The vehicle's speed is [tex]\mu g r[/tex]
When the car is in drive, all the forces are in
[tex]F_N cos\theta =mg + \mu_s\ F_N sin\theta[/tex]
It is a situation in which opposing forces or actions are in equilibrium and can be either static
like when forces act on a body and the resultant is zero or dynamic as in a reversible chemical reaction when the rates of reaction in both directions are equal
The state of equilibrium is one in which the forward and backward rates of response are equal.
equilibrium and harmony the vertical axis equation should be
[tex]F_N cos\theta +\mu_s F_N cos\theta =\frac{mv^2}{R}[/tex]
and along the horizontal axis,
[tex]F_N[/tex] = normal force= mg
solving equations 1 and 2 as a pair
[tex]v^2= \frac{(\mu_s \ cos\theta + sin\theta)Rg}{cos\theta - \mu_s sin \theta}[/tex]
in order to bank [tex]\theta = 0[/tex]
= [tex]\mu_s Rg[/tex]
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a river flows with a uniform velocity v. a person in a motorboat travels 1.42 km upstream, at which time a log is seen floating by. the person continues to travel upstream for 75 min at the same speed and then returns downstream to the starting point, where the same log is seen again. find the flow velocity of the river. assume the speed of the boat with respect to the water is constant throughout the entire trip.
Let's assume the speed of the boat relative to the water is s.
The time taken for the boat to travel 1.42 km upstream is t1.
The time taken for the boat to travel 1.42 km downstream is t2.
The velocity of the river is v.
Since the speed of the boat relative to the water is constant, we have:
Upstream:
v + s = s + (1.42 km) / t1 = (1.42 km) / t1 km/hr
Downstream:
v - s = (1.42 km) / t2 km/hr
Since the boat takes 75 min for the round trip, we have:
t1 + t2 = 75 min = 1.25 hours
Rearranging the above equations, we have:
v = (1.42 km / t1 - 1.42 km / t2) / 2 km/hr
Substituting t1 + t2 = 1.25 hours, we have:
v = (1.42 km / (1.25 hours - t2) - 1.42 km / t2) / 2 km/hr
Since t2 = 1.25 hours - t1, we have:
v = (1.42 km / (1.25 hours - (1.25 hours - t1)) - 1.42 km / (1.25 hours - t1)) / 2 km/hr
v = (1.42 km / (1.25 hours) - 1.42 km / (2.5 hours - t1)) / 2 km/hr
Finally, solving for t1, we have:
t1 = (1.42 km / v) * 2 km/hr / (1 + (1.42 km / (1.25 hours * v))) hours
So, the flow velocity of the river is v.
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the rear window in a car is approximately a rectangle, 1.6 m m wide and 0.55 m m high. the inside rearview mirror is 0.60 m m from the driver's eyes, and 1.70 m m from the rear window.
By the use of law of reflection To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm
According to the law of reflection, the angle of incidence and reflection is equal.
[tex]\theta_r=\theta_i[/tex]
Both the incident and reflected rays lay on the same plane.
Plane mirrors are reflective surfaces where each point of the mirror has the same normal direction to the surface. As a result, the size of the images produced by flat mirrors is equal to that of the object, and the image's distance is equal to that of the object.
Mathematically, the plane mirror equation yields,,
[tex]i=-o[/tex]
The virtual nature of the image is represented by the negative symbol. The plane mirror's lateral magnification is,
[tex]m=\frac{-i}{o}[/tex] = 1.
We are assuming that the top of the mirror, with unknown height
h, matches the driver's eyes. The height of the window is
H= 0.55m, while the distances from the mirror to the eyes and from the window to the mirror are d=0.60m and D=1.70m, respectively.
The following is how the reflection process works: An angle is created when a light beam from the window hits the mirror, reflected on the road, reaches the driver's sight. The worst case scenario occurs at the window's angle's lowest point. [tex]\theta_r[/tex], . The mirror's height must be adjusted to guarantee that the reflected light hits the driver's eyes.
. Using the trigonometric relations,[tex]Tan \theta=\frac{H-h}{D+d}[/tex]
for the large lower triangle, and,
[tex]Tan \theta=\frac{h}{d}[/tex] for the small upper one.
