Informative line

### Free Body Diagram

Learn free body diagram definition with examples and steps to find action reaction pair. Practice problems of drawing free body diagrams and FBD of Block Placed on an Inclined Plane.

# Free Body Diagram

• A free body diagram is a graphic, symbolic sketch of an object of interest with all the surrounding object stripped away and all the forces acting on the body shown.

## Block over Block System

• Consider two blocks of masses M and m are placed, as shown in figure.

• To study the parameters of motion on the system of different blocks, FBD of each block is drawn separately.
• Let $$N_2$$ be the normal contact force between mass $$M$$ and ground and $$N_1$$ be the normal contact force between mass $$M$$ and mass $$m$$.

#### For the given figure, what will be the correct FBD of lower block? Assume $$N_1$$ be the normal contact force between two blocks and $$N_2$$ as the normal contact force between block of mass $$M$$ and ground.

A

B

C

D

×

Hence, option (C) is correct.

### For the given figure, what will be the correct FBD of lower block? Assume $$N_1$$ be the normal contact force between two blocks and $$N_2$$ as the normal contact force between block of mass $$M$$ and ground.

A
B
C
D

Option C is Correct

# FBD of Blocks Hanging with Strings

## Free Body Diagram

• A free body diagram is a graphic, symbolic sketch of an object of interest with all the surrounding object stripped away and all the forces acting on the body shown.

### System of Blocks Hanging with Strings

• Consider three blocks of masses m1, m2 and m3.
• These three blocks are hanging with strings, as  shown in figure.

• To study the parameters of motion on the system of different blocks, FBD of each block is drawn separately.

• FBD of block of mass m1

Two tensions (T1 and T2) and gravitational force are acting on block of mass m1.

• FBD of block of mass m2

Two tensions (T2 and T3) and gravitational force are acting on block of mass m2.

• FBD of block of mass m3

Tension (T3) and gravitational force are acting on block of mass m3.

A

B

C

D

×

### FBD of Block of Mass m1

Two tensions ( Tand T2) and gravitational force are acting on block of mass m1.

### FBD of Block of Mass m2

Two tensions (T2 and T3) and gravitational force are acting on block of mass m2.

### FBD of Block of Mass m3

Tension ( T3) and gravitational force are acting on block of mass m3.

Hence, option (B) is correct.

### A system of blocks hanging with strings is shown in figure. What will be the correct FBD of block of mass m2?

A
B
C
D

Option B is Correct

# FBD of Blocks Hanging through Pulley Attached to a Wedge

A free body diagram is  a graphic, symbolic sketch of an object of interest with all the surrounding object stripped away and all the forces acting on the body shown.

System of Two Blocks on a Wedge

• Consider two blocks of masses m1 and m2, as shown in figure.

• To study the parameters of motion on the system of different blocks, FBD of each block is drawn separately.

### FBD of Block of Mass m1

Tension T, normal force N1 and gravitational force are acting on block of mass m1

### FBD of Block of Mass m2

Tension T and gravitational force are acting on block of mass m2

A

B

C

D

×

### FBD of Block of Mass m2

Tension T and gravitational force are acting on block of mass m2

Hence, option (A) is correct.

### Two blocks of masses m1 and m2 are placed on a wedge, as shown in figure. What will be the FBD of block of mass m2?

A
B
C
D

Option A is Correct

# FBD of Block Experiencing a Force and Placed on a Wedge

A free body diagram is a graphic, symbolic sketch of an object of interest with all the surrounding object stripped away and all the forces acting on the body shown.

### System of a Block placed on Wedge and a Force is Applied on it

• Consider a block of mass m, which is placed  on a wedge.
• A force F is applied on it, as shown in figure.

• To study the parameters of motion on the system of different blocks. FBD of each block is drawn separately.

• ### FBD of Block of Mass m

A normal force N1, applied force F and gravitational force are acting on block of mass m.

A

B

C

D

×

### FBD of Block of Mass m

A normal force N1 , applied force F and gravitational force are acting on block of mass m.

Hence, option (C)  is correct.

### A block of mass m is placed on wedge. A force F is applied on it, as shown in figure. What will be the FBD of block of mass m?

