Visual SolutionEasy

Question

Two blocks of masses

2 \text{ kg}

and

3 \text{ kg}

are placed in contact on a smooth horizontal surface. A horizontal force of

10 \text{ N}

is applied on the

2 \text{ kg}

block. Find the contact force between the two blocks.

(A)

4 \text{ N}

(B)

6 \text{ N}

(C)

5 \text{ N}

(D)

10 \text{ N}

Solution Path

System acceleration

a = 10/5 = 2 \text{ m/s}^2

. Contact force on 3 kg block:

N = 3 \times 2 = 6 \text{ N}

01Question Setup

1/4

Two blocks of masses

2 \text{ kg}

and

3 \text{ kg}

on a smooth surface. A

10 \text{ N}

force is applied on the

2 \text{ kg}

block. Find the contact force.

N = \;?

02Free Body DiagramKEY INSIGHT

2/4

Treat both blocks as a system first. Since the surface is smooth (no friction), both blocks accelerate together with the same acceleration

a

a = \frac{F}{m_1 + m_2} = \frac{10}{5} = 2 \text{ m/s}^2

03Isolate the 3 kg Block

3/4

Draw FBD of the

3 \text{ kg}

block alone. The only horizontal force on it is the contact force

N

from the

2 \text{ kg}

block. Apply Newton's second law:

N = m_2 \cdot a

N = 3 \times 2 = 6 \text{ N}

04Final Answer

4/4

The contact force between the blocks is

6 \text{ N}

. Note: if the force were applied on the

3 \text{ kg}

block instead, the contact force would be

\frac{2 \times 10}{5} = 4 \text{ N}

\boxed{6 \text{ N}}

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