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Physics Energy/Work problem with ramp.?
A box of mass 30 kg is being dragged from rest up a frictional ramp by a rope with tension 500 N. The ramp has coefficients of static and kinetic friction of 0.5 and 0.3, respectively.
The angle of the box up the ramp is 25 degrees.
a) Calculate the net work done on the object if it moves 5 m up the ramp.
b) At the end of 5 m what is the box's velocity?
1 Answer
- 7 years agoFavorite Answer
a) The net work is (net force on the box)x(distance).
Net force = Tension - frictional force - component of gravitational force parallel to motion
F = T- μmgcos(θ) - mgsin(θ).
The net work is thus:
W = FΔx = (500 - 0.3*30*9.8*cos(25) - 30*9.8*sin(25))*5
b) From the work energy theorem, the velocity, v, of the box satisfies:
1/2*m*v^2 = W (W was found in a). So the velocity is sqrt(2W/m) = sqrt(2W/30) directed up the ramp.
Now just plug & chug!