Equating the tangents results in the equation,
[tex]\frac{h}{d}=\frac{H-h}{D+d}[/tex]
solving for h
h=[tex]\frac{Hd}{D+2d}[/tex]
Substituting the numeric values,
[tex]h=\frac{0.55m\times0.60m}{1.70m +2\times0.60m}[/tex]
h=0.1137m
To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm
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Two orareind me with a mass of 4.00 kg and other with a mass of 6.00 kg, sit on a
frictionless surface. A worker pulls horizontally on the 6.00 kg crate with a force that gives the crate
an acceleration of 2.5 ms.
a. What is the acceleration of the 4.00 kg crate? (1 mark)
b. Draw a free-body diagram for the 4.00 kg crate and use it together with Newton's second
law to find the tension T in the rope that connects the two crates. (2 marks)
C. Calculate the magnitude and direction of the force the worker applies. (2 marks)
Foma
4.00 kg
T
6.00 kg
a. The acceleration of the 4.00 kg crate is 3.75 m/s^2.
b. A free-body diagram for the 4.00 kg crate is shown below:
4.00 kg
T
c. The direction of the force is to the right, since the crate is moving to the right. The magnitude of the force is 15 N.
What is acceleration?Acceleration can be described as the rate of change of the velocity of an object with respect to time.
We use Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration
(F_ = m * a).
The total force on each crate is equal to the force applied on it. If the force applied on the 6.00 kg crate produces an acceleration of 2.5 m/s^2, the total force on the 6.00 kg crate is 6.00 kg * 2.5 m/s^2 = 15 N.
Therefore, the total force on the 4.00 kg crate is 4.00 kg * a = 15 N,
a = 15 N / 4.00 kg
a = 3.75 m/s^2.
The tension T in the rope that connects the two crates can be found using Newton's second law of motion.
b. (F = m * a), so we can put out the the equation as :
T - 4.00 kg * 3.75 m/s^2 = 0
T = 4.00 kg * 3.75 m/s^2 = 15 N
c.
F - 6.00 kg * 2.5 m/s^2 = 0
F = 6.00 kg * 2.5 m/s^2 = 15 N
The direction of the force is to the right, since the crate is moving to the right. The magnitude of the force is 15 N.
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9. If two objects begin at rest, what is the total momentum of the system before they push off from one
another? What is the momentum of the system after they push off from one another?
10. If two objects are moving but the total momentum of the system is zero, what do you know about
the momentum of the two objects?
11. Two people stand facing each other at a roller skating rink then push off each other.
a. What is the momentum of the system before they push off each other?
b. What must be the momentum of the system after they push off each other?
c. If the girl skater has a mass of 30 kg and moves backward at 5 m/s, what is the velocity of the boy
skater if his mass is 50 kg?
d. If the force applied between the two skaters occurs over 2.5 seconds, what is the force exerted on
each of the skaters?
Answer:
10. If two objects are moving but the total momentum of the system is zero, the momentum of the two objects are equal in magnitude but opposite in direction.
11.
a. The momentum of the system before they push off each other is zero as they both start at rest.
b. The total momentum of the system after they push off each other must be zero, as the law of conservation of momentum states that the total momentum of a closed system remains constant.
c. If the girl skater has a mass of 30 kg and moves backward at 5 m/s, the velocity of the boy skater would be in the opposite direction at 5 m/s. This can be found using the equation p = mv, where p is momentum, m is mass, and v is velocity. Since the total momentum of the system is zero, the momentum of the girl skater (30 kg * -5 m/s) must be equal in magnitude but opposite in direction to the momentum of the boy skater (50 kg * v). So, v = (30 kg * -5 m/s) / 50 kg = -5/50 m/s = -0.1 m/s.
d. The force exerted on each skater can be found using the equation F = Δp/Δt, where F is force, Δp is the change in momentum, and Δt is the time over which the force is exerted. Using the known values, F = Δp/Δt = (0 - 0) / 2.5 s = 0 N. This means that the force exerted on each skater is zero.
find the magnitude of the electric field due to a charged ring of radius a and total charge q , at a point on the ring axis a distance a from the ring's center. express your answer in terms of the variables a , q , and coulomb constant k .
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ R^{2} + x^{2} } }[/tex]The magnitude of electic field at a distance 'a' from the center of the ring is
[tex]E = \frac{K Q q }{ 2\sqrt{2} a^{2} }[/tex] where K = [tex]\frac{1 }{4 \pi }[/tex]∈
a = radius of ring
Q = uniform charge distribution over ring
q = another point charge located at a distance a from centre of ring
We know that the electric field at distance x from the center of ring of radius R is given by
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ R^{2} + x^{2} } }[/tex]
according tho the question the radius of ring is equal to distance of q from centre of the ring
substituting R= a , x = a
we get
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ a^{2} + a^{2} } }[/tex]
[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ 2 a^{2} } } }[/tex]
[tex]E = \frac{K Q q }{ 2\sqrt{2} a^{2} }[/tex]
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A straight line drawn anywhere on a Mercator projection is a line of true compass direction, called a _____ line.
