Question

this is question i am stuck at plz help me with this class physics question ​

Answer 1

Answer:

Acceleration experienced by a block along an incline (without friction) of a particular angle is calculated by the formula:

⇒ a = g.sinθ

where, 'a' is the acceleration of the block, 'g.sinθ' is the gravity along the incline and 'θ' is the angle of the incline.

According to the question, the block is moving on a surface with friction. Hence the FBD equation would be:

⇒ F = mg.sinθ - μ.N

⇒ ma = mg.sinθ - μ.mg.cosθ

Cancelling mass, we get the acceleration to be:

⇒ a = g.sinθ - μ.g.cosθ   ...(1)

where, 'μ' is the coefficient of friction.

Now according to the second equation of motion, we know that:

⇒ s = ut + 0.5 at²

According to the question, the block was initially at rest hence having initial velocity to be 0 m/s. Hence we get:

⇒ s = 0.5 at²

Since the length of the path travelled by the block is 'l' we get:

⇒ l = 0.5 at²

Substituting the value of 'a' from (1) we get:

⇒ l = 0.5 ( g.sinθ - μ.g.cosθ ) t²

⇒ 2l = ( g.sinθ - μ.g.cosθ ) t²

$\implies t^2 = \dfrac{2l}{g.sin\theta - \mu.g.cos\theta}\\\\\\\implies \boxed{ \bf{t = \sqrt{ \dfrac{2l}{g.sin\theta - \mu.g.cos\theta} }}}$