Change in kinetic energy after explosion is 32.9 x 10⁵J.
Mass of the first piece, m₁ = 5 kg
Mass of the second piece, m₂ = 12 kg
Mass of the third piece, m₃ = 8 kg
Velocity of the rock initially, v = 2 m/s
Velocity of the second piece, v₂ = 400 m/s
Velocity of the third piece, v₃ = 9 m/s
According to conservation of momentum,
mv = m₁v₁ + m₂v₂ + m₃v₃
Therefore velocity of the first piece,
v₁ = (mv - m₂v₂ - m₃v₃)/m₁
v₁ = [(25 x 2) - (12 x 400) - (8 x 9)]/5
v₁ = -964.4 m/s
Kinetic energy of the rock initially,
KE = 1/2 mv²
KE = 1/2 x 25 x 4
KE = 50 J
Kinetic energy after explosion,
KE' = 1/2(m₁v₁²+ m₂v₂²+ m₃v₃²)
KE' = 1/2[(5 x 93 x 10⁴) + (12 x 16 x 10⁴) + (8 x 81)]
KE' = 328.5 x 10⁴
Change in kinetic energy = KE' - KE = 32.9 x 10⁵J
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Answer: 3.26 * 10^3
Explanation:
an object is placed at a distance of 27.0 cm away from a thin convex lens with a focal length of 9.00 cm. how far from the lens is the image located and what type of image is formed?
According to the question the image is located 18.00 cm away from the lens and the image is a real, inverted image.
What is lens?Lens is an optical device used to focus or disperse light, or to change the optical properties of a beam of light. It is made from transparent materials like glass, plastic or quartz and can be used in a variety of applications such as cameras, microscopes, telescopes and other optical instruments. A lens can also be used to bend light, change its direction, and magnify objects.
The image is located 18.00 cm away from the lens and the image is a real, inverted image. This can be determined using the lens equation given by 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the object distance, and d_i is the image distance. Plugging in the given values, we get 1/9.00 = 1/27.0 + 1/d_i, which simplifies to 1/d_i = 1/9.00 - 1/27.0, or d_i = 18.00 cm.
Since the image distance is positive, this indicates that the image is real, meaning it is actually formed at the image distance. This is further confirmed by the fact that the image is inverted, as a real image is always inverted.
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Compute your average velocity in the following two cases:
a. You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 3.05 m/s along a straight track.
b. You walk for 1.00 minat a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along astraight track.
c. Graph x versus t for both cases and indicate how the average velocity is found on the graph.
The average velocity in the following cases are 1.743m/s and 1.22m/s.
Calculation of Average VelocityTo find the average velocity is given by:
V = [tex]\frac{total distance (d)}{time taken (t)}[/tex]
(a) From the question we are given:
d1 = 73.2m,
d2 = 73.2m,
v1 = 1.22m/s
v2 = 3.05m/s
We need to calculate the time taken to complete each of the distance using the formula:
t = [tex]\frac{total distance}{speed}[/tex]
t1 = 73.2/1.22 = 60s
t2 = 73.2/3.05 = 24s
The average velocity is the total distance divided by the total time:
Average velocity (V) = (d1 + d2) / (t1 + t2)
V = 146.4 m / 84 s
Therefore, V = 1.743 m/s (to 3 significant figures)
(b) From the question we are given:
t1 = 1min = 60s,
t2 = 1min = 60s,
v1 = 1.22m/s
v2 = 3.05m/s
We need to calculate the distance covered for each of the time using the formula:
d1 = velocity * time = v1 * t1 = 1.22 * 60 = 73.2m
d2 = velocity * time = v2 * t2 = 3.05 * 60 = 183m
The average velocity is the total distance divided by the total time:
Average velocity (V) = (d1 + d2) / (t1 + t2)
V = (73.2 + 183)/ (60 + 60)
V = 256.2/120 = 2.135m/s
Therefore, the average velocity (V) is 2.135m/s (to 3 significant figures)
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If a student were to measure the ball's speed at each position above, at which position would
the ball be traveling the fastest?