Rhumb
A straight line drawn anywhere on a Mercator projection is a line of true compass direction, called a loxodrome line.
A loxodrome is a line of true compass direction on a Mercator projection map. Here are some key points to keep in mind:
Mercator projection: This type of map projection was created in 1569 by Gerardus Mercator, and it is widely used for nautical and aeronautical charts. It is also a popular choice for world maps due to its ability to show areas near the poles in their correct proportions.True compass direction: A loxodrome represents a line of constant compass bearing, meaning that it maintains a constant angle relative to true north. This is in contrast to a great circle, which represents the shortest path between two points on the surface of a sphere.Straight line appearance: On a Mercator projection map, a loxodrome appears as a straight line that intersects all meridians (lines of longitude) at the same angle. This makes it a useful tool for navigators, as they can simply steer a constant compass course and follow the loxodrome line to their destination.Limitations: While a loxodrome may appear as a straight line on a Mercator projection map, it is actually a curve in reality. This is because the Mercator projection distorts the shape of the earth's surface, especially near the poles. In addition, a loxodrome is not the shortest distance between two points, so it may not be the best route to follow in all cases.Learn more about Mercator projection here:
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Which of the following best describes why you can analyze this event using the conservation of momentum?a. The throwing action is quick enough that external forces may be ignored.b. There are no external forces acting on the system.c. External forces don't act on the system during the jump.d. Conservation of momentum is always the best way to analyze motion.
The option that best describes why you can analyze this event using conservation of momentum, is The throwing action is quick enough that external forces may be ignored. The best answer is A.
This is because the conservation of momentum is only applicable when the external forces acting on a system are negligible. In this case, the external forces can be ignored, so the conservation of momentum can be used to analyze the motion.
The conservation of momentum is a fundamental law of physics that states that the total momentum of a system is conserved, which means that the total momentum of a system remains constant. This means that if there are no external forces acting on the system, the momentum of the system will not change. This law is particularly useful for analyzing the motion of objects, and can be used to calculate the velocity, acceleration, and other parameters of an object's motion.
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a positive point charge q is at the center of a spherical shell of radius r carrying charge 2q distributed uniformly over its surface. find an expression for the electric field as a function of position r from the center of sphere inside the shell. use a minus sign if the field points inward
The total electric field at a point inside the shell is, [tex]E = \dfrac{kq}{r^{2}}[/tex].
Consider the point P placed inside the shell. As shown in the figure above, the Gaussian surface is said to have a radius r. The Gaussian surface contains no charge inside it.
Hence, q = 0
Therefore,
E = 0
It can be conclude that the field inside the spherical shell is always zero.
The electric field due to point charge q placed at the center at a point which is at a distance r from the center (inside the shell) is given by,
[tex]E = \dfrac{kq}{r^{2}}[/tex]
where, k is the permittivity of free space.
Hence, the total electric field at a point inside the shell is,
[tex]E = \dfrac{kq}{r^{2}}[/tex]
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Kepler's second law states that as a planet orbits the Sun, itsweeps out equal areas in equal times. Which of the followingstatements describe a characteristic of the solar system that isexplained by Kepler's second law?
Check all that apply
a) Venus orbits the Sun faster than Earth orbits the Sun.
b) Inner planets orbit the Sun at higher speed than outerplanets
c) The Sun is located slightly off-center from the middle ofeach planet's orbit.
d) All the planets orbit the Sun in nearly the same plane
e) Earth is slightly closer to the Sun on one side of itsorbit than on the other side
f) Pluto moves faster when it is closer to the Sun thanwhen it is farther from the Sun
Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. the options are b) Inner planets orbit the Sun at higher speed than outer planets, d) All the planets orbit the Sun in nearly the same plane, f) Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.
Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. The following statements describe characteristics of the solar system that are explained by Kepler's second law:
The correct options are option b, d and f.
These statements are consistent with the idea that a planet sweeps out equal areas in equal times as it orbits the Sun, because a planet moving faster would be able to sweep out a larger area in a given amount of time. Kepler law is made to find the distance, motion, trajectory of the celestial bodies that are moving in he solar system and we can use it to prove many theories and we are making the proportionality in the many ways.
