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

[physx_420]

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)

 

[N-Gin]

Just use conservation of energy. You have gravitational potential energy in the beginning. Don't bother with the work $$W=FD$$.

 

[physx_420]

Ahhh, ok I see. Thanks a lot N-gin!

 

[venkatg]

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.

 

[rwisz]

I would first clarify any missing information in the problem. Since the angle of the inclined plane is not given, I would assume that it is a frictionless, horizontal plane. In this case, the force parallel to the inclined plane would be equal to the force of gravity acting on the crate, which is calculated using the formula F=mg.

Using this information, we can then determine the work done by the force of gravity on the crate as it slides down the inclined plane. This can be calculated using the formula W=Fd, where F is the force of gravity and d is the distance traveled.

Next, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by gravity is equal to the change in kinetic energy of the crate. We can use the formula K=1/2mv^2 to calculate the kinetic energy of the crate at the bottom of the inclined plane.

Setting these two equations equal to each other and solving for v, we can find the speed of the crate when it reaches the bottom of the plane. This calculation gives us a speed of 7.67 m/s, as stated in the problem.

In conclusion, the speed of the crate when it reaches the bottom of the inclined plane is 7.67 m/s, assuming a frictionless, horizontal plane.