Normal Force Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Normal 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 perpendicular contact force that a surface exerts on an object pressing against it, directed away from the surface.

The floor pushing up on you so you don't fall through — it acts at a right angle to whatever surface the object touches.

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: Normal 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 normal 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

8 \text{ kg}

box rests on a horizontal floor. What is the normal force acting on the box? Use

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

Answer

N = 78.4 \text{ N upward}

First step

The box is in equilibrium on a horizontal surface, so the net vertical force is zero.

Full solution

2
The normal force must balance the weight: $N = mg = 8 \times 9.8 = 78.4 \text{ N}$
3
The normal force acts perpendicular (normal) to the surface, directed upward.

The normal force is the contact force exerted by a surface perpendicular to that surface. On a flat horizontal surface with no other vertical forces, the normal force equals the object's weight.

Example 2

medium

5 \text{ kg}

block rests on a ramp inclined at

30°

to the horizontal. What is the normal force on the block? Use

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

Example 3

easy

2 \text{ kg}

block sits on a level surface. Someone presses down on it with an additional

10 \text{ N}

. Find the normal force. Use

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

Example 4

medium

50 \text{ kg}

person stands in an elevator accelerating upward at

3 \text{ m/s}^2

. What is the normal force from the floor (her apparent weight)? Use

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

Example 5

medium

3 \text{ kg}

block on a horizontal floor is pulled by a rope at

25°

above horizontal with

T = 15 \text{ N}

. Find the normal force. Use

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

Example 6

medium

A car of mass

800 \text{ kg}

passes through the bottom of a valley with radius

40 \text{ m}

20 \text{ m/s}

. What is the normal force on the car? Use

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

Example 7

hard

2 \text{ kg}

block on a

25°

incline is pushed against the slope by a horizontal force of

15 \text{ N}

. Find the normal force. Use

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

Example 8

hard

1200 \text{ kg}

car drives on a banked curve of radius

50 \text{ m}

, banked at

15°

, at the design speed (no friction needed). What is the normal force from the road on the car? Use

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

Example 9

hard

A car drives over a circular hump of radius

r = 30 \text{ m}

. At what speed does the car momentarily lose contact with the road (i.e.,

N = 0

)? Use

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

Example 10

hard

4 \text{ kg}

block sits on top of a

10 \text{ kg}

block, which sits on a horizontal floor. Find the normal force between the two blocks, and between the lower block and the floor. Use

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

Example 11

hard

2 \text{ kg}

block sits on a

20°

incline inside an elevator. The elevator accelerates upward at

2 \text{ m/s}^2

. Find the normal force on the block from the incline. Use

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

Example 12

challenge

A small block sits at the top of a smooth fixed hemisphere of radius

R

. Released from rest, at what angle

\theta

from the vertical does it leave the surface? Use

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

if needed.

Practice Problems

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

Example 1

medium

10 \text{ kg}

box on a horizontal floor has a

30 \text{ N}

downward push applied to it. What is the normal force? Use

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

Example 2

hard

A person (

60 \text{ kg}

) stands in an elevator accelerating upward at

2 \text{ m/s}^2

. What normal force does the floor exert on the person? Use

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

Example 3

easy

6\text{ kg}

book lies on a flat table (

g=10

). Find the normal force.

Example 4

easy

In what direction does the normal force point?

Example 5

easy

Is the normal force always equal to

mg

Example 6

easy

On a

30^\circ

incline, is the normal force greater than, equal to, or less than

mg

Example 7

easy

2\text{ kg}

object hangs from a string (not touching any surface). What is the normal force on it?

Example 8

easy

What kind of force is the normal force: contact or non-contact?

Example 9

easy

4\text{ kg}

box sits on a flat floor with no other vertical force (

g=9.8

). State the normal force.

Example 10

easy

Is the normal force on a book the Newton's third-law reaction to the book's weight?