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provide an explanation on why motor vehicles use what is called a multigrade viscosity oil and explain what is meant by an oil viscosity rating such as 5W30.
a good diffraction grating has 2060 lines/cm what is the distance between two lines in the grating? answer in units of cm. answer in units of cm.
Distance between two lines of grating is 4.85*10^-4 cm.
The act of bending light around corners where it spreads out and illuminates regions is known as the diffraction of light.
A optical element known as a diffraction grating splits light into numerous beams that move in various directions. The directions, as well as diffraction angles of these beams, depending on the wavelength of the incident light, the angle at which the wave strikes, and the distance or spacing between consecutive diffracting elements.
The distance between the two grating lines is calculated by taking the reciprocal of the grating value which is provided.
Distance between two lines of grating is, 1/2060 = 4.85*10^-4 cm.
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2
Select all the correct answers.
Which two statements are true about a system?
A system is a group of objects analyzed as one unit.
Energy that moves across system boundaries is conserved.
There's only one way to define the boundaries of a system.
All systems are made by humans.
Answer: a AND B
Explanation:1, IS TRUE AND 2 AIS TRUE
The things that are true about a system are :
A system is a group of objects analyzed as one unit
Energy that moves across the system boundaries is conserved.
What is a System ?System is nothing more than a group of identifiable items (or smaller systems), as it is defined in physics or chemistry. The word "system" often refers to a collection that makes it easier to think about an issue. Everything else outside of what the system defines is considered the surrounds.
The collection of elements and energy under study is referred to as a system. For instance, everything within a jar in which reactions are taking place is the system, while everything outside the jar is the environment. Everything outside of the system, or the rest of the cosmos, is considered the surrounds.
The things that are true about a system are :
A system is a group of objects analyzed as one unit
Energy that moves across the system boundaries is conserved.
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A marble with a mass of .4 kg is rolling down a ramp at a speed of 5 m/s and collides with a .25 kg marble sitting at rest. What is the final velocity of the first marble?
Students monitor the progress of a marble by measuring its speed and distance travelled. They calculate the speed using the formula Speed = Distance / Time.
How do you find the velocity of a marble?
Look for a space on the table or counter that is larger than a metre.Two books should be placed on one end of the desk.Then, lean the grooved ruler against the books.Place a different book at each end of the desk. The marble will come to a halt as a result of this book.Measure the distance between the book's one end and the end of the grooved ruler on the desk. The projected rolling distance of the marble is. Pay attention to the length here.Install the stopwatch.Roll the marble down the grooved ruler and begin timing.The stopwatch should start timing the moment the stone touches the table. Look up time tracking that is easily accessible.Keep track of the distance travelled.Using the equation Speed = Distance / Time, calculate the speed in metres per second. It will be necessary to convert from centimeters to metres.2 more times through #6-#10.The results of the three speed computations should be averaged.To learn more about marble's progress refer to:
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What happens after we die on earth?
Your heart stops beating, your breathing stops, and your brain stops working. According to research, brain activity may continue for several minutes after a person is declared dead.
What do people see when they die?Visual or auditory hallucinations are common during the dying process. The reappearance of deceased family members or loved ones is common. These visions are thought to be normal.
The dying may shift their focus to "another world," where they may converse with people or see things that others do not.
Thus, brain activity is not synonymous with consciousness or awareness. It does not imply that the individual is aware that they have died.
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recall that means: for all there is a such that for all satisfying we have that . what if the limit does not equal ? think about what the means in language. consider the following phrases: 1. 2. 3. 4. 5. but 6. such that for all 7. there is some 8. there is some such that order these statements so that they form a rigorous assertion that and enter their reference numbers in the appropriate sequence in these boxes:
The correct sequence is 5, 1, 3, 8, 4, 6, 7, 2. The statement that is being discussed is:
"For all > 0 there exists a > 0 such that for all satisfying we have that ."
To explain the statement further, it means that for any given real number > 0, there exists a real number > 0 such that for all real numbers satisfying , we have that . In other words, if is sufficiently close to (i.e. if is less than ), then must also be close to (i.e. must be less than ).
This idea is essential to understanding limits. The statement can be written more formally as:
[tex]$$\lim_{x \to c} f(x) = L \iff \forall \epsilon > 0, \exists \delta > 0 \text{ such that } \forall x \in \mathbb{R}, 0 < |x - c| < \delta \Rightarrow |f(x) - L| < \epsilon$$[/tex]
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HURRYYYYYY 20 pointsssss
Which of the following statements is true?
