Question

A box sits on a 30^o incline as shown below, and is coasting up the ramp with an initial speed of 5.0 m/s. The coefficient of kinetic friction between the box and the ramp is 0.25.

1. Determine the acceleration of the box on the way up.
2. How long will it take for the box to come to rest?
3. How far up the ramp will it travel before coming to rest?

Answer 1

here,

theta = 30 degree

the initial speed , u = 5 m/s

the coefficient of kinetic friction , uk = 0.25

the acceleration of the box on the way up , a = - g * sin(theta)

a = - 9.81 * sin(30) m/s^2

a = - 4.9 m/s^2

the time taken for the box to come to rest , t = - u /a

t = 5/4.9 = 1 s

the distance traveled , s = - u^2 /2a

s = - 4.9^2 /(2*(-4.9))

s = 2.5 m