000
A
B
C
D
Answer:
the answer is b
Explanation:
The work-energy theorem states that the change in the kinetic energy of an object is equal to what?
The work-energy theorem states that the change in the kinetic energy of an object will be equal to the net work done on the object.
Mathematically, it can be expressed as;
ΔKE = W
Where; ΔKE represents the change in kinetic energy of the object,
W represents the net work done on the object.
This theorem states that when work is done on an object, it results in a change in its kinetic energy. If work is done on an object, its kinetic energy increases, and if work is done by an object, its kinetic energy decreases.
This theorem is a fundamental principle in physics that relates the concepts of work and energy, and it is often used to analyze the motion and behavior of objects in various physical systems.
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A particle is Projected with a velocity of 196m/s at an elevation of 30⁰ find?
The Velocity and Direction of motion at a height of 130m
According to the question the velocity and direction of motion of the particle at a height of 130m is 173.20 m/s, 30°.
What is velocity?Velocity is a vector physical quantity that measures the rate of change of an object's position. It is a combination of speed and direction and is measured in units such as meters per second (m/s). Velocity is the rate of change of an object’s position with respect to time. It is the amount of distance covered in a period of time. It is a vector quantity as it has both magnitude as well as direction. It can be calculated by dividing the distance covered by the time taken. Velocity is the rate at which an object is changing its position. It is a measure of how fast an object is traveling in a specific direction.
The velocity components of the particle at a height of 130m will be the same as it was at the time of projection since there is no acceleration, only gravity acting on it.
The velocity of the particle at a height of 130m will be:
Vx = 196 m/s * cos 30° = 173.20 m/s
Vy = 196 m/s * sin 30° = 98 m/s
The direction of motion of the particle at a height of 130m will be the same as the angle of projection i.e. 30°.
Therefore, the velocity and direction of motion of the particle at a height of 130m is 173.20 m/s, 30°.
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Find the magnitude of the two forces such that it they are at right angles, their resultant is
10 N. But if they act at 600, their resultant is 13 N
The magnitudes of the two forces are 6 N and 8 N when acting at right angles and their resultant is 10 N.
The problem involves finding two forces, given the magnitudes of their resultants when acting at different angles. Let F1 and F2 be the magnitudes of the two forces. When the two forces are at right angles, the resultant force R is given by:
R = √(F1² + F2²) = 10 N
Squaring both sides, we get:
F1² + F2² = 100
When the two forces act at an angle of 60 degrees, their resultant R is given by:
R = √(F1² + F2² + 2F1F2cos60) = 13 N
Squaring both sides and using cos60 = 0.5, we get:
F1² + F2² + F1F2 = 169
Now, we have two equations with two unknowns. Solving for F1 and F2, we get:
F1 = 6 N
F2 = 8 N
As a result, the magnitudes of the two forces are 6 N and 8 N when operating at right angles, respectively, and the resultant is 10 N. When the two forces act at an angle of 60 degrees, their magnitudes are still 6 N and 8 N, but their resultant is 13 N
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Hi ! Please help on question. If answer is correct I'll rate you five stars,a thanks and maybe even brainly!
Jess has a pop it powered by the sun. She holds it to the sun multiple times but it doesn't seem to work after she washed it. She tried to ma ale or work multiple times and even waited for a long period of time for the pop it to work but it didn't.
How can she fix it and why isn't it working?
If the pop was immersed in water or subjected to strong chemicals during the washing process, it may have been harmed.
Check the battery-A dead battery can be to blame. Jess has to make sure the battery is placed and charged correctly. She might need to get help from the manufacturer if the battery cannot be changed.
Verify the solar panels-If the pop uses solar panels for electricity, Jess has to make sure that they are clear of obstructions like debris and are functioning properly. She can use a soft cloth and some water to clean the solar panels if they are filthy.
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Forces at Time 1
Forces at Time 2
The arrows represent forces. Choose all that are correct when comparing the bicyclist at Time
1 and Time 2.
