Mass Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Mass.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The amount of matter in an object and a fundamental measure of how much it resists changes to its state of motion (inertia).

How 'heavy' something feels when you try to push it, regardless of gravity.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Mass asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to mass but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

easy

An object has a weight of

49 \text{ N}

on Earth where

g = 9.8 \text{ m/s}^2

. What is the mass of the object?

Answer

m = 5 kg

First step

Recall the relationship between weight and mass:

W = mg

, where

W

is weight,

m

is mass, and

g

is gravitational acceleration.

Full solution

2
Rearrange for mass by dividing both sides by $g$ : $m = \frac{W}{g}$
3
Substitute values: $m = \frac{49}{9.8} = 5 kg$

Mass is a measure of the amount of matter in an object and remains constant regardless of location. Weight depends on the gravitational field, but mass does not.

Example 2

medium

An astronaut has a mass of

75 \text{ kg}

. What would their weight be on the Moon where

g_{\text{moon}} = 1.6 \text{ m/s}^2

? Compare this to their weight on Earth (

g = 9.8 \text{ m/s}^2

Example 3

medium

On planet Zog, a

5 \text{ kg}

rock weighs

40 \text{ N}

. What is the gravitational acceleration on Zog?

Example 4

medium

A spring scale (calibrated for Earth) reads

24 \text{ N}

when an object hangs from it on the Moon (

g_{\text{moon}} = 1.6 \text{ m/s}^2

). What is the object's mass?

Example 5

medium

50 \text{ kg}

person stands in an elevator that is accelerating downward at

2 \text{ m/s}^2

(

g = 9.8 \text{ m/s}^2

). What does the scale (in newtons) read?

Example 6

hard

70 \text{ kg}

astronaut on the ISS is in free fall around Earth. What does a bathroom scale (calibrated in newtons) under their feet read?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A net force of

30 \text{ N}

accelerates an object at

6 \text{ m/s}^2

. What is the mass of the object?

Example 2

easy

A toolbox weighs

72 \text{ N}

on a planet where

g = 12 \text{ m/s}^2

. What is its mass?

Example 3

easy

What is the SI unit of mass?

Example 4

easy

An astronaut has a mass of

70\text{ kg}

on Earth. What is her mass on the Moon?

Example 5

easy

Which has more inertia: a

2\text{ kg}

ball or a

5\text{ kg}

ball?

Example 6

easy

A net force of

12\text{ N}

gives an object

3\text{ m/s}^2

. Find its mass.

Example 7

easy

Do all objects fall with the same acceleration regardless of mass (ignoring air resistance)?

Example 8

easy

Does pushing a heavier object require more or less force for the same acceleration?

Example 9

easy

Is mass a vector or a scalar?

Example 10

easy

6\text{ kg}

object and a

3\text{ kg}

object feel the same

18\text{ N}

force. Which accelerates more?

Example 11

medium

0.5\text{ kg}

ball is hit and accelerates at

40\text{ m/s}^2

. Find the force on it.

Example 12

medium

An object weighs

98\text{ N}

on Earth (

g=9.8\text{ m/s}^2

). Find its mass.

Example 13

medium

On the Moon (

g=1.6\text{ m/s}^2

) an object weighs

32\text{ N}

. Find its mass and its weight on Earth (

g=9.8\text{ m/s}^2

Example 14

medium

2\text{ kg}

cart goes from

4\text{ m/s}

10\text{ m/s}

2\text{ s}

. What constant force acted, and would a

4\text{ kg}

cart need more or less for the same change?

Example 15

medium

Two blocks,

3\text{ kg}

and

2\text{ kg}

, are glued together and pushed with

20\text{ N}

on a frictionless floor. Find the acceleration.

Example 16

medium

A scale reads

50\text{ kg}

for a person. What is their weight in newtons (

g=9.8\text{ m/s}^2

Example 17

medium

1000\text{ kg}

car must stop from motion with

5000\text{ N}

of braking force. Find its deceleration.

Example 18

challenge

4\text{ kg}

object feels two forces:

20\text{ N}

east and

15\text{ N}

south. Find its acceleration magnitude.

