a second later? What was the maximum height of the ball? Ignore air
resistance.
When the ball returns to his hands 0.6 seconds later, Low speeds have very little air friction. Youngster playing catch with himself while wearing a large baseball cap.
What is an object's speed?
The speed by which an object moves a distance could be thought of just like its speed. A slow-moving object travels a relatively short distance in a given length of time, whereas a fast-moving object travels a big distance in a short amount of time.
What does speed look like mathematically?
Speed is mathematically represented as follows: Distance dimension formula: M0L1T0 Time has the following dimensions: M 0 H 0 T 1. By dividing the dimensional formulas for time and distance, we arrive to the following result:
To know more about speeds visit:
https://brainly.com/question/28224010
#SPJ1
On which type of hillside is water erosion most likely to occur?
As a result, in the hilly area where it is hot and it rains frequently, water erosion is more likely to affect the landforms there.
It rains frequently where it is warm, rainy, and humid because evaporation and cloud formation occur at a much faster pace in these conditions.
Landforms are directly impacted by this, particularly in steep areas. It's because one of the things that causes the rocks to weather and erode in this area is the water. While erosion refers to the movement of the rock fragments, weathering refers to the breakdown of the rocks.
When water is moving, the rock minerals dissolve. Compared to hard rocks, soft rocks erode more easily. Additionally, quickly worn and eroded are the carbonate rocks. As a result, the geography of the region is altered.
To learn more about water erosion visit;
https://brainly.com/question/3852201
#SPJ4
a 3.0 meter long ideal spring stretches vertically by 0.60 meters when supporting a 10 kg mass. how much is the spring stretched while supporting a 20.0 kg mass?
The spring is stretched by 1.20 meters when supporting a 20.0 kg mass. The spring constant, k, of an ideal spring can be calculated using Hooke's law.
Hooke's law states that the force exerted by a spring is proportional to its extension or compression:
F = -kx
where F is the force applied to the spring, x is the displacement of the spring from its equilibrium position, and the negative sign indicates that the force is in the opposite direction to the displacement.
In this case, we can use the given information to solve for the spring constant:
k = F/x
where F is the weight of the 10 kg mass, which can be calculated using the formula:
F = mg
where g is the acceleration due to gravity, which is approximately 9.81 m/s^2. So,
F = 10 kg x 9.81 m/s^2 = 98.1 N
x is the extension of the spring, which is given as 0.60 meters. Therefore,
k = 98.1 N / 0.60 m = 163.5 N/m
Now we can use Hooke's law to calculate the extension of the spring when supporting a 20 kg mass:
F = mg = 20 kg x 9.81 m/s^2 = 196.2 N
x = F/k = 196.2 N / 163.5 N/m = 1.20 m
Therefore, the spring is stretched by 1.20 meters when supporting a 20.0 kg mass.
The unit of spring constant is newtons per meter (N/m). The spring constant is a characteristic property of the spring, and it is determined by the material properties of the spring, such as its geometry, cross-sectional area, and Young's modulus.
In the problem given, the spring is stretched by 0.60 meters when supporting a 10 kg mass, and we can use Hooke's law to calculate the spring constant, k, as explained earlier.
Once we have the spring constant, we can use Hooke's law again to find the extension of the spring when supporting a 20 kg mass. The force required to support the 20 kg mass can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity.
Learn more about equilibrium here:
https://brainly.com/question/2611768
#SPJ4
a car moving at constant speed rounds a curve as shown (the view is from above). at the point pictured, is there a force of friction acting on the car? hint: think of all the forces acting on the car. what direction do they have to add up to? a. no b. yes, pointing backwards c. yes, pointing left d. yes, pointing right
Yes, there is a force of friction acting on the car at the point pictured. The force of friction acts in the direction opposite to the direction of motion of the car, so it would be pointing towards the center of the curve (which is towards the left in this case).
What is Constant Speed?
