Question

Two blocks of weight w1 and w2 rest as shown. If the angle of friction of each block is , find the magnitude and direction of the least force p applied to the upper block that will induce sliding.

Answer 1

Given that,

Weight of first block = w₁

Weight of second block = w₂

Suppose, The angle is 30°

We need to calculate the friction force on first block

Using formula of friction force

$f_{1}=\mu N$

$f_{1}=\mu mg\sin\theta$

Put the value into the formula

$f_{1}=\mu w_{1}\sin30$

$f_{1}=\mu w_{1}\times\dfrac{1}{2}$

$f_{1}=\dfrac{\mu w_{1}}{2}\ N$

The direction of force f₁ is along to east.

We need to calculate the friction force on second block

Using formula of friction force

$f_{2}=\mu N$

$f_{2}=\mu mg\sin\theta$

Put the value into the formula

$f_{2}=\mu w_{2}\sin30$

$f_{2}=\mu w_{2}\times\dfrac{1}{2}$

$f_{2}=\dfrac{\mu w_{2}}{2}\ N$

We need to calculate the net force

Using formula of net force

$F=f_{1}+f_{2}$

Put the value into the formula

$F=\dfrac{\mu w_{1}}{2}+\dfrac{\mu w_{1}}{2}$

$F=\dfrac{\mu}{2}(w_{1}+w_{2})\ N$

Hence, The net force is $\dfrac{\mu}{2}(w_{1}+w_{2})\ N$

The least force p applied to the upper block is $\dfrac{\mu w_{2}}{2}\ N$

The direction of force f₁ is along to east.