Net Force Examples: 45 Problems with Answers

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

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 single resultant force obtained by vector addition of all individual forces acting on an object, which alone determines the object's acceleration according to Newton's second law, $\vec{F}_{net} = m\vec{a}$ .

What you get when you add up all pushes and pulls, accounting for direction.

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: Net Force 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 net force 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

Three forces act on an object:

10 \text{ N}

right,

4 \text{ N}

left, and

3 \text{ N}

left. What is the net force?

Three collinear forces on an object — find the net force

Answer

F_{net} = 3 N to the right

First step

Define right as positive. Forces:

+10 \text{ N}

-4 \text{ N}

-3 \text{ N}

Full solution

2
Sum the forces: $F_{net} = 10 + (- 4) + (- 3) = 3 N$
3
The net force is $3 \text{ N}$ to the right.

Net force is the vector sum of all forces acting on an object. It determines the object's acceleration according to Newton's second law.

Example 2

medium

4 \text{ kg}

object experiences forces of

20 \text{ N}

forward and

8 \text{ N}

backward. What is the net force and resulting acceleration?

Find net force and acceleration

Example 3

easy

A child pulls a sled with

25 \text{ N}

along the ground while friction resists with

10 \text{ N}

. What is the net force?

Child pulls sled with friction — find net force

Example 4

medium

5 \text{ kg}

block on a frictionless surface is pulled by a rope at

30°

above horizontal with tension

20 \text{ N}

. What is the horizontal component of the net force?

Example 5

medium

10 \text{ kg}

object slides down a frictionless ramp at

20°

. What is the net force along the slope? Use

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

Object on 20° frictionless ramp — find net force along slope

Example 6

medium

A skydiver of mass

80 \text{ kg}

falls at terminal velocity. What is the net force on her? What is air drag at that moment? Use

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

Skydiver at terminal velocity — what is the net force?

Example 7

hard

Forces on an object:

10 \text{ N}

0°

10 \text{ N}

120°

10 \text{ N}

240°

. Find the net force.

Example 8

hard

Two blocks (

m_1 = 3 \text{ kg}

m_2 = 5 \text{ kg}

) are connected by a rope over a frictionless pulley (Atwood). Find the net force on the system and the acceleration. Use

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

Example 9

hard

0.2 \text{ kg}

ball is whirled on a

1 \text{ m}

vertical string. At the top of the loop, its speed is

4 \text{ m/s}

. What is the tension in the string? Use

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

Example 10

hard

A boat experiences thrust

500 \text{ N}

east and water drag

200 \text{ N}

west, plus a wind force of

150 \text{ N}

north. Find the magnitude and direction of the net force.

Boat with three forces — find net force

Example 11

hard

Two forces

\vec F_1 = (3 \hat{i} + 4 \hat{j}) \text{ N}

and

\vec F_2 = (-1 \hat{i} + 2 \hat{j}) \text{ N}

act on a

1 \text{ kg}

particle. Find the net force and resulting acceleration.

Example 12

challenge

2 \text{ kg}

block on a

30°

incline (

\mu_k = 0.20

) is pulled up the slope by a rope parallel to the slope with

T = 20 \text{ N}

. Find the net force on the block and its acceleration. Use

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

Practice Problems

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

Example 1

medium

Two perpendicular forces act on an object:

6 \text{ N}

east and

8 \text{ N}

north. What is the magnitude of the net force?

Two perpendicular forces — find the net force magnitude

Example 2

easy

10 \text{ kg}

sled accelerates east at

1.5 \text{ m/s}^2

. What is the net force on the sled?

Example 3

easy

Two forces act on a box along one line:

6

N right and

4

N left. What is the net force?

Two collinear forces — find the net force

Example 4

easy

3

N and a

5

N force both point right on a cart. What is the net force?

Two same-direction forces — find the net force

Example 5

easy

An object feels

10

N up and

10

N down. What is the net force?

Equal and opposite forces — what is the net force?

Example 6

easy

4

kg object has a net force of

12

N. What is its acceleration?

Example 7

easy

2

kg cart accelerates at

5

m/s

^2

. What net force acts on it?

Example 8

easy

A car moves at a constant

20

m/s in a straight line. What is the net force on it?

