Exam 8: Conservation of Energy

A 25-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m).The block is pulled 10 cm to the right from its equilibrium position and released from rest.When the block has moved 2.0 cm toward its equilibrium position,its kinetic energy is 12 J.What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm?

A particle is acted upon by only two forces,one conservative and one nonconservative and neither being a force of friction,as it moves from point A to point B.The kinetic energies of the particle at points A and B are equal if

A 1.0-kg block is released from rest at the top of a frictionless incline that makes an angle of 37° 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?

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?

The equation below describes a physical situation: Which description best fits the equation?

A spring (k = 600 N/m)is at the bottom of a frictionless plane that makes an angle of 30° 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?

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30° above the horizontal?

For a force to be a conservative force,when applied to a single test body

A 2.0-kg block slides down a fixed,rough curved track.The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m.Assume the block starts from rest.What is the change in mechanical energy of the block caused by the force of friction during this descent?

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° with the vertical?

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 pendulum bob has potential energy U₀ when held taut in a horizontal position.The bob falls until it is 30° 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 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum.At the lowest point of its swing,the object has a kinetic energy of 10 J.Determine the speed of the object at the instant when the string makes an angle of 50° with the vertical.

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

The force a spring exerts on a body is a conservative force because

A single conservative force F_x = (6.0x − 12)N (x is in m)acts on a particle moving along the x axis.The potential energy associated with this force is assigned a value of +20 J at x = 0.What is the potential energy at x = 3.0 m?

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.

A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40° below the horizontal position.What is the tension in the string at the instant when the object passes through its lowest position?

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?

Any change of the energy of a system occurs because of