A
B
C
D

Option C is Correct

# FBD of Block Placed on an Inclined Plane

## Free Body Diagram

• A free body diagram is a graphic, symbolic sketch of an object of interest with all the surrounding object stripped away and all the forces acting on the body shown.

### System of Block Placed on an Inclined Plane

• Consider a block of mass m is placed on an inclined plane, as shown in figure.

• To study the parameters of motion on the system of different blocks, FBD of each block is drawn separately.

• FBD of Block of Mass m

A normal force N1 and gravitational force are acting on block of mass m.

• FBD of Wedge

Two normal forces N1 and N2 and gravitational force are acting on wedge.

A

B

C

D

×

### FBD of block of mass m

A normal force N1 and gravitational force are acting on block of mass m.

Hence, option (C) is correct.

### A block is placed on an inclined plane, as shown in figure. What will be the FBD of block?

A
B
C
D

Option C is Correct

# FBD of Blocks Hanging through Pulley

A free body diagram is a graphic, symbolic sketch of an object of interest with all the surrounding object stripped away and all the forces acting on the body shown.

### System of Two Blocks Hanging Through Pulley

• Consider two blocks of masses m1 and m2 hanging through a pulley, as shown in figure.

To study the parameters  of motion on the system of different blocks, FBD of each block is drawn separately.

### FBD of Block of  Mass m1

A tension T and gravitational force are acting on block of mass m1.

### FBD of Block of  Mass m2

A tension T and gravitational force are acting on block of mass m2.

A

B

C

D

×

### FBD of Block of  Mass m2

A tension T and gravitational force are acting on block of mass m2.

Hence, option (D) is correct.

### Two blocks of mass m1 and m2 are hanging through a pulley, as shown in figure. What will be the FBD of block of mass m2?

A
B
C
D

Option D is Correct

# Identification of Action - Reaction

• ### Newton's Third Law

According to Newton's third law , two interacting bodies exert equal and opposite forces on each - other, simultaneously.

• For instance, bodies A and B are coming towards each other. While interacting, two forces $$\vec F _{A\, on \,B}$$ and $$\vec F _{B\, on \,A}$$ are acting, as shown in figure.
• These forces $$\vec F _{A\, on \,B}$$  and  $$\vec F _{B\, on \,A}$$  are equal in magnitude and opposite in direction .

$$\vec F _{A\, on \,B} = -\vec F _{B\, on \,A}$$

•  Forces $$\vec F _{A\, on \,B}$$  and  $$\vec F _{B\, on \,A}$$  are known as "action - reaction" pair.
• We can not determine, which one is action and which one is reaction .
• Both forces act simultaneously and must be of same nature.
• Steps to Find Action Reaction Pair

Step 1 : Identify the body which is exerting force on the other body.

Step 2 : Identify the nature of force.

Step 3 : The body on which force was applied must be exerting force of equal magnitude and same nature but in opposite direction.

Note :  Action and reaction act on two different bodies.

#### For the given figure, what is the reaction pair of mg?

A Normal force by floor on block

B Normal force by block on floor

C Gravitational pull on block by earth

D Gravitational pull on earth by block

×

mg is the gravitational pull on block by earth.

So, its reaction will be gravitational pull on earth by the block.

Hence, option (D) is correct.

### For the given figure, what is the reaction pair of mg?

A

Normal force by floor on block

.

B

Normal force by block on floor

C

Gravitational pull on block by earth

D

Gravitational pull on earth by block

Option D is Correct

#### A horse is pulling a cart. Which one of the following statements is true?

A Cart exerts equal force on horse.

B Cart exerts less force on horse.

C Cart exerts more force on horse.

D Cart  does not exert force on horse.

×

According to Newton's third law, two interacting bodies exert equal and opposite forces on each other simultaneously .

Hence, option (A) is correct.

### A horse is pulling a cart. Which one of the following statements is true?

A

Cart exerts equal force on horse.

.

B

Cart exerts less force on horse.

C

Cart exerts more force on horse.

D

Cart  does not exert force on horse.

Option A is Correct