Question

A block of 400lbs is lying on a horizontal plane. A force, F of 100lbs is applied 30 degree with the plane. The block is about to move.
find the coefficient of friction between the block and the plane.
0.38
0.247
0.42
0.50

Answer 1

Given:

A block of 400lbs is lying on a horizontal plane. A force, F of 100lbs is applied 30 degree with the plane. The block is about to move.

To find:

Coefficient of friction ?

Calculation:

First of all ,let's calculate the normal reaction on block.

$\therefore \: N = mg - F \sin( {30}^{ \circ} )$

$\implies \: N = 400- 100 \sin( {30}^{ \circ} )$

$\implies \: N = 400- 100 (0.5)$

$\implies \: N = 400-50$

$\implies \: N = 350 \: lbs$

Now, when force is being applied, it's a critical condition (limiting condition):

$\implies \: F \cos( {30}^{ \circ} ) = \mu(N)$

$\implies \: 100 \cos( {30}^{ \circ} ) = \mu(350)$

$\implies \: 100 (0.86) = \mu(350)$

$\implies \: 86 = \mu(350)$

$\implies \: \mu = \dfrac{86}{350}$

$\implies \: \mu \approx \: 0.247$

So, coefficient of friction is approx 0.247