Informative line

### Various Forces

Learn direction of gravitational force, tension, spring and normal contact force. Practice examples of tension in a pulley system and normal force on an incline.

# Direction of Gravitational Force

• Direction of gravitational force is given towards the center of the earth.
• The magnitude of gravitational force is equal to product mg, where m is the mass of the body, g is the acceleration due to gravity.

Case I :- Stationary body of any shape placed on horizontal surface

• Consider a block of mass M placed on a surface.

• Direction of gravitational force will be as shown in figure.
• Mg always acts vertically downwards, towards the center of earth.

Case II :-  Moving body of any shape

• Consider a body of mass M, falls free under gravity.

Important Note

• Mg always acts vertically downwards, irrespective of path of motion.

Case III :- Stationary or moving body on any surface (other than horizontal surface)

• Consider a body of mass M placed upon an inclined plane at $$\theta$$.
• Mg always acts vertically downwards, irrespective of orientation of surface.

#### A block of mass M is kept on a smooth horizontal floor, which of the following figure shows the correct direction of Mg?

A

B

C

D

×

Mg always acts vertically downward

Option (A) is correct.

### A block of mass M is kept on a smooth horizontal floor, which of the following figure shows the correct direction of Mg?

A
B
C
D

Option A is Correct

# Normal Contact Force

## Push or Pull

• There are two types of forces, i.e., push and pull.
• Normal force comes into play when two bodies are in contact and either one or both are trying to push each other by penetrating the other's surface.

• Block A tends to penetrate into ground and ground does not allow to do so, thus pushing it back.
• So, block is being pushed by the ground away from itself hence normal force on the block is in upward direction.

### Steps to draw the normal force

1. Mark point of contact.
2. Draw a line perpendicular to the surface.
3. Its direction is towards the object experiencing the normal contact force.

• Normal force on block A is towards itself hence, in upward direction.
• Normal contact force on a block placed on inclined.

• Normal contact force on curved surface.
• Two bodies are in contact such that one having curved surface and other having flat surface, as shown in figure.

• The direction of normal contact force (N) is perpendicular to the flat surface.

NOTE: When two bodies are curved, then the normal contact force is perpendicular to the common tangent.

#### A ball is kept on a smooth floor. Which of the following figure shows the correct direction of normal force on the ball?

A

B

C

D

×

The direction of normal contact force (N) is perpendicular to the flat surface towards the ball.

Option (A) is correct.

### A ball is kept on a smooth floor. Which of the following figure shows the correct direction of normal force on the ball?

A
B
C
D

Option A is Correct

# Spring Force

• Spring applies force along its length.
• It can be both pushing or pulling in nature depending upon whether the spring is compressed or extended.

## Natural length

• Length of spring when it is not under any force is called its natural length.
• It is denoted by $$\ell_0$$

## Direction of spring force

• The direction of spring force is always directed towards its natural length.

#### A spring is extended towards right, as shown in figure. What is the direction of spring force?

A Towards right

B Towards left

C Upward

D Downward

×

The direction of spring force is always towards the natural length.

Option (B) is correct.

### A spring is extended towards right, as shown in figure. What is the direction of spring force?

A

Towards right

.

B

Towards left

C

Upward

D

Downward

Option B is Correct

# Tension Force on Pulley

• A pulley can change the direction of the force exerted by a cord.
• An ideal pulley has no mass and no friction.
• As a result the tension of an ideal cord that runs through an ideal pulley is the same on the both sides of the pulley.
• An ideal pulley can change the direction of the force exerted by a cord by change in the magnitude.
• Tension force acts away from the body, along the string/rope.

#### Consider an ideal pulley system. Find the direction and magnitude of F.

A

B

C

D

×

Over an ideal pulley the magnitude of tension force remains the same.

Tension force acts away from the body, along the string/rope.

Option (A) is correct.

### Consider an ideal pulley system. Find the direction and magnitude of F.

A
B
C
D

Option A is Correct

# Normal Contact Force on a Ladder

• In this case the normal is perpendicular to the flat surface, as shown in figure.

#### A ladder is kept, as shown in figure. Which of the following option correctly shows the direction of normal contact force at A?

A

B

C

D

×

The normal will be perpendicular to the flat surface and away to it.

Option (D) is correct.

### A ladder is kept, as shown in figure. Which of the following option correctly shows the direction of normal contact force at A?

A
B
C
D

Option D is Correct

# Tension

• Tension acts on a body when a string attached to the body is taut. As you must have experienced that by rope or a string you can only pull things towards you.
• Using rope or string you can not push objects away.
• It means tension is a pulling force.
• Tension force acts away from the body, along the string/rope.
• To draw tension force acting on block A due to string BC.
• Mark point of contact of string on the block as point B.
• Now draw a vector along string pointing away from the body.

#### A block is hanged with a string, as shown in figure. Choose the direction of tension force.

A

B

C

D

×

Tension force acts away from the body, along the string/rope.

Option (B) is correct.

### A block is hanged with a string, as shown in figure. Choose the direction of tension force.

A
B
C
D

Option B is Correct