If I threw a rock and it magically doubled in size, and the speed doubled, the momentum would?

Question

a) decrease by a factor of 1
b) increase by a factor of 1
c) remain constant
d) increase by a factor of 4

Answer 1

Wasn't this Dr. H's question yesterday?

Or course if the magic rock was traveling at c/2 to begin with, the answer is infinity....

p final / p initial
= mvgamma final / mvgamma initial

= 4 sqrt ((c^2 - v^2) / (c^2 - 4 v^2))

Answer 2

The answer is d, because momentum=mass*velocity. So, if you start with a rock of mass=1 going 1 meter/second, then momentum=1*1=1. Double both, and you get momentum=2*2=4.

Hmmm... David N has a point that just because the rock doubles in size doesn't mean that it doubled in mass. He's also right that velocity is speed and direction, but it doesn't matter what direction it's going. If its speed doubles, the momentum doubles. The answer: If the mass of the rock stays the same, then momentum will increase by a factor of 2. If you assume that the density of the rock is constant though, and it doubles in size, then its mass also doubles, and the answer is d.

Answer 3

Your "magic," does it need to follow the rules of physics? If it does, then the mass of the rock would remain fixed (e.g., at m) because mass/energy cannot be created or destroyed in the real world, but it can be converted from one to the other (e.g., E = mc^2). In which case, none of the answers is correct...in fact momentum would double...increase by a factor of 2.

This is how that could be.

When the size doubled, mass remained fixed; so the rock's mass density rho was half what it started out to be before the rock's size s doubled into S = 2s. That is Rho = m/s and rho = m/2s; where Rho is the mass density before the size change and rho is the mass density after.

And V = 2v; where v is the velocity before the size change and V is the velocity after. From p = mv and P = mV, the momenta before and after the size change, we find P/p = mV/mv = Rho s 2v/rho 2s v = Rho/rho = m/s//m/2s = 2 = P/p.

Thus, P = 2p showing the momentum doubles under your conditions...assuming mass remains fixed so the density goes down when the size is doubled. This is easier to see from p = mv and m2v = P, but I chose to show the mass densities to point out how mass can remain fixed even though the size "magically doubled."

And this follows the laws of physics because mass is neither created nor destroyed, while the velocity and size are doubled. Further, I don't need to assume I can throw a rock at near the speed of light...ordinary nonrelativity physics here. As I said earlier, none of the answers you gave as options is correct if you do not violate the laws of physics.

Answer 4

increase by a factor of 4.
the assumption i made is that doubling in SIZE equates doubling in MASS. Otherwise it would be increase by a factor of 2, which is not in the options.

Rmb: you cannot apply the principle of conservation of linear momentum here because this principle does not apply to magic (esp magic that makes the thing move faster). if you have a rocket, which relies on its fuel to move and in turn gets lighter with propulsion, you can examine this qn again.

Hope this helps=)

Answer 5

NONE OF THE ABOVE.

(We know that if the speed is changing so is the velocity; therefore "C" is incorrect.)

momentum = mv.

It would be "D" if the MASS had doubled and the VELOCITY had doubled.

Doubling the size doesn't necessarily double the mass (popcorn is a good example.)

Speed doesn't quite do it either...
Velocity has 2 elements: SPEED and DIRECTION.
.

Answer 6

d maybe?

i'm going on Newtonian mechanics though. Stupid relativity, I'm still trying to figure it out. Uhhhh, should have stayed at Psychology

Answer 7

momentum is mass* speed.

If the mass doubled and the speed, then the answer is d.

Answer 8

c