Exam 8: Conservation of Energy

A 7.0-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m).The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block,as shown.When the block is 8.0 cm from the equilibrium position,it has a speed of 0.80 m/s.How much work is done on the block by the force P as the block moves the 8.0 cm?

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 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 placed in a vertical position with its lower end supported by a horizontal surface.The upper end is depressed 20 cm,and a 4.0-kg block is placed on top of the depressed spring.The system is then released from rest.How far above the point of release will the block rise?

A block (mass = 4.0 kg)sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 100 N/m)which has its other end fixed.If the maximum distance the block slides from the equilibrium position is equal to 20 cm,what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position?

A rain cloud contains 2.66 × 10⁷ kg of water vapor.How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2 000 m?

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?

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?

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 μk.At the highest point,

A surprising demonstration involves dropping an egg from a third-floor window to land on a foam-rubber pad 2 in (5 cm)thick without breaking.If a 56-gram egg falls 12 m,and the foam pad stops the egg in 6.25 ms,by how much is the pad compressed?

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?

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 12-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m).The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N)acting parallel to the surface is applied to the block,as shown.What is the speed of the block when it is 13 cm from its equilibrium position?

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 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 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.

An all-terrain vehicle of 2000 kg mass moves up a 15.0° slope at a constant velocity of 6.00 m/s.The rate of change of gravitational potential energy with time is

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 0.40-kg particle moves under the influence of a single conservative force.At point A where the particle has a speed of 10 m/s,the potential energy associated with the conservative force is +40 J.As the particle moves from A to B,the force does +25 J of work on the particle.What is the value of the potential energy at point B?

A skier weighing 0.70 kN goes over a frictionless circular hill as shown.If the skier's speed at point A is 9.2 m/s,what is his speed at the top of the hill (point B)?