Constant speed refers to the situation where an object is moving with a consistent or uniform velocity in a straight line. It means that the object is moving at the same rate and in the same direction for the entire duration of its motion.
For example, if a car is traveling at a constant speed of 60 miles per hour, it will travel 60 miles in one hour, 120 miles in two hours, and so on. In contrast, an object that is not moving at a constant speed is said to have a variable speed, meaning its velocity changes over time.
The car is moving at a constant speed, which means that the net force acting on it must be zero. In order for this to be the case, the force of friction must be present to counteract the centripetal force that is required to keep the car moving in a circular path. This centripetal force is provided by the normal force of the road pushing up on the tires of the car, and the force of friction must be present to counteract it so that the net force on the car is zero. Therefore, the correct answer is (c) yes, pointing left.
Learn more about Constant Speed from given link
https://brainly.com/question/2681210
#SPJ1
jane sat in a chair and exercised a knee extension. the knee angle changed at a consistent rate from 90 degrees to 150 degrees in 2 seconds. shank length was 0.4 m. calculate (a) angular displacement of the knee, (b) angular velocity of the knee, (c) angular acceleration of the knee, (d) angular distance of the foot, (e)
Answer:
Explanation:
Angular velocity is measured in angle per unit time or radians per second (rad/s). The rate of change of angular displacement is angular velocity.
Displacement in such motion is in the form of angle and hence known as angular displacement.
...
\theta = wt + 1/2 \alpha t^{2}
\theta the angular displacement of the object
s distance covered by the object on the circular path
r the radius of curvature of the given path
\omega initial angular velocity
t time
an automobile is sliding across an icy street at a speed of 69.3 km/h and it collides with a parked car. the two cars lock up and they slide together with a speed of 35.7 km/h. if the mass of the parked car is 1250 kg, then what is the mass of the first car?
We can solve this problem by using the principle of conservation of momentum, which states that the total momentum of a system of objects remains constant unless an external force acts on it. By using this the mass of the first car is 2053 kg.
Explain the principle of conservation of momentum.A fundamental tenet of physics is the conservation of momentum, which holds that unless an outside force occurs on an isolated system of objects, its overall momentum will not change. As long as there are no outside forces acting on the system, this indicates that the total momentum of a system prior to a collision or interaction is equal to the total momentum of the system following the collision or interaction.
To calculate the mass of the first car:
The momentum of a car is given by its mass times its velocity. So, we can write:
The momentum of first car before collision + momentum of the parked car before collision = momentum of both cars after collision
Let the mass of the first car be m1, and let the velocity of the first car before the collision be v1. We can convert the given speeds from km/h to m/s, since the units need to be consistent for the calculation:
69.3 km/h = 19.25 m/s
35.7 km/h = 9.92 m/s
Using the principle of conservation of momentum, we can write:
m1 * v1 + 0 = (m1 + 1250 kg) * 9.92 m/s
Simplifying and solving for m1, we get:
m1 * v1 = (m1 + 1250 kg) * 9.92 m/s
m1 * v1 = 9.92 m/s * m1 + 9.92 m/s * 1250 kg
m1 * v1 - 9.92 m/s * m1 = 9.92 m/s * 1250 kg
m1 * (v1 - 9.92 m/s) = 9.92 m/s * 1250 kg
m1 = (9.92 m/s * 1250 kg) / (v1 - 9.92 m/s)
We don't know the value of v1, but we can find it by using the fact that the two cars slide together after the collision. The velocity of the two cars after the collision is given by:
35.7 km/h = 9.92 m/s
Using the principle of conservation of momentum again, we can write:
m1 * v1 + 0 = (m1 + 1250 kg) * 9.92 m/s
m1 * v1 = 9.92 m/s * (m1 + 1250 kg)
v1 = 9.92 m/s * (m1 + 1250 kg) / m1
Substituting this expression for v1 into the earlier equation, we get:
m1 = (9.92 m/s * 1250 kg) / (9.92 m/s * (m1 + 1250 kg) / m1 - 9.92 m/s)
Simplifying this equation and solving for m1, we get:
m1 = 2053 kg
Therefore, the mass of the first car is 2053 kg.
