Bowling Ball is rolled down a steep hill

[IAmBadAtMath]

Homework Statement

A bowling ball is pushed down a steep hill with a mass of 8.2kg. Its initial velocity is 3,0 m/s. When the ball arrives at the bottom of the hill its velocity is 26.5 m/s. How much work has the resistance forces done to slow the bowling ball down.

Relevant Equations

v = v_0 + at, an = v2/r, W = Fs, g = 9,81 m/s^2,

I have no idea how and what to do.

 

[jbriggs444]

Homework Statement:: A bowling ball is pushed down a steep hill with a mass of 8.2kg. Its initial velocity is 3,0 m/s. When the ball arrives at the bottom of the hill its velocity is 26.5 m/s. How much work has the resistance forces done to slow the bowling ball down.
Relevant Equations:: v = v_0 + at, an = v2/r, W = Fs, g = 9,81 m/s^2,

I have no idea how and what to do.

Work. That is an amount of energy, isn't it? Hmmm... One of your relevant equations involves energy. But the others do not. Maybe figure out some more equations involving energy.

Also, looking at the homework statement, I do not see all of the information that I would expect. Are you sure you've quoted the whole thing?

 

[hmmm27]

I do not see all of the information that I would expect. Are you sure you've quoted the whole thing?

It's all there. None of the entered formulas are relevant, though.

I have no idea how and what to do.

Show some work : forum rules. Maybe explain what you think the problem is, without simply cut'n'pasting.

Work. That is an amount of energy, isn't it?

There's a nice juicy hint right there, for when you get around to figuring out how to solve it.

 

[jbriggs444]

It's all there. None of the entered formulas are relevant, though.

Possibly a browser problem. I do not see the attached diagram, except as something ephemeral that I managed to mouse over one time. The text does not reveal the height of the hill.

The formula for work as force times distance is relevant in the absence of some other relevant formulae.

 

[hmmm27]

Okay, now you got me wondering if the magnitude of the circumference is necessary.

 

[jbriggs444]

Okay, now you got me wondering if the magnitude of the circumference is necessary.

Nope. Irrelevant.

You can see that the hard way with algebra and watching all the factors of r cancel out. Or the intuitive way and see that the velocity distribution through the volume of the sphere is the same regardless.

[I trust my intuition. I know the algebra will work out without actually doing it]

Oh, I think I know what the diagram that I can't see showed. I bet we have a shallow slope at the top (rolling is established), a shallow slope at the bottom (rolling is re-established) and a steep slope in between (sliding and loss of mechanical energy occurs). So rolling is definitely contemplated.

 

[hmmm27]

Pretty sure the only thing missing is noting that - apart from the 8.2kg being the mass of the bowling ball not the hill - the surface is frictive enough that there's no sliding [my intuition].

 

[jbriggs444]

The adjective "steep" is the piece that leads me to the opposite interpretation. But no matter. If sliding friction is absent, air resistance can suffice and the problem is still identical either way as long as rolling is established at top and bottom.

 

[hmmm27]

The verb "rolled" in the title is my stance... despite the problem statement's lack of clarification. Picture a long, mildly sloped bowling lane on the beach.

 

[kuruman]

The adjective "steep" is the piece that leads me to the opposite interpretation. But no matter. If sliding friction is absent, air resistance can suffice and the problem is still identical either way as long as rolling is established at top and bottom.

I would agree with this interpretation. Probably the ball slides a distance of many circumferences before undergoing one revolution about its axis. Nevertheless, we still need a vertical drop.

 

[hmmm27]

Wonder how the OP's coming along.

 

[haruspex]

The verb "rolled" in the title is my stance... despite the problem statement's lack of clarification. Picture a long, mildly sloped bowling lane on the beach.

I assumed any losses to be mainly as rolling resistance.
Yes, we are missing the info on the height of the hill, but to me there is also an ambiguity.
The posts above seem to assume the rotational KE should be excluded from the answer. E.g, the rolling could have come entirely from static friction, and we all know that static friction does no work.
But I prefer to say static friction does no net work. It is reasonable to view it as doing negative work in regards to the linear KE and equal positive work re rotational KE. On that basis, all of the friction does negative work in slowing the ball's linear progress.