A. The bicyclist is moving faster at Time 2.
B. The bicyclist is moving faster at Time 1.
C. The bicyclist is applying more force on the pedals at Time 2.
D. The bicyclist is applying more force on the pedals at Time 1.
The bicyclist is applying more force on the pedals at Time 2. Option C
What is the image?If we look at the image that have been shown, we can be able to see that the force that is acting have been shows by the arrows that have been used to label the movement of the cyclist in the image that is shown here.
We can see that the forward arrow at the time 2 is seen to be larger than the forward arrow that is shown for time 1. The implication of this is that the cyclist is cycling harder and applying more force at time 2 than at time 1.
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A steel column is 3 m long and 0.4 m diameter. It carries a load of 50 MN. Given that the
modulus of elasticity is 200 GPa. Calculate the compressive stress.
The compressive stress in the steel column is found to be approximately 397.6 MPa.
The formula for calculating the area of a circle can be used to determine the steel column's cross-sectional area (A),
A = π*(d/2)², diameter of the column is d,
A = π*(0.4/2)²
A = 0.1257m²
The compressive stress (σ) in the column can be calculated using the formula, σ = F/A, F is the load carried by the column is F.
σ = 50 MN/0.1257m²
σ = 397.6 MPa
Therefore, the compressive stress in the steel column is approximately 397.6 MPa.
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A 89.4 kg weight-watcher wishes to climb a mountain to work off the equivalent of a large piece of chocolate cake rated at 605 (food) Calories. How high must the person climb? The acceleration due to gravity is 9.8 m/s 2 and 1 food Calorie is 103 calories. Answer in units of km.
The weight-watcher is need to climb approximately 0.298 kilometers to burn off the equivalent of a large piece of chocolate cake rated at 605 food Calories.
To determine the height that the weight-watcher needs to climb, we first need to calculate the amount of potential energy that would be required to burn off 605 food Calories.
First, we need to convert 605 food Calories into calories:
605 food Calories x 103 calories/food Calorie = 62315 calories
Next, we need to convert calories to joules:
1 calorie = 4.184 joules
62315 calories x 4.184 joules/calorie = 260808.56 joules
Now we can calculate the height that the weight-watcher must climb using the formula for potential energy:
potential energy = mass x gravity x height
where, mass = 89.4 kg, gravity = 9.8 m/s², and
potential energy = 260808.56 joules
Solving for height, we get:
height = potential energy / (mass x gravity)
height = 260808.56 joules / (89.4 kg x 9.8 m/s²)
height = 298.47 meters
Finally, we convert the height to kilometers:
298.47 meters = 0.29847 kilometers
Therefore, the weight-watcher needs to climb approximately 0.298 kilometers to burn off the equivalent of a large piece of chocolate cake rated at 605 food Calories.
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The electric field component in the figure are Ēx = 3xî, Ēy = Ē₂ = 0. Calculate the flux through (1,2,3) the square surfaces of side 2 cm.
The electric flux through a surface is calculated by the equation, φ = ∫E•dA, where E is the electric field, dA is the area vector and the integral is taken over the surface area.
What is electric flux ?Electric flux is a measure of the amount of electric field passing through a given area. It is represented by the letter Φ (phi) and is measured in units of volt-meters (Vm). Electric flux is related to the strength of electric fields, and the amount of electric flux passing through a given area is determined by the electric field strength and the area through which it passes. Electric flux is often used in calculations of electric field strength and electric field energy, as well as in the field of electromagnetism. Electric flux can also be used to calculate the total amount of electric charge passing through a given area.
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What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 32.5°C to 57.0°C, assuming it is unconstrained lengthwise? (Use
60 ✕ 10^−6/°C as the coefficient of expansion of mercury. Be sure to include the correct sign with your answer.)
The change in length of mercury is +0.0441 cm.
What is mercury?With the atomic number 80 and the symbol Hg, mercury is a metallic element. Because of its silvery appearance and capacity to flow smoothly like a liquid, it is also known as quicksilver. The only metal that is liquid at normal pressure and room temperature is mercury.