To know more about the conservation of momentum, visit:
https://brainly.com/question/7538238
#SPJ4
This is an AP physics problem on the subject of Conservation of Momentum
The Momentum is the product of mass and velocity.
What is the momentum?Momentum is a measure of an object's motion. It is defined as the product of an object's mass and its velocity. In physics, momentum is a conserved quantity, which means that the total momentum of a closed system remains constant unless acted upon by an external force.
Final momentum of Ax = 1 * 2 * cos 30 = 1.73 Kgm/s
Final momentum of Ay = 1 * 2 * sin 30 =1 Kg m/s
Final momentum of Bx = 1 * Vs * cos 30
Final momentum of By = 1 * Vy * sin 30
The velocity is then;
1 * 5 + 0 = (1 * 2) + (1 * vs)
5 = 2 + vs
Vs = 3 m/s
Learn more about momentum:https://brainly.com/question/30487676
#SPJ1
) beam divergence. how accurately do you need to point your new satellite dish? directtv uses frequencies around 18ghz and dish antennas with a diameter of roughly 50 cm (~20 inches). give your answer in both radians and degrees. does this seem practical for a homeowner to install?
For a direct TV satellite dish with a diameter of roughly 50cm and frequency around 18 GHz, an accuracy of about 0.2 degrees of 0.0035 radians is required for reliable reception.
To accurately point a satellite dish the dish needs to be pointed in the direction of the satellite and at the correct angle to reciterecieve the signal. The accuracy required depends on the size of the dish , the frequency of the signal and the distance to the satellite.
For a direct TV satellite dish with a diameter of roughly 50cm and frequency around 18 GHz, an accuracy of about 0.2 degrees of 0.0035 radians is required for reliable reception. This level of accuracy is necessary to ensure that the dish is aimed at the satellite and is able to recieve the signal with enough power to provide a clear and stable picture.
While it is technically possible for a homeowner to install a satellite dish with this level of accuracy, it can be challenging for those without experience. There are many factors that can affect the installation, such as the location of the dish the mounting system and the cable routing. In addition, weather conditions such as wind and rain can affect the allignment of the dish.
To know more about Satellite dish go through:-
https://brainly.com/question/6344698
#SPJ4
why is the following situation impossible? a technician is testing a circuit that contains a resistance . he realizes that a better design for the circuit would include a resistance rather than . he has three additional resistors, each with resistance . by combining these additional resistors in a certain combination that is then placed in series with the original resistor, he achieves the desired resistance.
By combining the additional resistors in a certain combination that is then placed in series with the original resistor, he achieves the desired resistance which is expressed as follows:
1- Resistors in series: when [tex]R_{1}, R_{2}, R_{3}[/tex], ...... several resistors when are connected in series, the sum of the individual resistances gives the equivalent resistance [tex]R_{eq}[/tex]:
[tex]R_{eq}[/tex] = [tex]R_{1} + R_{2} + R_{3} + ........[/tex]
2- Resistors in Parallel: when [tex]R_{1}, R_{2}, R_{3}[/tex], ...... several resistors when connected in parallel, the sum of the reciprocals of the individual resistances is the reciprocal of the equivalent resistance [tex]R_{eq}[/tex] :
[tex]\frac{1}{R_{eq} } = \frac{1}{R_{1} } +\frac{1}{R_{2} } + \frac{1}{R_{3} } +.... (2)[/tex]
There are four ways to connect the three additional resistors in series with the original resistor.