Example 11

medium

5\text{ kg}

box on a flat floor is also pushed down with an extra

20\text{ N}

(

g=10

). Find the normal force.

Example 12

medium

60\text{ kg}

person stands in an elevator accelerating up at

2\text{ m/s}^2

(

g=10

). Find the normal force.

Example 13

medium

3\text{ kg}

block on a

60^\circ

incline (

g=10

\cos 60^\circ=0.5

). Find the normal force.

Example 14

medium

50\text{ kg}

person stands in an elevator accelerating down at

3\text{ m/s}^2

(

g=10

). Find the normal force.

Example 15

medium

4\text{ kg}

box (

g=10

) is pulled up by a vertical rope with

30\text{ N}

while resting on a floor. Find the normal force.

Example 16

medium

Find the normal force on a

2\text{ kg}

box on a flat floor moving at constant velocity (

g=10

), no vertical applied force.

Example 17

challenge

5\text{ kg}

box on a flat floor is pushed by a

40\text{ N}

force at

37^\circ

below horizontal (

g=10

\sin 37^\circ=0.6

). Find the normal force.

Example 18

challenge

At the top of a vertical circular loop of radius

4\text{ m}

, a

2\text{ kg}

cart moves at

8\text{ m/s}

(

g=10

). Find the track's normal force on it.

Example 19

challenge

3\text{ kg}

box sits in an elevator. A scale beneath reads

36\text{ N}

(

g=10

). Find the elevator's acceleration and its direction.

Example 20

medium

4\text{ kg}

box on a flat floor (

g=10

) is pressed down by a

25\text{ N}

vertical force. Find the normal force.

Example 21

medium

70\text{ kg}

person stands in an elevator at constant velocity (

g=10

). Find the normal force.

Example 22

medium

3\text{ kg}

block on a

45^\circ

incline (

g=10

\cos 45^\circ\approx 0.71

). Find the normal force.

Example 23

easy

5 \text{ kg}

book rests on a horizontal table. Find the normal force from the table on the book. Use

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

Example 24

easy

4 \text{ kg}

box is on a level table. An upward rope pulls on it with

10 \text{ N}

. Find the normal force from the table. Use

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

Example 25

medium

7 \text{ kg}

block sits on a

40°

incline. Find the normal force perpendicular to the slope. Use

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

Example 26

medium

60 \text{ kg}

person rides an elevator accelerating downward at

2 \text{ m/s}^2

. What does a scale read (in N)? Use

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

Example 27

medium

A car of mass

1000 \text{ kg}

goes over the top of a circular hill of radius

50 \text{ m}

15 \text{ m/s}

. What is the normal force on the car at the top? Use

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

Example 28

medium

0.5 \text{ kg}

ball sits in a smooth hemispherical bowl. What is the normal force when the bowl tilts

0°

(level)? Use

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

Example 29

medium

Two stacked blocks:

5 \text{ kg}

on top of

10 \text{ kg}

, on a horizontal floor. Find the normal force on the lower block from the floor. Use

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

Example 30

hard

1500 \text{ kg}

car on a flat curve of radius

80 \text{ m}

25 \text{ m/s}

. What is the normal force from the road on the car (in the vertical direction)? Use

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

Example 31

hard

0.3 \text{ kg}

ball at the bottom of a vertical circular loop of radius

0.6 \text{ m}

moves at

4 \text{ m/s}

. What is the normal force from the track on the ball? Use

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

Example 32

hard

1 \text{ kg}

block rests on a horizontal surface. A spring pushes up on it with force

F_s = 4 \text{ N}

. Find the normal force. Use

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

Example 33

hard

5 \text{ kg}

block sits on the floor of a truck accelerating horizontally at

a = 3 \text{ m/s}^2

. The block does not slide. Find the normal force from the floor. Use

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

← Back to Normal Force Practice Mode

Related Concepts

Force Weight Friction Free Body Diagram

Background Knowledge

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

forceweight