Kinetic Energy and Angle of Velocity - Clarification

[Sandy_221]

THE QUESTION IS THIS:

A skier of mass 55.0 kg slides down a slope 11.7 m long, inclined at an angle f to the horizontal. The magnitude of the kinetic friction is 41.5 N. The skier’s initial speed is 65.7 cm/s and the speed at the bottom of the slope is 7.19 m/s. Determine the angle f from the law of conservation of energy. Air resistance is negligible.

I know the answer to this question. What I don't understand though is why is it that we don't use the vertical component of velocity here (or in any other conservation of energy for that matter) when calculating 1/2 v1 squared and 1/2 v2 squared . I mean why aren't you supposed to take the vertical components of velocity for both v1 and v2, but only use their own values. Whereas for the height in calculating the poential energy you do.

This is kind of bugging me. So, I appreciate your thorough response everyone!

Sandy

 

[grzz]

The gravitational PE means the work against the pull of gravity. But work = force x distance in the DIRECTION of the force. Hence for this PE we use the VERTICAL distance since the gravitational pull is in the vertical.

But KE means the energy of motion - whether in the vertical or in any other direction. So for the KE the whole magnitude of the velocity is used and not just some componet of velocity.

 

[Doc Al]

When calculating the change in gravitational potential energy you are calculating the work done against gravity. Since gravity acts vertically, only the vertical component of distance matters.

But when calculating the kinetic energy--the energy due to a body's speed--direction doesn't matter. You must use the entire velocity, not just one component.

(Looks like grzz beat me to it.)