Example 9

easy

Forces of

3

N right,

5

N right, and

4

N left act on a block. Net force?

Three collinear forces — find the net force

Example 10

easy

A box on a frictionless floor is pushed with

15

N right and nothing opposes it horizontally. Net horizontal force?

Box on frictionless surface — what is the net horizontal force?

Example 11

medium

5

kg object feels

20

N east and

15

N west. Find its acceleration.

Find net force and acceleration on 5 kg object

Example 12

medium

A box feels

3

N east and

4

N north (perpendicular). Find the magnitude of the net force.

Perpendicular forces east and north — find net force magnitude

Example 13

medium

2

kg object accelerates at

4

m/s

^2

right while a

6

N friction force acts left. What is the applied force?

Find the applied force given friction and net force

Example 14

medium

Three forces give a net force of zero. Two are

8

N north and

6

N east. What is the third force?

Example 15

medium

10

kg sled is pulled with

40

N right; friction is

10

N. Find its acceleration.

Sled pulled with friction — find acceleration

Example 16

medium

0.5

kg ball changes velocity from

0

6

m/s in

2

s. What net force acted?

Example 17

medium

4

N force points at

30^\circ

above the horizontal. What is its horizontal component?

Example 18

medium

Forces

7

N right,

2

N left, and

5

N left act on a

2

kg block. Find acceleration.

Three collinear forces on 2 kg block — find acceleration

Example 19

medium

1

kg object has velocity

+8

m/s and a constant

-2

N net force. What is its velocity after

3

Example 20

challenge

2

kg block on a

30^\circ

frictionless incline. Find its acceleration down the slope (

g=10

m/s

^2

Block on 30° frictionless incline — find acceleration

Example 21

challenge

Two forces,

5

N and

12

N, act on an object at right angles. What single force balances them?

Two perpendicular forces — find the equilibrant

Example 22

challenge

3

kg mass hangs from two ropes, each at

60^\circ

from vertical, supporting it equally (

g=10

m/s

^2

). Find each rope's tension.

Example 23

easy

Two forces act along a line on a box:

12 \text{ N}

east and

5 \text{ N}

west. What is the net force?

Two collinear forces — find the net force

Example 24

easy

2 \text{ kg}

ball accelerates at

5 \text{ m/s}^2

. What net force acts on it?

Example 25

medium

Two perpendicular forces act on a hockey puck:

9 \text{ N}

north and

12 \text{ N}

east. Find the magnitude and direction of the net force.

Two perpendicular forces on hockey puck — find net force

Example 26

medium

An elevator of mass

500 \text{ kg}

accelerates upward at

2 \text{ m/s}^2

. What is the net force, and what is the tension in the cable? Use

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

Elevator accelerating upward — find cable tension

Example 27

medium

Three coplanar forces act on a particle:

F_1 = 6 \text{ N}

east,

F_2 = 4 \text{ N}

north,

F_3 = 6 \text{ N}

west. What is the magnitude of the net force?

Three coplanar forces — find the net force

Example 28

medium

Two ropes tied to a heavy load pull at

40°

on either side of vertical, each with tension

T = 100 \text{ N}

. What is the magnitude of the net force from the ropes?

Example 29

medium

0.5 \text{ kg}

ball moves in a horizontal circle of radius

0.4 \text{ m}

at speed

2 \text{ m/s}

. What is the net force on the ball, and which direction?

Example 30

hard

2 \text{ kg}

block on a

25°

frictionless incline is held by a rope pulled parallel to the slope with tension

T

so the block stays at rest. What is

T

? Use

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

Example 31

hard

1500 \text{ kg}

car turns a flat curve of radius

50 \text{ m}

20 \text{ m/s}

. What net horizontal force is required (and from what does it come)?

Example 32

hard

4 \text{ kg}

block on a horizontal surface (

\mu_k = 0.25

) is pushed with

30 \text{ N}

. Find the net force and acceleration. Use

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

Example 33

hard

A rocket of mass

1000 \text{ kg}

has thrust

15000 \text{ N}

upward. What is its net force and acceleration just after launch? Use

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

Rocket at launch — find net force and acceleration

← Back to Net Force Practice Mode

Related Concepts

Force Vectors Equilibrium Free Body Diagram

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcevectors