Berkeley Review Physics Section 3 Question 20

[lightblueskies]

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"If the mass of a car doubles, but its speed remains the same, the distance required to stop the car..."

a) remains the same
b) increases by a factor of sqrt(2)
c) increases by a factor of 2
d) increases by a factor of 4

Berkeley review says the answer is A.

But this this website http://web.phys.ksu.edu/fascination/Chapter9.pdf says:
"we would find that doubling the mass of the car doubles the stopping distance required"

Help?

 

[Cmdr_Shepard]

Hmm. They seem wrong. I think it's C.

Doubling the mass means doubling the kinetic energy.

This means double the work necessary to stop it.

This means either double the force, or double the distance required.

If we assume the braking system cannot get more forceful, then C must be correct.

 

[brood910]

Change in KE = work = F x d
= 1/2mv2 - 1/2mv2 = f x d = ma x d
Mass cancels out.

 

[Cmdr_Shepard]

Oh yeah! I shouldn't assume the braking system is static. The increase in mass will cause the braking force to also increase by an amount necessary to make the mass increase irrelevant (and thus the mass cancels as not effecting anything).

Brood is correct. I'll edit my post later.

 

[brookssp66]

For the purposes of the MCAT, yes Brood would be right. In real life, a train and a semi obviously take longer to stop than a much smaller car if they are both traveling at the same speed which is what your intuition is telling you. There's a lot more things going on there like drag force, friction, braking power, etc.. Remove these and it would be the same regardless of mass.