Exam 7: Conservation of Energy

In a given frictionless displacement of a particle,its kinetic energy increases by 25 J while its potential energy decreases by 10 J.Determine the work of the nonconservative forces acting on the particle during this displacement.

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the same direction.If the coefficient of kinetic friction is 0.400,the magnitude of the mechanical energy dissipated,in J,caused by the force of friction on the block in 8.00 s is

A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m)as shown.The speed of the mass at point A is 3.2 m/s,and at point B,it is 6.0 m/s.What is the change in mechanical energy done on the system between A and B by the force of friction?

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the opposite direction.If the coefficient of kinetic friction is 0.400,the magnitude of the mechanical energy dissipated,in J,caused by the force of friction on the block in 8.00 s is

A spring (k = 600 N/m)is at the bottom of a frictionless plane that makes an angle of 30 $\degree$ with the horizontal.The upper end of the spring is depressed 0.10 m,and a 2.0-kg block is placed against the depressed spring.The system is then released from rest.What is the kinetic energy of the block at the instant it has traveled 0.10 m and the spring has returned to its uncompressed length?

The mat of a trampoline is held by 32 springs,each having a spring constant of 5 000 N/m.A person with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline.Determine the stretch of each of the springs.

A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string.When pulled to the side and released,it has a speed of 4.0 m/s at the lowest point of its path.What maximum angle does the string make with the vertical as the object swings up?

A skier weighing 0.80 kN comes down a frictionless ski run that is circular (R = 30 m)at the bottom,as shown.If her speed is 12 m/s at point A,what is her speed at the bottom of the hill (point B)?

A 10-kg object is dropped from rest.After falling a distance of 50 m,it has a speed of 26 m/s.What is the change in mechanical energy caused by the dissipative (air)resistive force on the object during this descent?

The solution to a problem is the equation below.Which description best fits this solution? $\frac { 1 } { 2 } \left( 500 \frac { \mathrm { N } } { \mathrm { m } } \right) ( 0.120 \mathrm {~m} ) ^ { 2 } - ( 2.00 \mathrm {~kg} ) \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 0.120 \mathrm {~m} )$ $= \frac { 1 } { 2 } ( 2.00 \mathrm {~kg} ) \left( 0.824 \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } + ( 2.00 \mathrm {~kg} ) \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 0.029 0 \mathrm {~m} )$

A 1.0-kg block is released from rest at the top of a frictionless incline that makes an angle of 37 $\degree$ with the horizontal.An unknown distance down the incline from the point of release,there is a spring with k = 200 N/m.It is observed that the mass is brought momentarily to rest after compressing the spring 0.20 m.How far does the mass slide from the point of release until it is brought momentarily to rest?

An ore car of mass 4 000 kg starts from rest and rolls downhill on tracks from a mine.A spring with k = 400 000 N/m is located at the end of the tracks.At the spring's maximum compression,the car is at an elevation 10 m lower than its elevation at the starting point.How much is the spring compressed in stopping the ore car? Ignore friction.

A champion athlete can produce one horsepower (746 W)for a short period of time.If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate,she would reach the summit in ____ seconds.

When an automobile moves with constant velocity the power developed is used to overcome the frictional forces exerted by the air and the road.If the power developed in an engine is 50.0 hp,what total frictional force acts on the car at 55 mph (24.6 m/s)? One horsepower equals 746 W.

A 2.0-kg block is projected down a plane that makes an angle of 20 $\degree$ with the horizontal with an initial kinetic energy of 2.0 J.If the coefficient of kinetic friction between the block and plane is 0.40,how far will the block slide down the plane before coming to rest?

A 1.5-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 200 N/m)which has its other end fixed.If this system is displaced 20 cm horizontally from the equilibrium position and released from rest,the block first reaches the equilibrium position with a speed of 2.0 m/s.What is the coefficient of kinetic friction between the block and the horizontal surface on which it slides?

A spring with spring constant k = 800 N/m is extended 12 cm from its equilibrium position.A spring with 6.0 cm extension from equilibrium will have the same potential energy as the first spring if its spring constant is

A spring with spring constant 800 N/m compressed 0.200 m is released and projects a 0.800 kg mass along a frictionless surface.The mass reaches a surface area where $\mu$ _k = 0.400 and comes to a stop.The following student solution contains at least one error.What is the error? $\frac { 1 } { 2 } \left( 800 \frac { \mathrm { N } } { \mathrm { m } } \right) ( 0.200 \mathrm {~m} ) ^ { 2 } = \frac { 1 } { 2 } ( 0.500 \mathrm {~kg} ) \left( 8.00 \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } + 0.400 ( 0.500 \mathrm {~kg} ) \left( 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) ( 8.16 \mathrm {~m} )$

An automobile (m = 1.00 * 10³ kg)is driven into a brick wall in a safety test.The bumper behaves like a spring (k = 5.00 *10⁶ N/m),and is observed to compress a distance of 3.16 cm as the car is brought to rest.What was the initial speed of the automobile?

As an object moves from point A to point B only two forces act on it: one force is conservative and does -70 J of work,the other force is nonconservative and does +50 J of work.Between A and B,