what energy does a spherical ball have when it is rolled down a wooden slope?

Question

Does any one know it in detail?

Answer 1

A ball on a slope will have two types of energy: kinetic energy from its movement, and gravitational potential energy from the fact that it will be pulled down the slope by gravity.

Kinetic energy=0.5*m*v^2
Potential energy=mgh

As the ball continues down the slope, the potential energy will decrease, but the kinetic energy will increase. On a frictionless slope the sum of the two will always be equal, as energy cannot be lost. In reality the friction will create heat, dissipating some of the energy.

Answer 2

The potential energy is PE = mgh; where m is the mass of the ball, g = 9.81 m/sec^2 or 32.2 ft/sec^2, and h = the height of the ball above some reference point (like the floor the slope is sitting on). The ball has that potential energy because you had to lift it up to that height (h). In doing that, you performed work; you put energy into lifting the weight of the ball W = mg.

When you let the ball roll down, it initially has that potential energy PE = mgh. But then, as it picks up speed, that PE is converted into kinetic energy (KE). If there is no friction or drag on the ball, all that PE it had at height h, will be converted to KE = 1/2 mv^2; where v is the velocity of the ball at the bottom of the slope where h = 0.

Thus, we can write PE = mgh = 1/2 mv^2 = KE when there is no friction or drag. If we want to know how fast that ball will roll off the slope onto the floor, we can note that gh = 1/2 v^2 because the m's cancel out. Thus, v^2 = 2gh; so that v = sqrt(2gh).

Answer 3

Well the ball is not a point particle and so as a rigid body a different approach needs to be taken.

The moment of inertia, I, of a solid sphere of mass m and radius a is (2ma^2)/5. Then the total kinetic energy is the sum of the linear kinetic energy and the rotational kinetic energy.

KE=(mv^2)/2 + (Iw^2)/2 where w is the angular velocity, m is the mass of the body, and I is the moment of inertia about a line perpendicular to the plane of the motion.

Then at an angle T to the floor, the angle of the wooden slope. Total E=PE+KE, PE= mghCos(T) where h is the hight of the slope.

Thats as far as I know, you would also need to know the coefficient of friction of the wood. Hopefully this points you in the right direction.

Answer 4

When the ball is at the top of the slope it will have potential energy equal to massxgravityxheight but no actuall energy

When it gets to the bottom of the slope it will have no more potential energy but all the potential energy it had at the top of the slope is now kinetick energy.

Answer 5

mjf is right - the ball has rotational and translational kinetic energy.

Rot K.E. = (1/2)*I*omega^2

Trans K.E. =(1/2)*m*v^2

omega is the ball's angular velocity (radians/sec)

I is its moment of inertia about its centre.

What this means, in practice, is that a rolling ball will move down the slope slower than a ball which slides down a frictionless slope without rolling.

Answer 6

Kinetic energy because the ball is in motion.

Answer 7

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Answer 8

It has kinetic energy, It also gives off energy in the form of sound. there would also be friction.

Answer 9

it will have rotational kinetic energy =1/2(rotational inertia of sphere * angular speed)

Answer 10

potential energy > kenetic energy