Practice Conservation of 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

A fundamental law of physics stating that the total energy of an isolated system remains constant over time — energy can be transferred between objects.

Energy is like money—you can spend it, save it, or change its form, but you can't make more out of nothing.

Showing a random 20 of 50 problems.

Example 1

easy
Kinetic energy alone is conserved only in ___ collisions.

Example 2

hard
A roller coaster car (500 kg500 \text{ kg}) starts from rest at 30 m30 \text{ m} high and descends to 10 m10 \text{ m}. What is its speed at 10 m10 \text{ m}? Use g=10 m/s2g = 10 \text{ m/s}^2.

Example 3

medium
A 0.5 kg ball is thrown up at 8 m/s (g = 9.8). Find its KE when it is 2 m high.

Example 4

hard
A pump lifts 100 kg100\text{ kg} of water per minute to a height of 15 m15\text{ m}. Find the pump's minimum power. Use g=10 m/s2g = 10\text{ m/s}^2.

Example 5

medium
A 1 kg ball dropped from 4 m onto a spring (k = 500 N/m), g = 9.8. Find the spring's max compression (assume small compared to drop, ignore extra PE in spring).

Example 6

easy
A roller coaster is highest at the start. Where is its speed greatest (frictionless)?

Example 7

medium
A 0.5 kg ball dropped from 3 m rebounds to 2.4 m (g = 9.8). What fraction of its mechanical energy was retained?

Example 8

medium
A 0.2 kg ball is launched at 10 m/s up a frictionless ramp. Find its speed when it has risen 2 m (g = 9.8).

Example 9

easy
In an isolated system, total energy is ___.

Example 10

easy
A 2 kg object at rest at 3 m falls (g = 9.8). What is its total mechanical energy throughout (frictionless)?

Example 11

medium
A 2 kg2 \text{ kg} ball is dropped from 20 m20 \text{ m}. What is its speed just before hitting the ground? Use g=10 m/s2g = 10 \text{ m/s}^2.

Example 12

hard
A 1 kg1\text{ kg} block slides down a 5 m5\text{ m} ramp at 30∘30^\circ with μk=0.2\mu_k = 0.2. Find its speed at the bottom. Use g=10 m/s2g = 10\text{ m/s}^2.

Example 13

medium
A 2 kg2\text{ kg} block slides 4 m4\text{ m} along a horizontal surface with μk=0.25\mu_k = 0.25 before stopping. Find its initial speed. Use g=10 m/s2g = 10\text{ m/s}^2.

Example 14

easy
A pendulum at its highest point has 6 J of PE and 0 KE. What is its KE at the lowest point (frictionless)?

Example 15

medium
A 0.2 kg0.2\text{ kg} ball is thrown straight up at 12 m/s12\text{ m/s}. Find the maximum height it reaches. Use g=10 m/s2g = 10\text{ m/s}^2.

Example 16

hard
A roller coaster car (800 kg800\text{ kg}) descends a frictionless hill from rest at 40 m40\text{ m} and enters a vertical loop of radius 10 m10\text{ m}. Find its speed at the top of the loop. Use g=10 m/s2g = 10\text{ m/s}^2.

Example 17

easy
A 0.5 kg0.5\text{ kg} ball is dropped from 10 m10\text{ m}. Find its speed just before hitting the ground (frictionless). Use g=10 m/s2g = 10\text{ m/s}^2.

Example 18

easy
If friction is present, is mechanical energy alone conserved?

Example 19

hard
A 0.1 kg0.1\text{ kg} ball at 30 m/s30\text{ m/s} encounters air drag that does 25 J25\text{ J} of work over its trajectory. Find its KE at the end.

Example 20

easy
A 1 kg1\text{ kg} object has 50 J50\text{ J} of mechanical energy. If its PE is 30 J30\text{ J}, what is its KE?
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