Group of answer choices
A correlation of -.50 is weaker than a correlation of .50.
A correlation of 1.33 is stronger than a correlation of .33.
A correlation of .56 is better than a correlation of .55.
A correlation of .33 is just as strong as a correlation of -.33.
The following statement which is true is : A correlation of .33 is just as strong as a correlation of -.33.
What is meant by correlation?The tendency of two or more systems that independently exhibit simple behavior to show complex and novel behavior together because of their interaction is called correlation.
Correlation is a statistical measure that expresses extent to which two variables are linearly related implying that they change together at a constant rate. It is common tool for describing simple relationships without making statement about cause and effect.
Correlation between variables does not mean that the change in one variable is the cause of the change in the values of other variable.
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A ball is thrown upwards and returns to the same position. Compared with its original speed after release, its speed when it returns is about _____. Free Fall: If the air resistance is ignored, then the acceleration of an object moving upward or falling towards the ground is numerically equal to the acceleration due to gravity. Energy Conservation: Energy cannot be created or destroyed, but it can flow from one form to another. This is a powerful and wide-ranging principle that can help us solve many problems. In situations where friction and thermal energy are insignificant, we can apply the conservation of mechanical energy. Mechanical energy includes kinetic energy and potential energy. A common application of this is projectile motion, in which the sum of kinetic energy and gravitational potential energy is constant. We can state this as follows: K E 1 + P E 1 = K E 2 + P E 2 Here, K E represents kinetic energy (J), and P E represents the potential energy (J). Also, the subscript 1 represents some particular point in the path of the projectile, and the subscript 2 represents another point. For most situations, the kinetic energy basically only depends on the speed of the projectile: K E = 1 2 m v 2 . The gravitational potential energy depends on the height: P E = m g h . Here, m is the mass (kg), v is the speed (m/s), g is the acceleration of gravity (9.8 m/ s 2 ), and h is the height (m).
A ball is thrown upwards and returns to the same position. Compared with its original speed after relase, its speed when it returns is about the same.
To solve this case, we will use energy conservation and free fall concepts.
Energy conservation defines that the energy in a system will remains the same as long as no other external force working in the system. Energy in a system will not be created or destroyed, but only change its form from one to another.
We will use the energy conservation concepts in this case under the kinetic and potential energies approach.
When the ball is thrown upwards, the ball has its kinetic energy and zero potential energy. As the ball goes higher, it will reach its highest peak once all of its kinetic energy has change into potential energy. The potential energy then will change into kinetic energy directly as the ball falls into its initial position. We can formulazid these moments as:
E1 = E2 = E3
where:
E1 = total energy when the ball is thrown upwards
E2 = total energy when the ball just stop at its highest peak
E3 = total energy when the ball starts to drop into its initial position
E1 = E2 = E3
Ek1 + Ep1 = Ek2 + Ep2 = Ek3 + Ep3
1/2 mv1² + mgh1 = 1/2mv2² + mgh2 = 1/2mv3² + mgh3
1/2mv1² + mg(0) = 1/2m(0)² +mgh = 1/2mv3² + mg(0)
1/2v1² = gh = 1/2v3²
v1² = v3² =2gh
v1 = v3 = √2gh
The ball will falls with the same speed as the speed when it was thrown upwards.
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Two stones are separated by a vertical distance y (in meters) from each other. One stone is thrown down with an initial velocity v01 = -23 m/s and the other is thrown up from the ground with an initial v02 = 5 m/s at the same time the other is thrown.
How far, in meters, must they be separated so they hit the ground at the same time?
The formula y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2 describes the vertical distance from the ground, where g is the acceleration of gravity and h is a height.
When you throw two stones of an equal sizes do they hit the ground at the same time why?It took both stones two hours and twenty minutes to fall to the ground. As a result, since height is constant for both particles, time is solely dependent on height. Both will fall to the ground simultaneously since the forces and height are equal.Things with various masses will nevertheless strike the ground at the same time if they are dropped from the same height because Earth provides them the exact same acceleration.The formula t=g2h provides the free fall time. Both stones hit the ground at the same time because t is independent of mass and h and g are equal.To learn more about vertical refer to:
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Distance to Epicenter (km) using equation
The distance to the epicenter by using the equation D = ΔT 8.4 is 16.8 kilometers.
What is the epicenter?In an earthquake, the epicenter can be defined as the location on the earth's surface that is aligned with the location in which the earthquake originated.