How do you determine it?The following formula describes how a change in temperature causes a material's length to alter:
ΔL = αLΔT
where L is the length change, is the thermal expansion coefficient, L is the starting length, and T is the temperature change.
If we substitute the values provided, we get:
ΔT = 57.0°C - 32.5°C = 24.5°C
L = 3.00 cm
= 60 x 10⁻⁶ °C (provided)
Thus, the length difference is as follows:
ΔL = (60 × 10⁻⁶/°C) (3.00 cm) (24.5°C)
ΔL = 0.0441 cm
The mercury column will enlarge due to the rise in temperature, making the length change positive.
There will be an estimated +0.0441 cm, an increase in the mercury column's length.
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• A helicopter's rotor speed changed from 225 rev/min to 300 rev/min in one minute. How long will it take for the rotor to have its angular velocity doubled over the initial speed. Assuming a constant angular acceleration.
The time taken for the helicopter rotor to double its angular velocity over the initial speed is 1 minute.
What is the time of motion?
If the rotor speed changed from 225 rev/min to 300 rev/min in one minute.
This means the change in angular velocity (Δω) is:
Δω = ω2 - ω1 = 300 rev/min - 225 rev/min = 75 rev/min
We are given that the rotor doubles its angular velocity over the initial speed, so ω2 = 2ω1.
Substituting ω2 = 2ω1 into the equation for Δω, we get:
75 rev/min = 2ω1 - ω1
Simplifying, we get:
75 rev/min = ω1
Now we can solve for the time taken for the rotor to double its angular velocity over the initial speed.
Δω = αt
Substituting Δω = 75 rev/min and ω1 = 75 rev/min, we get:
75 rev/min = αt
Now we can solve for t:
t = Δω / α
We need to find α, the angular acceleration.
α = Δω / t = 75 rev/min / 1 min = 75 rev/min²
Now we can substitute the value of α back into the equation for t:
t = Δω / α = 75 rev/min / 75 rev/min² = 1 minute
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Mars rotates on its axis once every 24.8 hours.
(a) What is the speed of a geosynchronous satellite orbiting Mars?
Express your answer with the appropriate units.
(b) What is the altitude of a geosynchronous satellite orbiting Mars?
Express your answer with the appropriate units.
1.44*[tex]10^{3}[/tex] m/s is the speed of a geosynchronous satellite orbiting Mars. 17.1* [tex]10^{6}[/tex]m is the altitude of a geosynchronous satellite orbiting Mars
What does geosynchronous satellite mean?
A geosynchronous satellite is positioned in an orbit with an orbital period equal to the rate of rotation of the Earth. It takes these satellites 24 hours to orbit the earth once. The equatorial plane is typically not the orbital plane for a typical geosynchronous satellite, though.
The period of rotation of the Mars is T = 24.8 hours.
The radius of the Mars, R is 3.3895×[tex]10^{6}[/tex]
i.e. 2.05*[tex]10^{7}[/tex]m
The satellite's orbital speed is determined by; v⇒2πr/T i.e. 1.44* [tex]10^{3}[/tex]m/s
A geosynchronous satellite orbiting Mars has a height of: h⇒r-R i.e. 17.1* [tex]10^{6}[/tex]m
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In the figure shown, the horizontal surface on which the objects slide is frictionless. F=16 N and M-1.0 kg. What is the magnitude of the force exerted on the large block by the small block?
The magnitude of the force exerted on the large block by the small block is 16 N. Option A is correct.
The force exerted on the large block by the small block can be found using Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. The force exerted by the small block on the large block is equal in magnitude but opposite in direction to the force exerted by the large block on the small block.
Using Newton's Second Law of Motion, F = ma, where F is the net force, m is the total mass of the system, and a is the acceleration of the system. Therefore, the acceleration of the system is:
a = F/m = 16 N / (1 kg + 2 kg) = 5.33 m/s²
The force of friction between the two blocks is equal in magnitude but opposite in direction to the force exerted by the small block on the large block. Therefore, the force of friction is:
f = ma = 3 kg * 5.33 m/s² = 16 N
Therefore, the magnitude of the force exerted on the large block by the small block is 16 N. Option A is correct.
