Question

.If a block slides without friction down a fixed, inclined plane with θ=300. I. What is block acceleration? II. If coefficient of static friction between block and plane 0.4, at what angle will the block start sliding if it is initially at rest. ​

Answer 1

Question 1:

A block slides without friction down a fixed, inclined plane with θ=30°. What is block acceleration?

Question 2:

If coefficient of static friction between block and plane 0.4, at what angle will the block start sliding if it is initially at rest.

Solutions:

1. Let the acceleration be a :

$\therefore \: a = g \sin( \theta)$

$\implies \: a = g \sin( {30}^{ \circ} )$

$\implies \: a = g \times \dfrac{1}{2}$

$\implies \: a = 10 \times \dfrac{1}{2}$

$\implies \: a = 5 \: m/ {s}^{2}$

2. Now, in case of equilibrium conditions, the frictional force will be equal and opposite to the pulling force:

$\therefore \: F = f$

$\implies \: mg \sin( \theta) = \mu \bigg \{mg \cos( \theta) \bigg \}$

$\implies \:\sin( \theta) = \mu \cos( \theta)$

$\implies \: \mu = \tan( \theta)$

$\implies \: \tan( \theta) = 0.4$

$\implies \: \theta= { \tan}^{ - 1}( 0.4)$

So, at this angle , the block will start moving.