Exam 7: Conservation of Energy

Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m,initially at rest,when equal forces are applied separately to the two bodies.Jake says that equal forces applied for equal times do equal amounts of work on the two bodies.Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces.Which one,if either,is correct?

A 0.75-kg sphere is released from rest and is moving 5.0 m/s after falling 2.0 m in a viscous medium.What is the change in mechanical energy caused by the force the viscous medium exerts on the sphere during this descent?

A pendulum bob has potential energy U₀ when held taut in a horizontal position.The bob falls until it is 30 $\degree$ away from the horizontal position,when it has potential energy U_A.It continues to fall until the string is vertical,when it has potential energy U_B.Compare its potential energies at O,A,and B.

A 2.0-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 250 N/m)which has its other end fixed.The block passes through the equilibrium position with a speed of 2.6 m/s and first comes to rest at a displacement of 0.20 m from equilibrium.What is the coefficient of kinetic friction between the block and the horizontal surface?

A spring with spring constant k = 800 N/m is compressed 12 cm from its equilibrium position.A spring with spring constant k = 400 N/m has the same elastic potential energy as the first spring when its extension is

As an object moves from point A to point B only two forces act on it: one force is nonconservative and does -30 J of work,the other force is conservative and does +50 J of work.Between A and B,

A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero.The mass strikes the ground with a downward velocity of 25 m/s.Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground?

A 2.0-kg block slides down a plane (inclined at 40 $\degree$ with the horizontal)at a constant speed of 5.0 m/s.At what rate is the gravitational force on the block doing work?

Two equal masses are raised at constant velocity by ropes that run over pulleys,as shown below.Mass B is raised twice as fast as mass A.The magnitudes of the forces are F_A and F_B,while the power supplied is respectively P_A and P_B.Which statement is correct?

Objects A and B,of mass M and 2M respectively,are each pushed a distance d straight up an inclined plane by a force F parallel to the plane.The coefficient of kinetic friction between each mass and the plane has the same value $\mu$ _k.At the highest point,

An astronaut tosses a ball out in space where gravitational forces may be neglected.What will happen to the ball?

The equation below describes a physical situation: $\frac { 1 } { 2 } ( 1.70 \mathrm {~kg} ) \left( 3.30 \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } + ( 1.70 \mathrm {~kg} ) \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 2.35 \mathrm {~m} ) \sin 30 ^ { \circ }$ $= \frac { 1 } { 2 } ( 1.70 \mathrm {~kg} ) \left( 4.60 \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } + 0.320 ( 1.70 \mathrm {~kg} ) \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 2.35 \mathrm {~m} ) \cos 30 ^ { \circ }$ Which description best fits the equation?

A 1.2-kg mass is projected from ground level with a velocity of 30 m/s at some unknown angle above the horizontal.A short time after being projected,the mass barely clears a 16-m tall fence.Disregard air resistance and assume the ground is level.What is the kinetic energy of the mass as it clears the fence?

A large spring is used to stop the cars after they come down the last hill of a roller coaster.The cars start at rest at the top of the hill and are caught by a mechanism at the instant their velocities at the bottom are zero.Compare the compression of the spring,x_A,for a fully loaded car with that,x_B,for a lightly loaded car when m_A = 2m_B.

A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m)as shown.The speed of the mass at point A is 8.4 m/s,and at point B,it is 5.6 m/s.What is the change in mechanical energy between A and B caused by the force of friction?

The equation below is the solution to a physics problem: $\frac { 1 } { 2 } ( 2.30 \mathrm {~kg} ) \left( 3.90 \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } = \frac { 1 } { 2 } ( 2.30 \mathrm {~kg} ) \left( 2.33 \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } + ( 2.30 \mathrm {~kg} ) \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 1.00 \mathrm {~m} ) \cos \left( 60 ^ { \circ } \right)$ . The most likely physical situation it describes is

Any change of the energy of a system occurs because of

A certain pendulum consists of a 1.5-kg mass swinging at the end of a string (length = 2.0 m).At the lowest point in the swing the tension in the string is equal to 20 N.To what maximum height above this lowest point will the mass rise during its oscillation?

A 2.0-kg mass swings at the end of a light string (length = 3.0 m).Its speed at the lowest point on its circular path is 6.0 m/s.What is its kinetic energy at an instant when the string makes an angle of 50 $\degree$ with the vertical?

Identical masses m are attached to identical springs of spring constant k suspended from the ceiling.With both masses hanging in their equilibrium positions,mass A is pulled down 10 cm and released while mass B is pushed up 10 cm and released.Which statement is correct?