How to calculate the distance to the epicenter?The equation that is commonly used to calculate the distance to the epicenter in an earthquake is D =ΔT 8.4. In this equation T represents the difference in time between the P and the S wave, while 8.4 represents a constant.
Based on this, let's calculate the distance:
D =ΔT 8.4
D = 2 x 8.4
D = 16.8 km
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A red cart is moving rightward with a momentum of 60 kg*cm/s when it collides
with a blue cart that is also moving rightward with a momentum of 30 kg*cm/s.
The collision causes the red cart to slow down and the blue cart to increase its
momentum to 50 kg*cm/s.
Enter the momentum values of each individual cart and of the system of two carts
before and after the collision. Also indicate the change in momentum of the carts
and of the system.
The momentum of the red cart before and after the collision is 60 kgm/s and 40 kgm/s respectively.
The momentum of the blue cart before and after the collision is 30 kgm/s and 50 kgm/s respectively.
What is the final momentum of the carts after the collision?
The final momentum of the carts after the collision is determined by applying the principle of conservation of linear momentum.
Sum of initial momentum = sum of final momentum
60 kgm/s + 30 kg m/s = 50 kgm/s + Pr
where;
Pr is the final momentum of the red cart90 kgm/s - 50 kgm/s = Pr
40 kgm/s = Pr
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A rock is dropped from a high tower and falls freely under the influence of gravity.
Which one of the following statements concerning the rock as it falls is true? Neglect
the effects of air resistance.
A) The rock will gain an equal amount of momentum during each second.
B) The rock will gain an equal amount of kinetic energy during each second.
C) The rock will gain an equal amount of speed for each meter through which it falls.
D) The rock will gain an equal amount of momentum for each meter through which it
falls.
E) The amount of momentum the rock gains will be proportional to the amount of
potential energy that it loses.
Neglecting the effects of air resistance, the statement that is true about a freely falling rock is the one that says "the rock will gain an equal amount of momentum during each second (of its fall)." Therefore, the correct answer is option A.
According to the question, a rock is dropped from a tower. It falls freely, meaning that there is no initial force that was applied to it and that the falling is purely under the influence of gravity. In cases like this, the primary force that is working on the rock, besides gravity, is the friction that it experiences with the air (air resistance).
Falling objects get faster the longer they are in the air because of the momentum it gains. Air resistance slightly slows the speed, but since we're instructed to ignore the air resistance, only the acceleration of gravity would affect the object.
The formula you can use to calculate a falling object is:
v = g * t
v = 2 * g * h
h = 0.5 * g * t²
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A tennis player tosses a tennis ball straight up and then catches it after 1.57 s at the same height as the point of release.
PART A:
-9.8 m/s^2 (S)
PART B:
0 meters (N)
PART C:
≈ 7.7 (ROUNDED)
Accurate: 7.69300
PART D:
4.9 m (Δy)
Transcribed Text:
A tennis player tosses a tennis ball straight up and then catches it after 1.57 seconds at the same height as the point of release.
Required:
Acceleration of the ball while in flightVelocity of the ball at maximum heightInitial velocityMaximum height reachedUse the following kinematic equations:
[tex]v=v_o+at[/tex]
Final velocity = Initial Velocity + Acceleration × Time
Δ[tex]x=v_ot+\frac{1}{2}at^2[/tex]
Change in position (displacement) = Initial velocity × time + (0.5) (acceleration × final time)²
[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]
Final velocity (squared) = Initial velocity (two times) + (two times) acceleration * change in position
*A illustration shall be provided for better understanding*
Part A:
Once the tennis player releases the ball, the only force acting on that ball is the gravitational force which exerts an acceleration of -9.8 m/s^2.
Part B:
At that maximum height (as seen in the attached picture) would have a velocity of 0 for just a split moment making this the answer.
PART C: *Be aware that the PART A and B are just conceptual type questions and now we have actual calculations to figure out*.
Reviewing what we know,
Acceleration = -9.8 m/s^2
Time = 2.00 seconds
Now we have to find the initial velocity.
Reviewing the picture and the final velocity, it should turn out this way:
[tex]Vi=V_i,V=-V_o[/tex]Looking at the kinematic equations we would use:
[tex]V_f=V_i+at[/tex]
Current equation:
[tex]-V_o=V_o+(-9.8)(1.57)[/tex]
* MULTIPLY -9.8 and 1.57!!!
Now we must subtract the V(naught) from both sides.
