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 = 2 meters and a slope of 13 degrees with respect to the ground. The box has a mass of 8 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?
J

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

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

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

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

f) What is this velocity if the box starts with a mass of 24 kg?
m/s

Explanation / Answer

a) U1 = m*g*h = 156.96 J

b) K2 = 156.96 J

c) Total = K2 + U2 = 156.96 + 0 = 156.96 J

d) Total E = U1+K1 = 156.96+ 0 = 156.96 J


e) 0.5*m*v^2 = m*g*h

==> v = sqrt(2*g*h) = 6.26 m/s

f) same 6.26 m/s

final velosity does not depend on mass of the body

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