Question

A 1.23-kg box slides down an incline plane with a speed of 8.6 m/s. If the angle of the plane with respect to the horizontal is 11 degrees and the coefficient of friction is 0.33, how long will it take for the box to come to rest?

Answer 1

A 1.23-kg box slides down an incline plane with a speed of 8.6 m/s. If the angle of the plane with respect to the horizontal is 11° and the coefficient of friction is 0.33.

We have to find the time taken for the box to come to rest.

here, m = 1.23 kg , θ = 11° , μ = 0.33

net force along vertical = 0

⇒N = mgcos11°

net force along horizontal = ma

⇒mgsin11° - μN = ma

⇒gsin11° - μgcos11° = a

⇒a = g(sin11° - μcos11°) = -1.305 m/s²

now using formula, v = u + at

here, v = 0 , u = 8.6 m/s , a = -1.305

⇒0 = 8.6 - 1.305t

⇒t = 8.6/1.305 = 6.6s

Therefore the time taken by box to come to rest is 6.6 sec