Question

A worker wants to load a 12 kg crate into a truck by sliding the crate up a straight ramp which is 2.5 m long and which makes an angle of 30 degrees with the horizontal. The worker believes that he can get the crate to the very top of the ramp by launching it at 5 m/s at the bottom. Note that the worker does not keep pushing on the crate. But the worker underestimated or even forgot about friction, and the crate slides only 1.6 m up the ramp, stops, and slides back down. You may assume that the friction is constant along the ramp. Draw a Free Body Diagram. (thank you)

(a) How fast is the crate moving when it reaches the bottom of the ramp? Use the work-energy approach to calculate this.

(b) Using Newton’s 2nd law, find the acceleration of the crate on the way up and on the way down. If you were not able to solve part a), you may ask me for the value of μk

Answer 1

a) the speed of the crate on reaching the bottom of the ramp is 2.52 m/s

B) while moving the acceleration of crate is - 7.8 m/s2 and while moving down its acceleration is + 1.9875 = 2 m/s2