Finding final kinetic energy and final velocity?

Question

A solid ball of mass 15 kg is at the top of a frictionless incline 2 m high and 10 m long. If it rolls down the incline, find its:

(a) initial potential energy
(b) final kinetic energy
(c) final velocity.

So far, I've done (a), hopefully it's right.

I did ...

GPE = mgh, so 15 x 9.8 x 2 = 294 J.

I'm stuck with the next part, (b).

The formule is KE = mv2 (squared) divided by 2.

I've got the mass but the thing is I don't have the velocity to work out the kinetic energy.

To work out the velocity you generally need the kinetic energy.

I'm confused.

If anyone could help out that'd be great.

This is tenth grade physics by the way =)

Answer 1

in the absence of friction, the KE of the object after it falls will be equal to the PE before the fall.

You already found that GPE = mgh, so 15 x 9.8 x 2 = 294 J., so the KE at the end will be 294 J

Answer 2

DanE is right on the money. The concept here is conservation of energy. Potential energy Pe at the top will be equal to kinetic energy Ke at the bottom provided that no losses say due to friction took place during the motion.
Your calculation for Pe is correct and since
Pe=Ke=(1/2)mV^2

V= sqrt (2 PE/m) or since Pe=m g h
V=sqrt(2 mgh/m)
V=sqrt(2 g h) Interesting... we don't need a mass of the object to compute its velocity.

Answer 3

How To Find Kinetic Energy

Answer 4

Because there are no frictional losses on the way down the ramp, the energy at the top of the ramp is equal to the energy at the bottom of the ramp except the energy is in a different form at the bottom. At the top the ball has PE=mgh=294J and at the bottom the ball has KE=mvv/2=294J So
mgh=mvv/2, m drops out and
gh=vv/2 or 2gh=vv and v=sqrt[2gh]
=6.3m/s

Answer 5

From coservation of energy
KE = PE = 294 when it is on 0 level
1/2mv^2 = 294
v = sqrt(294 x 2 / 15) = 6.26


It can be shown by detailed calculations, when you need to do with gSinA along the surface, gCosA perpendicular to the surface, etc
Incline = A
SinA =
CosA =