Absurdly basic Physics Question I'm not getting

[leoni101]

---

Members do not see this ad.

A motorcycle is moving at constant speed around a horizontal circular track. What happens to the centripetal acceleration, ac, of the motorcycle if the speed is doubled?
a) It remains the same.
b) It is decreased by a factor of one-half.
c) It increases by a factor of 2.
d) It is decreased by a factor of one-fourth.
e) It increases by a factor of 4.

Ac = (v^2)/r

So if you double v, then Ac should increase by 4. But the solution says the answer is b. Can someone explain please?

 

[leoni101]

Maybe solution is wrong? Does anyone agree?

 

[Pisiform]

v = 2 pi r/t
so if speed is doubled, the r doubles.

Cent Acc = v^2 / r

since r doubles, centripetal acceleration becomes half. Tangential velocity remains constant.

 

[leoni101]

v = 2 pi r/t
so if speed is doubled, the r doubles.

Cent Acc = v^2 / r

since r doubles, centripetal acceleration becomes half. Tangential velocity remains constant.

I follow the thought process here, but if speed is doubled in actuality the time is halved, not the radius increasing right? If we're on a track, the radius of the track never actually increases am I wrong?

 

[FishyTheFish]

I follow the thought process here, but if speed is doubled in actuality the time is halved, not the radius increasing right? If we're on a track, the radius of the track never actually increases am I wrong?

You are the right, the solution is wrong. The radius does not change, but rather the time gets halved.

 

[Ssina]

yeah no idea why it would (b)!!!! also thought it would be (e)

 

[Pisiform]

ya forget what I said .. sorry. I was thinking smth else

 

[leoni101]

thanks everyone

 

[Erythropoietin]

A motorcycle is moving at constant speed around a horizontal circular track. What happens to the centripetal acceleration, ac, of the motorcycle if the speed is doubled?
a) It remains the same.
b) It is decreased by a factor of one-half.
c) It increases by a factor of 2.
d) It is decreased by a factor of one-fourth.
e) It increases by a factor of 4.

Ac = (v^2)/r

So if you double v, then Ac should increase by 4. But the solution says the answer is b. Can someone explain please?

There are two formulas for centripetal acceleration:
a = v^2 / r
a = omega^2 * r

Omega is constant anywhere on a spinning object, and r does not change. So we cannot use the 2nd equation. Since r is the same, doubling velocity increases acceleration by a factor of 4 from the first equation.