Question

I was wanting help with my physics post and since no one replied I thought there wasn't a physics tutor on Jiskha, but came back on today cause I really need to get a hang of my physics stuff and luckily seen you Drwls.

A bike rider approachea a hill with a speed of 8.5m/s. The total mass of the bike and rider is 85kg.

A. Find the kinetic energy of the bike and rider.

Formula for Kinetic Energy I got given is...

Ek = 1/2mv62
1/2(85)(8.5)^2
= 3070.6J

^ That was the easy part. But ughh I am hating the second part to it so much.

The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to a stop?

I have no idea what formula to use to solve the question. Formulas I'm given are...

Egp = mgh

Ek = 1/2mv^2

Eh = mcT

Ee = 1/2kx^2

All these formulas are driving me crazy. My teacher with one question did this.. ET = ET'
Ek + Egp = Ek' = Egp
1/2mv^2 + mhg = 1/2mv^2 + mgh

And the mass crosses out for some odd reason. But before we get to this, I seriously need to know meaning of those formulas. Physics is not my strong area, just took this subject because I may need it in the future. But please help.

And the third part to that.

Does your answer depend on the mass of the bike and rider? Explain.

I guess not because there is no friction, but still how would that take away mass? I mean if I were on frictionless ice standing on top of it, my mass wouldn't automatically be erased :\

Answer 1

The answer will not depend upon the mass of the bike and rider. That will cancel out.

Coasting up the hill, the bike will stop when the initial kinetic energy equals the potential energy increase, M g H. H is the increase in altitude.
Vo^2/2 = g H

Solve for H.

Strictly speaking, the initial kinetic energy is higher because of the rotating wheels, but that additional effect is negligible since the wheels are usually a small fraction of the total weight.