Newton's Second Law Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Newton's Second Law.

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 acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, with the acceleration pointing in the same direction as the net force.

Push harder and you get faster acceleration; heavier object means slower acceleration for the same push.

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: Newton's Second Law 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 newton's second law 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

10 \text{ kg}

cart is pushed with a net force of

50 \text{ N}

. What is the acceleration of the cart?

10 kg cart pushed with 50 N net force — find acceleration

Answer

a = 5 {m/s}^{2}

First step

Write Newton's second law:

F_{\text{net}} = ma

, where

F_{\text{net}}

is net force,

m

is mass, and

a

is acceleration.

Full solution

2
Rearrange to solve for acceleration: $a = \frac{F_{net}}{m}$
3
Substitute the given values: $a = \frac{50}{10} = 5 {m/s}^{2}$

Newton's second law quantifies the relationship between net force, mass, and acceleration. Greater force produces greater acceleration for the same mass.

Example 2

medium

1200 \text{ kg}

car accelerates from rest to

20 \text{ m/s}

8 \text{ seconds}

. What net force is required?

1200 kg car: find net force for acceleration from rest to 20 m/s in 8 s

Example 3

medium

2 \text{ kg}

puck on a frictionless surface is pushed east with

10 \text{ N}

and pulled west with

4 \text{ N}

. Find its acceleration.

2 kg puck pushed east 10 N and pulled west 4 N — find acceleration

Example 4

medium

3 \text{ kg}

block on a frictionless table is pulled by

T = 12 \text{ N}

horizontally while a

6 \text{ N}

horizontal drag opposes the motion. Find the acceleration.

3 kg block pulled by T=12 N with 6 N drag — find acceleration

Example 5

medium

2 \text{ kg}

object experiences perpendicular net force components

F_x = 6 \text{ N}

and

F_y = 8 \text{ N}

. Find the magnitude of its acceleration.

2 kg object with F_x=6 N and F_y=8 N — find net acceleration magnitude

Example 6

hard

Two masses

m_1 = 4 \text{ kg}

and

m_2 = 2 \text{ kg}

are connected by a light cord over a frictionless pulley (Atwood machine). Find the acceleration of the system. Use

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

Example 7

hard

Two blocks (

m_1 = 3 \text{ kg}

on top of

m_2 = 5 \text{ kg}

) sit on a frictionless floor. A horizontal

32 \text{ N}

force pushes

m_2

. Friction between the blocks is enough to keep

m_1

from sliding. Find the system acceleration and the friction on

m_1

Example 8

challenge

5 \text{ kg}

block on a frictionless

30°

incline is connected over a pulley to a hanging

3 \text{ kg}

block. Find the system 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

hard

5 \text{ kg}

block on a frictionless surface is pulled by a

30 \text{ N}

force at an angle of

30°

above the horizontal. What is the horizontal acceleration?

5 kg block pulled at 30° — find horizontal acceleration

Example 2

medium

1500 \text{ kg}

truck accelerates at

1.2 \text{ m/s}^2

while resistive forces total

300 \text{ N}

opposite the motion. What forward force must the engine provide?

1500 kg truck: find engine force given 1.2 m/s² acceleration and 300 N resistance

Example 3

easy

A net force of

15\text{ N}

acts on a

3\text{ kg}

object. Find its acceleration.

Example 4

easy

State the equation form of Newton's second law.

Example 5

easy

Find the force needed to accelerate a

2\text{ kg}

object at

7\text{ m/s}^2

Example 6

easy

If net force doubles and mass stays the same, what happens to acceleration?

Example 7

easy

If mass doubles and net force stays the same, what happens to acceleration?

Example 8

easy

10\text{ N}

net force gives a body

2\text{ m/s}^2

. Find its mass.

Example 9

easy

In what direction does the acceleration point relative to the net force?

Example 10

easy

What is the acceleration of a

6\text{ kg}

object with a

0\text{ N}

net force?

Example 11

medium

5\text{ kg}

box has

40\text{ N}

forward and

15\text{ N}

friction back. Find the acceleration.

5 kg box with 40 N forward and 15 N friction — find acceleration

Example 12

medium

1200\text{ kg}

car accelerates from rest to

24\text{ m/s}

8\text{ s}

. Find the net force.

Example 13

medium

2\text{ kg}

block on a

30^\circ

frictionless incline (

g=10

) slides down. Find its acceleration (

\sin 30^\circ=0.5

2 kg block on 30° frictionless incline — find acceleration down the slope

Example 14

medium

Forces

9\text{ N}

east and

12\text{ N}

north act on a

3\text{ kg}

object. Find its acceleration magnitude.

3 kg object with 9 N east and 12 N north — find acceleration magnitude

Example 15

medium

A constant

6\text{ N}

net force acts on a

3\text{ kg}

cart for

4\text{ s}

from rest. Find its final speed.

Example 16

medium

An elevator cable lifts a

200\text{ kg}

load upward at

2\text{ m/s}^2

(

g=10

). Find the cable tension.

