A crate of mass 80kg sits on the floor. the crate must be brought to the top of a loading dock by sliding it up a ramp 2.5m long, inclined at 30 degrees. the worker, giving no thought to the force of friction, calculates that he can get the crate up the ramp by giving it an initial speed of 5m/s at the bottom and letting it go. unfortunately, friction is not negligible, the crate slides up 1.6m on the ramp, stops, and slides back down.
Using conservation of energy, show that the initial speed of 5.0 m/s as calculated by the worker is correct if friction is negligible.
Answer:
Initial kinetic energy = Final increase in potential energy
Because the ramp is angled at 30 degrees and is 2.5 m long, the vertical height increase is 2.5 sin 30 = 1.25m
1/2 m v² = mgh
1/2 m v² = m(10)(1.25)
v² = 25
Hence v = 5 m/s (shown)
