Answer to Question #290936 in Classical Mechanics for Stans

Question

a) If a block slides at a frictionless plane inclined at theta equal 30 ° what's the acceleration of the block

b) if the coefficient of static friction between the plane and block in part (a) is miu equals 0.4 at what angle will the block start sliding if is initially at rest

Answer 1

a) The acceleration of the block:

$$a=g\sin30°=4.9\text{ m/s}^2.$$

b) The angle at which the block will start sliding if is initially at rest:

$$\theta=\arctan\mu=21.8°.$$