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 \text{ kg}

) starts from rest at

30 \text{ m}

high and descends to

10 \text{ m}

. What is its speed at

10 \text{ m}

? Use

g = 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\text{ kg}

of water per minute to a height of

15\text{ m}

. Find the pump's minimum power. Use

g = 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

2 \text{ kg}

ball is dropped from

20 \text{ m}

. What is its speed just before hitting the ground? Use

g = 10 \text{ m/s}^2

Example 12

hard

1\text{ kg}

block slides down a

5\text{ m}

ramp at

30^\circ

with

\mu_k = 0.2

. Find its speed at the bottom. Use

g = 10\text{ m/s}^2

Example 13

medium

2\text{ kg}

block slides

4\text{ m}

along a horizontal surface with

\mu_k = 0.25

before stopping. Find its initial speed. Use

g = 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

0.2\text{ kg}

ball is thrown straight up at

12\text{ m/s}

. Find the maximum height it reaches. Use

g = 10\text{ m/s}^2

Example 16

hard

A roller coaster car (

800\text{ kg}

) descends a frictionless hill from rest at

40\text{ m}

and enters a vertical loop of radius

10\text{ m}

. Find its speed at the top of the loop. Use

g = 10\text{ m/s}^2

Example 17

easy

0.5\text{ kg}

ball is dropped from

10\text{ m}

. Find its speed just before hitting the ground (frictionless). Use

g = 10\text{ m/s}^2

Example 18

easy

If friction is present, is mechanical energy alone conserved?

Example 19

hard

0.1\text{ kg}

ball at

30\text{ m/s}

encounters air drag that does

25\text{ J}

of work over its trajectory. Find its KE at the end.

Example 20

easy

1\text{ kg}

object has

50\text{ J}

of mechanical energy. If its PE is

30\text{ J}

, what is its KE?

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Related Concepts

Kinetic Energy Potential Energy Work-Energy Theorem Thermal Energy