Example 19

challenge

Object A (

m

) accelerates at

6\text{ m/s}^2

under force

F

. Object B accelerates at

2\text{ m/s}^2

under the same

F

. Find B's mass in terms of

m

Example 20

challenge

60\text{ kg}

person stands in an elevator accelerating up at

2\text{ m/s}^2

(

g=9.8

). Find the scale reading (apparent weight).

Example 21

medium

3\text{ kg}

and a

5\text{ kg}

mass are joined and pulled with

32\text{ N}

on a frictionless floor. Find the acceleration.

Example 22

medium

0.25\text{ kg}

apple accelerates at

12\text{ m/s}^2

when thrown. Find the force on it.

Example 23

easy

A box has a mass of

8 \text{ kg}

. What is its weight on Earth where

g = 9.8 \text{ m/s}^2

Example 24

easy

A net force of

18 \text{ N}

produces an acceleration of

2 \text{ m/s}^2

on a cart. Find the cart's mass.

Example 25

easy

A bag of flour weighs

19.6 \text{ N}

on Earth (

g = 9.8 \text{ m/s}^2

). What is its mass?

Example 26

easy

4 \text{ kg}

object is pushed with a net force of

24 \text{ N}

. Find its acceleration.

Example 27

medium

1.5 \text{ kg}

object moves at

4 \text{ m/s}

and is then pushed by a

9 \text{ N}

net force in the direction of motion for

2 \text{ s}

. Find its final speed.

Example 28

medium

Two objects of mass

m

and

3m

are pushed with the same net force

F

. The ratio of their accelerations

a_1 / a_2

(for

m

3m

) is what?

Example 29

medium

0.4 \text{ kg}

hockey puck slides on frictionless ice and is struck by a

12 \text{ N}

force for

0.1 \text{ s}

. By how much does its velocity change?

Example 30

medium

2 \text{ kg}

block and a

6 \text{ kg}

block are tied together and pulled on a frictionless surface with a

24 \text{ N}

force. Find the acceleration of the system.

Example 31

medium

An object's weight on Jupiter (

g = 24.8 \text{ m/s}^2

) is

496 \text{ N}

. What would the same object weigh on Earth (

g = 9.8 \text{ m/s}^2

Example 32

medium

A truck of mass

2000 \text{ kg}

accelerates from rest to

20 \text{ m/s}

10 \text{ s}

. What is the net force on it?

Example 33

medium

Doubling the mass while keeping the net force the same does what to the acceleration?

Example 34

hard

3 \text{ kg}

block on a rough surface (kinetic friction

\mu_k = 0.2

) is pulled horizontally by a

15 \text{ N}

force. Find the acceleration (

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

Example 35

hard

0.2 \text{ kg}

ball collides with a wall and reverses direction: before

+15 \text{ m/s}

, after

-10 \text{ m/s}

. The collision lasts

0.05 \text{ s}

. Find the average force on the ball.

Example 36

hard

5 \text{ kg}

object on a frictionless horizontal surface is pulled by a rope at

30^\circ

above horizontal with

20 \text{ N}

. Find the horizontal acceleration.

Example 37

hard

Two masses are connected by a string over a frictionless pulley:

m_1 = 3 \text{ kg}

on the floor side and

m_2 = 5 \text{ kg}

hanging. Find the magnitude of the acceleration (

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

Example 38

hard

An object of mass

m

slides down a frictionless incline at angle

\theta

. Show that its acceleration is independent of

m

, and find the acceleration when

\theta = 30^\circ

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

Example 39

challenge

A balance (lever-style, not a spring scale) on Earth reads

4 \text{ kg}

for an object. What would the same balance read on the Moon?

Example 40

challenge

A rocket of total mass

1000 \text{ kg}

(including fuel) ejects exhaust at a rate such that the thrust is

15{,}000 \text{ N}

upward while the rocket lifts off (

g = 9.8 \text{ m/s}^2

). Find the upward acceleration just at liftoff.

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Related Concepts

Force Weight Inertia