Two boxes sit at the top of two straight ramps of the same height. One ramp is s

Question

Two boxes sit at the top of two straight ramps of the same height. One ramp is steeper than the other (makes a greater angle with the horizontal). If the two boxes are released from rest and slide down the ramps without friction, which will be travelling the fastest when they reach the bottom of the ramps? Why?

AThe both have the same speed at the bottom.

BThe box on the steeper ramp.

CThe box on the less-steep ramp.

DThe box that has the greatest mass.

Which box will arrive first at the bottom of the ramp? Why?

AThe box on the steeper ramp.

Bboth arrive at the bottom at the same time.    

CThe box on the less-steep ramp.

D The box that has the greatest mass.

Explanation / Answer

at the top potential energy of boxes will be mgh

at bottom the kinetic energy will be = 0.5 * m * v^2

by conservation of energy

mgh = 0.5 * m * v^2

gh = 0.5 * v^2

since in both the cases h is same so

both have the same speed at the bottom

since the force will be mg * sin(theta) so more the angle is more will be the force due to gravity so more acceleration

box on the steeper ramp will arrive first at the bottom of the ramp

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