[Homework Home > Conservation_of_Energy]

[1]A ball is dropped from meters above the ground. The ball has a mass of kg . Using conservation of energy, calculate how fast it will be traveling when it hits the ground. Note: neglect air resistance.

[2]A ball of mass m= kg is rolled, from rest, down a metal track, starting from point A as shown. Point A is meters above the ground, and the radius of the loop in the track is R= meters . How fast is it moving at points B, C, D,E and F?

[3]A roller coaster of mass m= kg starts from rest, at a height h= meters as shown here. It is clocked to be moving at m/s at point A. How high is point A?

[4]A kid with a mass of m= kg slides down a slide meters high and has a speed of m/s at the bottom. How much energy was lost due to friction?

[5]A ball is launched at an upward angle of \theta= degrees from the top of a cliff meters high, with a speed of m/s . Use conservation of energy to find how fast it will be traveling when it hits the ground.

[6]A block is at rest at point A as shown. It slides down the track without friction until point B, where suddenly it encounters "a whole lot of friction" and eventually stops in meters . A and B are part of a circle with a radius of meters .

a) how fast is the block moving at point B

b) what is the coefficient of friction between the block and the track as it moves past point B?

[7]A pendulum, made of a mass m= kg tied to the end of a string of length L= m as shown in the left figure here. This position is called the "equilibrium" or "relaxed" position of the pendulum. If pulled and released, the pendulum can can swing freely from side to side. If it is pulled up to an angle \theta= degrees as shown in the right figure, then released, what speed does it have when it again swings through the "equilibrium" position shown in the left figure?

[8]A block of mass m= kg is moving with speed v= m/s toward a spring-plunger system. The spring has a spring constant of k= N/m . The block collides with the plunger and sticks to it. How far is the spring compressed when the block stops?

[9]A toy gun that shoots rubber balls of mass m= kg is loaded by inserting the ball into the barrel of the gun. The spring inside the gun has a spring constant of k= N/m . When the gun is loaded, the spring is compressed by an amount x= m . The gun is pointed straight up. How far up will the rubber ball go?

[10]Some "extreme sport fun loving person" wants to go bungee jumping. They're not sure if the cord is strong enough to stop them from hitting the ground, but decide to jump and try anyway. The bungee cord's "strength" is measured by its spring constant, which is by k= N/m . The person has a mass of m= kg . Here is a picture of how it all happens: (1) The person gets ready to jump from a platform which is a height h= meters high.

(2) After falling some distance, y1= meters , the bungee cord begins to get tight.

(3) The person is eventually stopped by the bungee cord, a distance y2 from the point where the cord began to get tight.

The question: will the bungee cord stop the person before they hit the ground?

[11]As shown in the left figure, a ball of mass m= kg is held at a distance h= meters above the ground. A spring with spring constant k= N/m , in a relaxed state, holds a platform a distance h0= meter above the ground. The ball is released, and falls until it sticks onto the platform. When the ball is eventually stopped by the spring, the spring is compressed down as shown in the right figure. By how much is the spring compressed?

[12]A block of mass m= kg can slide along a curved track as shown here. The block, initially at a height h= meters above the ground is released. It slides down the frictionless track, and hits the spring-stopper to the right. The spring has a a spring constant k= N/m . How far does the spring compress when it brings the block to a stop?

[13]A block of mass m= kg can slide along a curved track as shown here. The block, initially at a height h= meters above the ground is released. It slides down a track which is all frictionless, except for a rough zone having a length of d= meters . In this rough zone, there is friction between the block and the track with a \mu= . In either case, the block eventually hits the spring-stopper to the right. The spring has a a spring constant k= N/m . How far does the spring compress when it brings the block to a stop?

[14]A block with mass m= kg can slide down a track with a loop in it. The loop has a radius of r= meters . From what height h must the block be slid in order to make it around the loop? Assume there is no friction in the loop.

[15]Two blocks are connected by a rope as shown. Block m2 with mass kg hangs freely from the rope. Block m1 with mass kg is connected to the other end of the rope, and is on a rough surface with coefficient of friction \mu= . It is also also connected to a spring with spring constant k= N/m .

When released, m2 will move down and m1 will move toward the right, until the spring's stretch stops the system. The question is: how far will m1 move before the system stops? (your answer will also correspond to how much the spring stretches and how far down m2 will move).

[16]A block of mass m= kg is connected, through a pulley, to a spring with spring constant k= N/m . Initially, m is held at a level which leaves the spring unstretched. How far down will m go when released?