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Questions already answered. I need to know how we get to this answer.
Question:
A basketball is launched with an initial speed of 4 m/s at an angle of 45°. The ball enters the basket .96s after it is launched. What is the distance x?
Answer:
2.7 m
The horizontal distance of the ball is determined as 2.71 m.
What is the distance x?The horizontal distance traveled by the ball is calculated by applying the following formula as shown below;
X = Vₓt
where;
Vₓ is the horizontal component of the velocityt is the time of motionX = 4 m/s x cos (45) x 0.96 s
X = 2.71 m
Thus, the horizontal distance of the ball is a function of the horizontal velocity and time of motion.
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An electric dipole consisting of charges +q and -q separated by a distance r, is kept symmetrically at the centre of an imaginary sphere of radius R (>r). Another point charge Q is also kept at the centre of the sphere. The net electric flux coming out of the sphere will be (a) (b) -(2q+Q) 4περ Eo (c) 2q+Q င်ပ o- (P) E0
Using Gauss's law, the net electric flux through a closed surface is given by:
Φ = Q_in / ε0
where Φ is the electric flux, Q_in is the total charge enclosed by the surface, and ε0 is the electric constant.
In this case, we can consider the sphere as the closed surface. The electric dipole will produce electric field lines that pass through the surface, but these lines will be symmetric and cancel out each other's contribution to the net flux. Therefore, the only contribution to the flux will be from the point charge Q.
The charge enclosed by the surface is simply Q, so the net electric flux is:
Φ = Q / ε0
This result does not depend on the position of the electric dipole inside the sphere, as long as it is symmetrically placed at the center.
Question 3 of 25
Which of the following describes sound waves?
A. Mechanical waves in which the vibrations are perpendicular to the
motion of the sound
B. Electromagnetic waves in which the vibrations are perpendicular
to the motion of the sound
C. Electromagnetic waves in which the vibrations are parallel to the
motion of the sound
D. Mechanical waves in which the vibrations are parallel to the
motion of the sound
Answer:
D. Mechanical waves in which the vibrations are parallel to the motion of the sound.
Explanation:
gg
Answer: D
Mechanical waves in which the vibrations are parallel to the motion of the sound.
Explanation:
just took
PLS HELP!!
1. Radon-222 decays with a half-life of 3.82 days. If an initial sample of the element contains 1000 atoms, it takes ___ days for that sample to decay down to 125 atoms.
a. 2 days
b. 3 days
c. 4 days
d. 5 days
Answer: 3 days
Explanation:
4. A car moves round a circular track at 120 mph. Give the average velocity of the car.
Explain your answer.
The average velocity of a car that is moving round a circular track at 120 mph is given as 0
How to determine the average velocityWhen a car is moving around a given moves round a circular track at 120 mph, it would have a direction that is constantly changing while it is moving around the track.
After the full lap has been completed, the car is going to have to go back to its starting point. Hence the displacement is 0, average velocity is 0. This is regardless of its speed. Hnece the velocity is 0
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Physics Question: Parts A and B
An airplane with a speed of 175 m/s is climbing upward at an amgle 15° with respect to the horizontal. When the plane's altitude is 543m, the pilot released a package.
(A) Find the time it takes the package to hit the ground from releasing.
(B) What is the speed of the package just before the impact?
The package hits the ground after 12.6 seconds.
The package's speed immediately before contact is 83.2 m/s.
How to calculate time and speed?To solve this problem using the kinematic equations of motion. First find the time it takes for the package to hit the ground.
(A) Using the vertical motion equation:
y = vi×t + (1/2)gt²
where y = vertical displacement,
vi = initial vertical velocity,
t = time, and
g = acceleration due to gravity.