200 kg load lifted upward at 2 m/s² — find cable tension

Example 17

medium

4\text{ kg}

object's speed changes from

10\text{ m/s}

2\text{ m/s}

2\text{ s}

. Find the magnitude and direction of the net force.

4 kg object slowing from 10 m/s to 2 m/s in 2 s — find braking force

Example 18

challenge

3\text{ kg}

and

2\text{ kg}

block, connected by a string, are pulled by

25\text{ N}

on a frictionless floor. Find the acceleration and the string tension.

Example 19

challenge

1\text{ kg}

ball is thrown up and slows under gravity (

g=9.8

). Ignoring air, find its acceleration at the highest point.

Example 20

challenge

Two masses,

5\text{ kg}

and

3\text{ kg}

, hang over a frictionless pulley (Atwood). Find the system acceleration (

g=10

Atwood machine: 5 kg and 3 kg masses over frictionless pulley — find acceleration

Example 21

medium

0.2\text{ kg}

ball is struck and reaches

30\text{ m/s}

from rest in

0.01\text{ s}

. Find the average force.

Example 22

medium

5\text{ kg}

object on a flat floor (

g=10

\mu=0.2

) is pushed with

30\text{ N}

. Find its acceleration.

5 kg block on floor with μ

Example 23

easy

A net force of

24 \text{ N}

accelerates an object at

3 \text{ m/s}^2

. What is the object's mass?

Example 24

easy

4 \text{ kg}

object speeds up at

2.5 \text{ m/s}^2

. What net force acts on it?

Example 25

easy

An object of mass

0.5 \text{ kg}

experiences a net force of

4 \text{ N}

. Find its acceleration.

Example 26

medium

0.145 \text{ kg}

baseball is accelerated from rest to

40 \text{ m/s}

during a

0.020 \text{ s}

contact with the bat. What is the average net force on the ball?

Example 27

medium

1500 \text{ kg}

car traveling at

25 \text{ m/s}

brakes to rest in

5.0 \text{ s}

. What net braking force was applied (magnitude)?

Example 28

medium

Two blocks (

m_1 = 2 \text{ kg}

m_2 = 3 \text{ kg}

) are in contact on a frictionless surface. A horizontal force of

20 \text{ N}

pushes

m_1

. Find the system acceleration.

Example 29

medium

An elevator of mass

800 \text{ kg}

accelerates upward at

1.5 \text{ m/s}^2

. Find the tension in the supporting cable. Use

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

800 kg elevator accelerating upward at 1.5 m/s² — find cable tension

Example 30

medium

0.5 \text{ kg}

ball is dropped from rest and falls freely ignoring air resistance (

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

). What is the net force on the ball as it falls?

0.5 kg ball in free fall — only weight acts, F_net

Example 31

medium

1500 \text{ kg}

rocket experiences

25{,}000 \text{ N}

thrust upward and weighs

14{,}700 \text{ N}

. Find its upward acceleration. Use

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

1500 kg rocket with 25000 N thrust vs 14700 N weight — find upward acceleration

Example 32

hard

10 \text{ kg}

block slides down a frictionless incline at

37°

. Find its acceleration along the incline. Use

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

\sin 37° = 0.6

10 kg block on 37° frictionless incline — find acceleration down the slope

Example 33

hard

2 \text{ kg}

object's velocity changes from

\vec{v}_i = (3, 0) \text{ m/s}

\vec{v}_f = (3, 4) \text{ m/s}

over

2 \text{ s}

. Find the magnitude of the average net force.

Example 34

hard

70 \text{ kg}

person stands in an elevator that accelerates downward at

2 \text{ m/s}^2

. What is the apparent weight (normal force) on the person? Use

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

70 kg person in elevator accelerating downward at 2 m/s² — find apparent weight

Example 35

hard

20 \text{ kg}

crate is pushed across a horizontal floor by a

100 \text{ N}

force at

37°

below the horizontal. Friction is negligible. Find the horizontal acceleration. Use

\cos 37° = 0.8

20 kg crate pushed by 100 N at 37° below horizontal — find horizontal acceleration

Example 36

hard

1000 \text{ kg}

car experiences a net forward force whose magnitude grows linearly from

0

t=0

2000 \text{ N}

t=4 \text{ s}

. What is the car's acceleration at

t = 2 \text{ s}

Example 37

challenge

A rope of mass

2 \text{ kg}

and length

4 \text{ m}

is pulled along a frictionless horizontal table by a

12 \text{ N}

horizontal force at one end. Find the tension in the rope at its midpoint.

Example 38

challenge

1200 \text{ kg}

car on level ground experiences a drag force

F_d = bv

with

b = 60 \text{ N}\cdot\text{s/m}

and a constant engine force of

3000 \text{ N}

. What is the car's terminal (top) speed?

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Related Concepts

Force Mass Acceleration Free Body Diagram Net Force

Background Knowledge

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

forcemassacceleration