Conceptual Energy vs Momentum question

[Feodalherren]

Homework Statement

In tryouts for the national bobsled team, each competing
team pushes a sled along a level, smooth surface for 5
meters. One team brings a sled that is much lighter than all
the others. Assuming that each team pushes with the same
net force, compare the kinetic energy of the light sled to
that of the others after 5 meters. Compare the momentum
of the light sled to that of the others after 5 meters. (Hint:
Think about the times involved.)

Suppose the rules were changed in Question 19 so that
the teams pushed for a fixed time of 5 seconds rather
than a fixed distance of 5 meters. Compare the momentum
of the light sled to that of the others after 5 seconds.
Compare the kinetic energy of the light sled to that of the
others after 5 seconds.

Homework Equations

Don't need to calculate anything but
P=mv
KE=(1/2)mv^2

The Attempt at a Solution

For the first one. Wouldn't the team need to push as many times faster as their bobsled is less massive?
For the KE they could push much slower as the velocity is squared.

For the the 2nd question:
same thing!?

Also, what's the difference between Force and Energy, apart from the obvious that one is in N and the other in J. I feel like it's the same concept twice .

 

[SammyS]

Homework Statement

In tryouts for the national bobsled team, each competing team pushes a sled along a level, smooth surface for 5 meters. One team brings a sled that is much lighter than all the others. Assuming that each team pushes with the same net force, compare the kinetic energy of the light sled to that of the others after
5 meters. Compare the momentum of the light sled to that of the others after 5 meters. (Hint: Think about the times involved.)

Suppose the rules were changed in Question 19 so that the teams pushed for a fixed time of 5 seconds rather than a fixed distance of 5 meters. Compare the momentum of the light sled to that of the others after 5 seconds. Compare the kinetic energy of the light sled to that of the others after 5 seconds.

Homework Equations

Don't need to calculate anything but
P=mv
KE=(1/2)mv^2

The Attempt at a Solution

For the first one. Wouldn't the team need to push as many times faster as their bobsled is less massive?
For the KE they could push much slower as the velocity is squared.

For the the 2nd question:
same thing!?

Also, what's the difference between Force and Energy, apart from the obvious that one is in N and the other in J. I feel like it's the same concept twice .

For the first case, use the work-energy theorem. How does the final KE of the light sled compare to that of a standard sled?

Then, what does that say about their relative momenta?


For the second case, use the impulse-momentum theorem. How does the final momentum of the light sled compare to that of a standard sled?

Then, what does that say about their relative kinetic energies?

 

[Feodalherren]

You mean w=Fd

... hmm ok so F=ma
The mass is less, the acceleration is greater... The force could technically be the same... I have no idea where to go with this...

 

[SammyS]

You mean w=Fd

... hmm ok so F=ma
The mass is less, the acceleration is greater... The force could technically be the same... I have no idea where to go with this...

No. w=Fd is just a definition of work.

The work done by the net force exerted on an object is equal to the change in Kinetic Energy of the object.


The impulse-momentum theorem is somewhat similar.

The impulse imparted to an object by the net force exerted on an object is equal to the change in the momentum of the object.

 

[Feodalherren]

I have no idea where to go with that. Okay the mass is smaller, but the velocity will probably be greater. So the KE could be the same or even greater in any case (for q1). The same goes for the momentum. m is decreased but V is most likely increased. These questions are retarded!

 

[SammyS]

I have no idea where to go with that. Okay the mass is smaller, but the velocity will probably be greater. So the KE could be the same or even greater in any case (for q1). The same goes for the momentum. m is decreased but V is most likely increased. These questions are retarded!

They push the same distance, with the same force. → They all do the same amount of work.

Same amount of work implies what relationship for the relative KE ?