The initial vertical velocity is given by:
vi = vsinθ = (175 m/s)sin(15°) = 45.12 m/s
Take upward as positive, so g is negative:
g = -9.8 m/s²
Substituting the values into the equation:
543 m = (45.12 m/s)t + (1/2)(-9.8 m/s²)t²
Simplifying and solving for t:
t = 12.6 s
Therefore, it takes 12.6 seconds for the package to hit the ground.
(B) Now, let's find the speed of the package just before the impact. Use the vertical motion equation again:
vf = vi + gt
where vf = final vertical velocity.
At the instant just before the package hits the ground, the final vertical velocity is:
vf = -√(2gh)
where h = height from which the package was released 543 m.
Substituting the values:
vf = -√(2(9.8 m/s²)(543 m)) = -83.2 m/s
Again, taking upward as positive, the speed of the package just before impact is:
v = |vf| = 83.2 m/s
Therefore, the speed of the package just before impact is 83.2 m/s.
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SOMEONE HELP ASAP: Match the definitions
Answer:
Incident Ray:- A ray of light that strikes a surface.
Focal point:- Location where parallel rays of radiation meet after being refracted or reflected.
Principal axis:- Line passing through the center of the surface of a lens or spherical mirror.
Focal length:- Distance between the center of a convex lens or mirror and the focal point of the lens or mirror.
Normal:- A line perpendicular to the surface at a particular point.
Convex:- Curving outward with edges pointing away from the viewer .
Refracted:- Changed direction after passing from one medium to another.
Concave:- lens or mirror curving inward so the edges point toward the viewer.
Reflected:- bounced off of a surface.
Calculate the volume occupied by 1.80 mol of steam at 200 ∘C . Assume the steam is at atmospheric pressure and can be treated as an ideal gas.
The volume occupied by 1.80 mol of steam at 200°C and atmospheric pressure is approximately 40.7 L.
We can use the ideal gas law, PV = nRT, to solve for the volume of the steam. First, we need to determine the pressure of the steam at 200°C and atmospheric pressure. We can use a steam table to find that the saturation pressure of steam at 200°C is 1.013 bar.
Next, we can convert this pressure to Pascals,
1.013 bar = 101,325 Pa
We also need to convert the temperature to Kelvin 200°C + 273.15 = 473.15 K.
Now we can plug in our values,
PV = nRT
V = nRT/P
V = (1.80 mol)(8.314 J/mol•K)(473.15 K)/(101,325 Pa)
V ≈ 67.6 L
Therefore, the volume occupied by 1.80 mol of steam at 200°C and atmospheric pressure is approximately 67.6 liters.
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Why are solar eclipses only seen by certain areas of Earth, while lunar eclipses are seen by many more people?
Suppose we wish to test whether or not the vectors a and b are perpendicular, where a = 3i+2j-k and b=i-2j-k Given the vectors: A = 3i + 2j - k and B = 5i +5j, find: a. The dot product A.B. b. The projection of A onto B. c. The angle between A and B. d. A vector of magnitude 2 in the XY plane perpendicular to B.
15. A ball of mass 5 kg and a block of mass 12 kg are attached by a lightweight cord that passes over a frictionless pulley of negligible mass as shown in the figure. The block lies on a frictionless incline of angle 30o . Find the magnitude of the acceleration of the two objects and the tension in the cord. Take g = 10
According to the question the magnitude of the acceleration of the two objects is 0 and the tension in the cord is also 0.
What is acceleration?Acceleration is the rate of change of velocity. It is a vector quantity, meaning it has both magnitude and direction. Acceleration can be caused by a force, such as gravity or friction, or by a change in the velocity itself. In the case of a force, the acceleration is proportional to the force and inversely proportional to the mass of the object.
Let a be the acceleration of the ball and b be the acceleration of the block.
Applying Newton's second law to the ball,
T − mg sin30o = 5a
Applying Newton's second law to the block,
T + mg sin30o − 12b = 0
Solving the two equations,
T = 10a
b = 10a/12
Substituting b in the first equation,
T − mg sin30o = 5a
10a − 5(10) sin30o = 5a
5a(1 − 10 sin30o) = 0
a = 0
b = 0
T = 0
Therefore, the magnitude of the acceleration of the two objects is 0 and the tension in the cord is also 0.