The left and right side would become:
[tex]-2v_o=-15.38600[/tex]
Divide -2 from both sides.
Initial velocity = 7.69300
Rounded
≈ 7.7 m/s
This would make the initial velocity equal to 7.7 m/s
PART D:
In order to solve for maximum height, we must use some values we would need to find this answer.
Initial velocity = 7.69300 m/s
Acceleration = -9.8m/s^2
Final velocity (or velocity at max height) = 0 m/s
Δy = ...
The kinematic equation we would be using is:
[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]
Because the situation is in the vertical dimension, the 'delta x' will be changed to:
[tex]v^2=v_o2+2a[/tex]Δ[tex]y[/tex]
Subtract the initial velocity squared from both sides of the equation.
This would give us:
[tex]v^2-v_0^2=2a[/tex]Δ[tex]y[/tex]
Divide both sides by 2a.
By finding this we can find the vertical displacement.
[tex]\frac{v^2-u^2}{2a}[/tex]=Δ[tex]y[/tex]
Let plug in the known values
[tex]\frac{(0)^2-(9.8)^2}{2(-9.8^2)} = 4.9m[/tex]
Done
Assume that a typical driver has 1 sec reaction time (i.e., it takes 1 second before a typical driver starts reacting to changes in traffic light, e.g., after the light turns yellow, the driver starts slowing down after 1 sec). assume that 0.3g deceleration is a comfortable rate of slowing down (g is the gravitational acceleration)
between the moment the driver sights an obstacle and the moment he applies the brakes
What is a driver’s response time?
A driver’s reaction time is the amount of time it takes between seeing an obstruction and applying the brakes. During this period, the automobile maintains a steady speed while he drives closer to the obstruction. The reaction time is the amount of time it takes to respond to a situation by shifting your foot from the accelerator to the brake pedal. A typical reaction time is ¾ of a second. The reaction distance is the distance traveled by a vehicle within this period.
Method that is more exact.D = (s * r) / 3.6 d = response distance in meters (to be calculated). S denotes the speed in kilometers per hour. R denotes the response time in seconds. 3.6 = fixed conversion figure
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A person pushes a 15.5-kg shopping cart at a constant velocity for a distance of 28.5 mon a flat horizontal surface. She pushes in a direction 32.2 below the horizontal. A 30.4-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.
A uniform rod of mass M is in the shape of a semicircle of radius R (Fig. P14.45). Calculate the force on a point mass m placed at the center of the semicircle.
To calculate the force on the point mass m placed at the center of the semicircle, we need to consider the gravitational force acting on the mass m due to the uniform rod.
The gravitational force acting on the point mass m can be calculated using the equation:
F = G * (m * M) / R^2
where G is the gravitational constant, m is the mass of the point mass, M is the mass of the uniform rod, and R is the radius of the semicircle.
The uniform rod can be considered as a point mass located at the center of the semicircle, so the force on the point mass m can be simplified as:
F = G * (m * M) / R^2 = G * m * M / R^2
In conclusion, the force on the point mass m placed at the center of the semicircle is equal to the gravitational force between the point mass and the uniform rod, which is given by the equation F = G * m * M / R^2.
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The current sensitivity of a moving coil galvanometer increase with decrease in _________?
The current sensitivity of a moving coil galvanometer increases with a decrease in its resistance.
What is Current Sensitivity?
Current sensitivity is a measure of the responsiveness of an instrument to the current flowing through it. In particular, it is the deflection produced by a given amount of current passing through a device. The higher the current sensitivity, the smaller the amount of current required to produce a given deflection, and thus the more sensitive the instrument is to changes in current.
This is because the current sensitivity of a galvanometer is defined as the deflection produced per unit of current passed through it. Therefore, a higher current sensitivity means that a smaller current can produce a larger deflection, which can be achieved by decreasing the resistance of the galvanometer. This is because a lower resistance will allow a larger current to flow through the coil, which will result in a larger deflection of the coil.
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Answer:
Resistance
Explanation:
Sensitivity of a moving coil galvanometer can be increased by increasing the number of turns in the coil, the area of coil and magnetic field whereas by decreasing the couple per unit twist of the suspension.
A lead ball is dropped in a lake from a diving board 6.31 m above the water. It hits the water with a certain velocity and then sinks to the bottom with the same constant velocity. It reaches the bottom 5.05 s after it is dropped. (a) How deep is the lake? (b) What is the magnitude of the average velocity of the ball for the entire fall? (c) Suppose the water is drained from the lake. The ball is now thrown from the diving board so that it again reaches the bottom in 5.05 s. What is the magnitude of the initial velocity of the ball?
