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

Acceleration = 2.35 m/
`s^(2)`

Speed = 8.67 m/s

Step-by-step 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° =
`(mg)/(2)` = 0.5 mg

Friction along incline = umg cos30° = mg
`0.3* (√(3))/(2)`

Friction along incline = 0.26 mg

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

Acceleration =
`(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* 0.24 * 9.8* 16`

v= 8.67 m/s