A box starts out at the top of a frictionless ramp, then slides down. The ramp h

Question

A box starts out at the top of a frictionless ramp, then slides down. The ramp has a height h = 3 meters and a slope of 5 degrees with respect to the ground. The box has a mass of 1 kg. The system is under normal gravity, so g = 9.81 m/s2  Let the potential energy be zero at the bottom.

a) What is the initial gravitational energy of the box at the top of the ramp?
1 J

b) What is the kinetic energy of the box at the bottom of the ramp?
2 J

c) What is the total mechanical energy of the box at the bottom of the ramp?
3 J

d) What is the total mechanical energy of the box at the top of the ramp?
4 J

e) What does this make the velocity of the box at the bottom?
5 m/s

f) What is this velocity if the box starts with a mass of 3 kg?
6 m/s

Explanation / Answer

a) m g h = 1*9.81*3=29.4 J

b) Ef = KE = EI = 29.4 J

c) 29.4 J

d) 29.4 J

e) 0.5*1*v^2=29.4
v=7.67 m/s

f) gravity is independent of mass so 7.67 m/s

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