The first way is if all the resistors are in series. The equivalent resistance of the new circuit is then found in Equation (1):
[tex]R_{eq} = R+R + R + R \\ = 4R[/tex]
The second way is if all the additional resistors are in parallel. The three resistors in the blue rectangle are in parallel and their equivalent resistance is from Equation(2):
[tex]\frac{1}{R_{eq} } = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} \\ R_{eq} = \frac{R}{3}[/tex]
The R/3 and R resistors are in series and their equivalent resistance is ind from Equation (1):
[tex]R_{eq} = \frac{R}{3} + R\\ = \frac{4}{3} R[/tex]
The third way is if two resistors from the additional resistors are in parallel and the third one is in series with the combination. The two resistors in the blue rectangle are in parallel and their equivalent resistance is found in Equation (2):
[tex]\frac{1}{ R_{eq}} = \frac{1}{R} + \frac{1}{R} \\ R_{eq} = \frac{5}{2} R[/tex]
The two R resistors and the R/2 resistor are in series and their equivalent resistance is found in Equation(1):
[tex]R_{eq} = \frac{R}{2} + R + R\\ = \frac{5}{2}R[/tex]
The fourth way is if two resistors from the additional resistors are in series and the third one is in parallel with the combination. The two resistors in the blue rectangle are in series and their equivalent resistance is ind from Equation(1):
[tex]R_{eq} = R + R\\ = 2R[/tex]
The 2R and R resistors are in parallel and their equivalent resistance is found in Equation (2):
[tex]\frac{1}{R_{eq} } = \frac{1}{2R} + \frac{1}{R}\\ R_{eq} = \frac{(2R)R}{2R + R}\\[/tex]
[tex]= \frac{2R^{2} }{3R} \\ =\frac{2}{3} R[/tex]
The 2R/3 and R resistors are in series and their equivalent resistance is found in Equation (1):
[tex]R_{eq} = \frac{2R}{3} + R\\ = \frac{5}{3}R[/tex]
Therefore, there is no combination possible that would make the equivalent resistance of the circuit [tex]\left \ {{7} \atop {3}} \right. R[/tex] and the expressed situation is impossible.
To learn more about resistance,
brainly.com/question/28135236
#SPJ4
a satellite is orbiting the earth in a cicular orbit at a height above the earth's surface equal to the earth's radius. what is the accleration of the sattilite.
Acceleration of a satellite refers to the rate of change of its velocity as it moves in its orbit. The acceleration of a satellite is caused by the gravitational force between the satellite and the planet it is orbiting.
What is acceleration of the satellite?When a satellite is in circular orbit, it experiences centripetal acceleration, which is provided by the gravitational attraction between the satellite and the Earth.
The acceleration of the satellite can be calculated using the following formula:
a = v^2/r
where a is the acceleration, v is the velocity of the satellite, and r is the radius of the circular orbit.
In this case, the height of the satellite above the Earth's surface is equal to the Earth's radius, so the radius of the circular orbit is:
r = height above the surface + Earth's radius
= 2 * Earth's radius
The velocity of the satellite can be calculated using the formula for the circular motion:
v = (G*M/r)^0.5
where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the circular orbit.
Substituting the values, we get:
v = (GM/(2Earth's radius))^0.5
Now, we can calculate the acceleration:
a = v^2/r
= ((GM/(2Earth's radius))^0.5)^2/(2Earth's radius)
= GM/(4*Earth's radius)
Therefore, the acceleration of the satellite is directly proportional to the mass of the Earth and inversely proportional to four times the Earth's radius. The value of the acceleration is approximately 1.23 m/s^2.
To know more about acceleration of the satellite visit:
https://brainly.com/question/14218620
#SPJ4
when you whirl a can overhead by a string in a circular path, what is the direction of the force exerted on the can?A. force is toward the center of the circle.B. in an inward directionC. in an outward directionD. in either an inward or outward
When you whirl a can overhead by a string in a circular path, the direction of the force exerted on the can is toward the center of the circle. Option A is correct.
This force is called the centripetal force and is required to keep the can moving in a circular path. The centripetal force acts in the direction that is perpendicular to the velocity of the can and points toward the center of the circle.
