Question

A Block slides down an incline that makes an angle of 30? with the horizontal direction. The coefficient of kinetic friction between the incline and the block is µk = 0.3
i) Determine the acceleration of the block.
ii) The block starts at rest from a height of 8m above the ground. What is the speed of the block when it reaches the bottom of the incline.

Answer 1

Answer:

Acceleration = 2.35 m/$s^{2}$

Speed = 8.67 m/s

Explanation:

The coefficient of friction , u =0.3

The angle of incline = 30°

The two forces acting on block are weight and friction.

weight along the incline = mg cos60° = $\frac{mg}{2}$ = 0.5 mg

Friction along incline = umg cos30° = mg $0.3\times \frac{\sqrt{3}}{2}$

Friction along incline  = 0.26 mg

Net force acting on the weight = (0.5 - 0.26) mg = 0.24 mg

Acceleration = $\frac{net force}{mass}$ = 0.24 g = 2.35 m/$s^{2}$

The height of incline = 8 m

Length of the inclined edge = 16 m

$v^{2}=u^{2}+2as$

$v^{2}= 2\times 0.24 \times 9.8\times 16$

v= 8.67 m/s