Name: Two Block System
Uploaded: 2019-07-19
Duration: 6 min 20 s
Description: Two blocks placed on a surface exerts a force between them and also with the surface. Let us discuss how these forces can be solved numerically in this video.

Question

In the given figures find the accelerations and the friction forces involved,

Accepted Answer

$(i)$ Consider acceleration $a_{A}$ for block $A$ and $a_{B}$ for block $B$ .

Free body diagram equation,

$F = 15 = 5 a_{A}$

$a_{A} = 3 m s^{- 2}$

Frictional force between $A$ and $B$ , $f = 0$

Hence, Acceleration of block $B$ , $a_{B} = 0$ .

$(ii)$

Free body diagram equation,

$F = 30 - 0.5 \times 50 = 5 a_{A}$

$\Rightarrow 5 = 5 a_{A}$

$\Rightarrow a_{A} = 1 m s^{- 2}$ .

Acceleration of $A$ is $1 {ms}^{- 2}$

On $B$ limiting friction $= 150 \times 0.5 = 75 N$ .

As limiting friction $(f_{l} = 75 N)$ is more than the applied force $(f = 25 N)$ .

Hence, acceleration of $B$ is $0$ .

The friction force between $B$ and ground $f_{B} = 25 N$ .

The friction force between $A$ and $B$ , $f_{A} = 25 N$ .

$(iii)$

From free body diagram, applied force $(200 N) >$ Limiting friction force $(75 N)$ , but for block $A$ friction force $(25 N) <$ Applied force on $A$ .

So, both move with different acceleration.

Acceleration of $A$ , $25 = 5 a_{A}$

$\Rightarrow a_{A} = 5 m s^{- 2}$ .

For $B$ ,

$100 = 10 a_{B}$

$\Rightarrow a_{B} = 10 m s^{- 2}$ .

The friction force between $B$ and ground $f_{B} = 75 N$ .

The friction force between $A$ and $B$ , $f_{A} = 25 N$ .

$(iv)$

From free body diagram, applied force $(90 N) >$ Limiting friction $(75 N)$ and on $B$ friction $(25 N) >$ Applied force on $B$ $(15 N)$ .

So, both blocks move together with the same acceleration.

Free body diagram equation,

$90 - 75 = 15 a$

$\Rightarrow a_{A} = a_{B} = 1 m s^{- 2}$ .

The friction force between $B$ and ground $f_{B} = 75 N$ .

The friction force between $A$ and $B$ , $f_{A} = 25 N$ .

In the given figures find the accelerations and the friction forces involved,

Important Questions on Friction

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