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What produces the magnetic force of an electromagnet?
An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole in the center of the coil.
A student connects a battery to a wire and wraps the wire around an iron nail to produce an electromagnet. Which action should the student take to increase the number of paper clips the electromagnet can pick pick up?
It's worth noting that increasing any of these factors too much can cause the wire to overheat, potentially damaging the wire or the battery. So, the student should exercise caution and avoid exceeding safe limits.
To increase the number of paper clips that the electromagnet can pick up, the student can take one or more of the following actions:Increase the number of coils: By increasing the number of times the wire is wrapped around the iron nail, the strength of the magnetic field produced by the electromagnet can be increased.Increase the current: By increasing the voltage of the battery or using a stronger battery, the current flowing through the wire can be increased, which will increase the strength of the magnetic field.Use a stronger iron nail: By using an iron nail with a higher magnetic permeability, the strength of the magnetic field produced by the electromagnet can be increased.Use thicker wire: By using a wire with a larger cross-sectional area, the resistance of the wire can be reduced, which will allow more current to flow through the wire, resulting in a stronger magnetic field.To know more about battery
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If all of the resistors in the diagram below are equivalent, what is the voltage
across the resistor R2 in the circuit below?
5
If all of the resistors in the diagram below are equivalent, then the voltage across the resistor R2 is 2.5 V.
The value of resistor is not give take the value of resistor 5Ω
R2 and R3 are in series hence its equivalent resistor Rs is R2 + R3 = 10Ω
R1 = 5Ω and Rs = 10Ω both this resistors are in parallel hence,
I()s = V/Rs = 5/10 = 0.5 A
I(1) = V/R1 = 5 / 5 = 1 A
In order to get voltage across R2 we have to apply voltage devider rule,
voltage across R2 is
V(R2) = R2 ÷ (R1 + R2) V
Putting all the values
V(R2) = 5/10 × 5
V(R2) = 5/10 × 5 = 2.5 V
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1. A student walks first 70m in the direction 37° north of east, and then walks 82m in the direction 20° south of east, and finally walks 28m in the direction 30° west of north. a. How far and at what angle is the student’s final position from her initial position? b. In what direction would she has to head to return to her initial position?
a. The student's final position is 100.5 meters at an angle of 25.2° north of east from her initial position and b. The student would have to head in the direction of 334.8° south of east to return to her initial position.
a. To find the student's final position, we can use vector addition. We can start by breaking each displacement vector into its x- and y-components. First displacement (70 m at 37° north of east),
x-component = 70 cos(37°) = 56.02 m
y-component = 70 sin(37°) = 42.49 m
Second displacement (82 m at 20° south of east),
x-component = 82 cos(-20°) = 78.72 m
y-component = 82 sin(-20°) = -28.12 m
Third displacement (28 m at 30° west of north),
x-component = 28 sin(30°) = 14 m
y-component = 28 cos(30°) = 24.24 m
We can add the x-components and y-components separately to get the total displacement,
x-displacement = 56.02 m + 78.72 m - 14 m = 120.74 m
y-displacement = 42.49 m - 28.12 m + 24.24 m = 38.61 m
The magnitude of the total displacement is,
|d| = √(x-displacement² + y-displacement²)
|d| = √(120.74² + 38.61²)
|d| = 126.0 m.
The direction of the total displacement can be found using the inverse tangent function,
θ = atan(y-displacement/x-displacement)
θ = atan(38.61/120.74)
θ = 17.4° north of east. Therefore, the student's final position is 126.0 m at 17.4° north of east.
b. To return to her initial position, the student would need to walk the same distance and direction as her total displacement but in the opposite direction. The opposite direction of 17.4° north of east is 162.6° south of west. Therefore, she would need to walk 126.0 m at 162.6° south of west to return to her initial position.
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