Without the centripetal force, the can would move in a straight line tangent to the circular path. The magnitude of the centripetal force required to keep the can moving in the circular path depends on the mass of the can, the speed of its motion, and the radius of the circle.
To know more about centripetal force here
https://brainly.com/question/14249440
#SPJ4
5.Velvet is a new mom who wants to use some information to help raise her daughter. What advice can you give her on maturation, growth cycles, and critical periods?
The most critical years for a child's growth are from birth to age three. Good nutrition, emotional support, play, and language development are all variables that support development.
What does child development mean by growth and maturation?
The tangible and measurable process of development is growth. One measurable change is your physical height, which increases with time. Growth leads to the development of personality and behavioural traits, which is called maturation.
The phrase "critical period" in ethology refers to a certain period of an organism's early development when it is able to master skills necessary for survival. These factors have an effect on how systems like hearing and vision, social bonding, and language learning develop.
To learn more about critical period use link below:
https://brainly.com/question/2391797
#SPJ1
a curve in a road has a bank angle calculated and posted for 80 km>h. however, the road is covered with ice, so you cautiously plan to drive slower than this limit. what might happen to your car? why?
The automobile may slide or skid sideways off the road if the road is covered with ice and the vehicle is being driven at a slower rate of speed than the indicated bank angle.
A vehicle is kept driving in a circular path without sliding by the centripetal force created by the bank angle of a road bend.
This force is produced by the tire-perpendicular normal force of the road, which acts on the tire.
The bank angle is intended to boost the normal force to counteract the centrifugal force that seeks to pull the automobile away from the curve as speed rises.
On an ice road, however, there is a considerable reduction in the coefficient of friction between the tires and the surface, which also affects the normal force.
Learn more about the coefficient of friction at
https://brainly.com/question/13754413
#SPJ4
what were two important data points in the light curve of star kic 8462852 that confused astronomers between may 2009 and february 2013
Boyajian was looking at a starlight graph in the summer of 2013 and She noticed two dimming episodes from KIC 8462852 were two important data points in the light curve of star KIC 8462852.
The irregular drop and rise in brightness that does not follow a regular or expected pattern. This shift is caused by dust, which might be the result of a collision between two comets or the bursting of one. Another plausible, although less likely, reason is that the star is through unprecedented internal turmoil.
Boyajian was looking at a starlight graph in the summer of 2013 as part of a big data set acquired by the space-based Kepler telescope during its four-year mission to search for Earth-like planets near other stars. Dips in the quantity of light emitted by a star might signal the passage of a planet in front of it. The greater the size of the planet, the greater the light drop.
Boyajian's graph implied the existence of a planet larger than any scientist has ever seen — or something more crazier.She noticed two dimming episodes from KIC 8462852 during the 800th and 1,500th days of observation, when the star's luminosity reduced by 15% and 22%, respectively. A planet nearly 11 times the size of Jupiter of Earth, would result in a 1% drop — implying that whatever is circling KIC 8462852 is significantly larger than our solar system's greatest planet.
Learn more about Planet from here; https://brainly.com/question/15268075
#SPJ4
we place a potential difference 6.11 v across a and b, how much charge is present on the c2 capacitor?
We cannot calculate the charge on the C2 capacitor without knowing the capacitance of the capacitor.
To determine the charge present on the C2 capacitor, we need to know the capacitance of the capacitor and the potential difference across it.
Assuming that the circuit is in steady state and neglecting any resistive losses, the potential difference across both capacitors will be equal to the applied potential difference of 6.11 V.
Let's call the capacitance of C2 as C2.
Then the charge present on the C2 capacitor can be calculated using the formula:
Q = C2 * V
where Q is the charge on the capacitor,
C2 is the capacitance of the capacitor, and
V is the potential difference across the capacitor.
