What is the speed of the crate when it reaches the bottom?

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To find the speed of a 20.0-kg crate sliding down a frictionless inclined plane, the conservation of energy principle is applied. The gravitational potential energy at the top converts entirely into kinetic energy at the bottom, leading to the formula V = sqrt(2*g*H). The height of the incline is 3.00 m, allowing the calculation of speed without needing the length of the incline. The final speed of the crate when it reaches the bottom is determined to be 7.67 m/s, demonstrating that mass does not affect the speed in this scenario. This approach simplifies the problem by eliminating the need to consider angles or friction.
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Homework Statement


A 20.0-kg crate slides down an inclined plane that is 3.00-m high and 20.0-m long. If friction is negligible, what is the speed of the crate when it reaches the bottom of the plane?



Homework Equations


W= F*D
K= 1/2 m*(v^2)


The Attempt at a Solution


They don't give me an angle so I'm not sure how I'm supposed to go about solving for the force parallel to the inclined plane. Once I have that I'll be able to finish out the problem. Help please!
(The answer turns out to be 7.67 m/s; I just need to know how to get there)
 
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Just use conservation of energy. You have gravitational potential energy in the beginning. Don't bother with the work W=FD.
 
Ahhh, ok I see. Thanks a lot N-gin!
 
The 20 M long is not needed for this problem because the friction is assumed to be zero. No energy is lost in friction and so M*g*H = (1/2)*M*V^2

So V = sqrt(2*g*H)

So the velocity is independent of the Mass!

If you had friction, then still mass is irrelevant.
 

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