Answer:
a) To find the depth of the lake, we can use the following equation:
distance = initial velocity x time + (1/2) x acceleration x time^2
As the ball sinks to the bottom with the same constant velocity, we can assume that the acceleration is due to gravity, which is 9.8 m/s^2 (going downward)
We know that the time it takes for the ball to hit the bottom is 5.05 seconds, so we can substitute these values into the equation:
distance = 0 x 5.05 s + (1/2) x 9.8 m/s^2 x (5.05 s)^2
distance = 12.6125 m
So the lake is 12.6125 m deep
b) To find the magnitude of the average velocity of the ball for the entire fall, we can use the equation:
average velocity = distance / time
We know that the distance is the depth of the lake, which is 12.6125 m, and the time is 5.05 s, so we can substitute these values into the equation:
average velocity = 12.6125 m / 5.05 s
average velocity = 2.49 m/s
c) To find the magnitude of the initial velocity of the ball when it is thrown, we can use the following equation:
initial velocity = final velocity^2 + 2 x acceleration x distance
As the ball reaches the bottom in the same time as when it was dropped, 5.05 s, we can assume that the final velocity is 0 m/s. We know that the acceleration is 9.8 m/s^2 (going downward), and the distance is the depth of the lake, which is 12.6125 m. So we can substitute these values into the equation:
initial velocity = 0^2 + 2 x 9.8 m/s^2 x 12.6125 m
initial velocity = 24.6 m/s
Note that the magnitude of initial velocity is 24.6 m/s, which is a scalar value, it doesn't have any direction.
How much work is done in lifting a 60.0 kg crate a vertical distance of 10.0 m at a
constant velocity?
Formula for work:
[tex]w=Fd[/tex]
work(measured in joules) = force(measured in newtons) * distance(measured in meters)
Formula for force:
[tex]F=ma[/tex]
force(measured in newtons) = mass(measured in kilograms) * acceleration(measured in m/s^2)
__________________________________________________________
Given:
[tex]m=60kg[/tex]
[tex]d=10m[/tex]
[tex]a=9.8m/s^2[/tex]
[tex]w=?[/tex]
__________________________________________________________
Finding force:
[tex]F=ma[/tex]
[tex]F=60\times9.8[/tex]
[tex]F=588N[/tex]
__________________________________________________________
Finding work:
[tex]w=Fd[/tex]
[tex]w=588\times10[/tex]
__________________________________________________________
Answer:
[tex]\fbox{w = 5880 Joules}[/tex]
a system is composed of two blocks. the blocks, sliding on a horizontal frictionless surface, collide and stick together. which of the following statements are correct regarding the system? there are two correct answers.(4 points) this is an open system. this is a closed system. friction is an external force on this system. there is no net external force on this system.
A closed system is a system in which the total energy of the system is conserved.
Which of the following statements are correct regarding the system?This system is an example of a closed system. In this system, two blocks are sliding on a horizontal frictionless surface and collide and stick together.Since there is no friction present, the external forces on the system are zero, meaning that there is no net external force on this system.This means that the total energy of the system is conserved, as no energy is being added or taken away. This makes it a closed system.The system in question is a closed system, meaning that no energy or matter can enter or leave the system. This is because the two blocks are stuck together after the collision, and thus the system is completely isolated from its environment. Friction, however, is an external force on this system, since it acts on the blocks when they collide. At the same time, there is no net external force on this system. This is because the forces that are acting on the system are balanced out and thus there is no net force on the system as a whole.In conclusion, the system in question is a closed system, and friction is an external force acting on it. However, since the forces acting on the system are balanced out, there is no net external force on the system.To learn more about closed system refer to:
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The energy given off as heat by 500 g of an alloy as it cools by 25°C raises the
temperature of 250 g of water from 20°C to 28°C. Calculate the specific heat
of the alloy (in J/kg K). Remember that the specific heat of water is 4180 J/kg-K.
Upload a copy of your calculations and your answer.
Answer:
Below
Explanation:
The heat the water gains is the heat lost by the metal ...
Hw = .25 kg * (28- 20 C) * 4180 J/(kg K) = 8360 J
So the metal gains 8360 J and cools by 25 °C
500g = .5 kg
8360 /(.5kg* 25 C) = 668.8 J /(kg K)
Note: Remember that a degree C = one K)
