Question

a 12kg box is placed at the top of an incline that is 5.5 m long and makes an angle of 38 degrees to the horizontal. the coefficient of static friction between box and the surface is 0.67. a) use calculations to show that the box will overcome static friction and slide down the incline b) if the coefficient of kinetic friction between box and surface is 0.43, what will be the acceleration of the box as it slides down the 38 degree incline?

Answer 1

a)

$$ma=mg\sin{38}-\mu mg\cos{38}$$

$$a=g(\sin{38}-\mu \cos{38})$$

$$(\sin{38}-0.67 \cos{38})=0.088>0$$

$$a>0$$

Thus the box will overcome static friction and slide down the incline.

b)

$$a=9.8(\sin{38}-0.43 \cos{38})=2.7\frac{m}{s^2}$$