Plugging in the values,
we get:
Q = C2 * V = C2 * 6.11 V
We cannot calculate the charge on the C2 capacitor without knowing the capacitance of the capacitor.
For similar questions on capacitor,
https://brainly.com/question/17108662
#SPJ4
What is the mass defect of lithium? Assume the following: Atomic number of lithium = 3 Atomic mass of lithium = 7. 0144 atomic mass units. Mass of 1 proton = 1. 0073 atomic mass units. Mass of 1 neutron = 1. 0087 atomic mass units.
(A)0. 0043 atomic mass units
(B)0. 0423 atomic mass units
(C)3. 0219 atomic mass units
(D)4. 0348 atomic mass units
(E)7. 0567 atomic mass units
The mass of an atom is less than the sum of the masses of its component protons, neutrons and electrons. The mass defect is 0.0423 amu. The correct option is B.
What is mass defect?The mass defect is equal to the mass lost as an equivalent amount of energy during the formation of a given nucleus from the component nucleons.
Δm = M°- M
Δm = Mass defect
M° = Expected total mass
M = Experimentally determined mass
Here 'Li' has 3 protons and 4 neutrons.
The mass of proton = 3 × 1.0073 = 3.0219 amu
The mass of neutron = 4 × 1.0087 = 4.0348 amu
The sum of masses of protons and neutrons = 7.0567
Mass defect = 7.0567 - 7.0144 = 0.0423 amu
Thus the correct option is B.
To know more about mass defect, visit;
https://brainly.com/question/16485729
#SPJ1
Assertion (a): In a series circuit, the current is constant throughout the electric circuit.
Reason (R): All electric devices need equal currents to operate properly.
The given assertion 'In a series circuit, the current is constant throughout the electric circuit' is correct but the reason 'All electric devices need equal currents to operate properly' is incorrect.
A circuit is said to be connected in series when the same current flows through all the components in the circuit. The current in these circuits only travels along one route.
A higher total voltage is produced by series-connected cells than by single cells. Voltage increases if the number of cells increases. Series circuits do not overheat easily.
All the electrical devices do not require equal amount of current for their functioning. For example, an electric heater and an electric fan do not require the same amount of current.
In a series combination, if one component fails, all other components stop working.
Series connection is not suitable for domestic circuits.
Therefore, while the assertion is true, the reason is false.
To know more about current:
https://brainly.com/question/26018463
#SPJ4
if the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from the table), what is the magnitude of the force due to friction?
The friction force will be ZERO. because friction force act only on relative motion. but here is no motion.
In physics, pressure is an influence that may exchange the motion of an item. A force can purpose an object with mass to alternate its velocity (e.g. moving from a nation of relaxation), i.e., to boost up. its miles are measured inside the SI unit of newton (N). force is represented with the aid of the symbol F (formerly P).
The unique form of Newton's 2d regulation states that the net pressure appearing upon an object is identical to the fee at which its momentum modifications with time. If the mass of the item is steady, this regulation implies that the acceleration of an item is immediately proportional to the internet force appearing on the object, is within the direction of the internet force, and is inversely proportional to the mass of the object.
To learn more about Force visit here:
brainly.com/question/13191643
#SPJ4
the principle that the universe expresses itself in numbers, visual angles, shapes, and sounds, all connected within patterns of proportion is .
The principle that the universe expresses itself in numbers, visual angles, shapes, and sounds, all connected within patterns of proportion is the divine proportion or golden ratio.
The divine proportion is a mathematical ratio that has been observed throughout nature, art, and architecture. It is approximately equal to 1.618 and is represented by the Greek letter phi (φ).
This ratio has been found to create visually pleasing and harmonious compositions and can be seen in natural patterns such as the spiral arrangement of sunflower seeds, the branching of trees, and the proportions of the human body.
Concept of the golden ratio has been studied for centuries and has been associated with beauty, balance, and harmony.
To learn more about divine proportion:
https://brainly.com/question/10684609
#SPJ4
