Practice Mechanical Energy in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The total of kinetic energy and potential energy in a mechanical system at any given moment.

The combined 'useful' energy for mechanical motion — kinetic plus all forms of potential energy.

Showing a random 20 of 50 problems.

Example 1

easy
A pendulum has ME=12 JME = 12 \text{ J} and at one instant its kinetic energy is 7 J7 \text{ J}. Find the potential energy.

Example 2

challenge
A 0.5 kg0.5 \text{ kg} block slides on a frictionless track from rest at height HH, around a vertical loop of radius R=1 mR = 1 \text{ m}. Find the minimum HH so the block just maintains contact at the top of the loop (g=10 m/s2g = 10 \text{ m/s}^2).

Example 3

easy
A system has ME=100 JME = 100 \text{ J} and PE=40 JPE = 40 \text{ J}. What is its kinetic energy?

Example 4

hard
A roller coaster car of mass 400 kg400 \text{ kg} at the top of a 25 m25 \text{ m} hill moves at 5 m/s5 \text{ m/s} (g=10 m/s2g = 10 \text{ m/s}^2, no friction). Find its speed at a low point 5 m5 \text{ m} above the ground.

Example 5

easy
A 1 kg1 \text{ kg} ball at height 5 m5 \text{ m} moves at 6 m/s6 \text{ m/s}. What is its total mechanical energy? Use g=10 m/s2g = 10 \text{ m/s}^2.

Example 6

medium
A 2 kg ball is thrown up at 10 m/s from the ground (use g=10 m/s2g = 10 \text{ m/s}^2, no air resistance). Find the maximum height using mechanical energy.

Example 7

medium
A 3 kg3 \text{ kg} object at 2 m2 \text{ m} height moves at 4 m/s4 \text{ m/s} (g=10 m/s2g = 10 \text{ m/s}^2). Find its mechanical energy.

Example 8

medium
A pendulum bob swings from rest at 0.2 m0.2 \text{ m} above its lowest point. Find its maximum speed (g=10 m/s2g = 10 \text{ m/s}^2).

Example 9

easy
A 5 kg rock is dropped from rest. The instant before release, what is its kinetic energy?

Example 10

medium
A 1 kg1 \text{ kg} ball is dropped from 10 m10 \text{ m} (g=10 m/s2g = 10 \text{ m/s}^2, no air resistance). Using mechanical-energy conservation, find its speed when it is 4 m4 \text{ m} above the ground.

Example 11

medium
A 1.5 kg1.5 \text{ kg} ball is dropped from 20 m20 \text{ m} and lands with speed 18 m/s18 \text{ m/s} (g=10 m/s2g = 10 \text{ m/s}^2). How much energy was lost to air resistance?

Example 12

hard
A 2 kg2 \text{ kg} block slides down a 30∘30^\circ frictionless incline of length 4 m4 \text{ m} starting from rest (g=10 m/s2g = 10 \text{ m/s}^2). Find its speed at the bottom.

Example 13

hard
A 0.1 kg0.1 \text{ kg} ball is dropped onto a vertical spring (k=200 N/mk = 200 \text{ N/m}) from a height 1 m1 \text{ m} above the spring's top (g=10 m/s2g = 10 \text{ m/s}^2, no air resistance). Find the maximum compression of the spring (ignore PE change during compression).

Example 14

challenge
A 2 kg ball is launched up at 20 m/s. Air resistance dissipates 40 J before it reaches the top. Find the maximum height (use g=10 m/s2g = 10 \text{ m/s}^2).

Example 15

medium
A 0.5 kg ball is dropped from 20 m (use g=10 m/s2g = 10 \text{ m/s}^2, no air resistance). Find its speed just before hitting the ground.

Example 16

medium
A roller-coaster car (frictionless) starts at rest 30 m high (use g=10 m/s2g = 10 \text{ m/s}^2). How fast is it going at a point 10 m high?

Example 17

medium
A 2 kg2 \text{ kg} object slides down a frictionless ramp from 8 m8 \text{ m} high. What is its speed at the bottom? Use g=10 m/s2g = 10 \text{ m/s}^2.

Example 18

medium
A skateboarder coasts up a curved ramp without pumping or pushing off. Ignoring friction, what determines the maximum height they reach?

Example 19

challenge
A 1 kg block slides down a frictionless ramp from 2 m, then onto a rough flat surface (μ=0.25\mu = 0.25) where it stops. How far does it travel on the flat part? (use g=10 m/s2g = 10 \text{ m/s}^2)

Example 20

easy
A stationary 3 kg book rests 2 m above the floor (use g=10 m/s2g = 10 \text{ m/s}^2). What is its mechanical energy?
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