Conceptual Energy vs Momentum question

In summary: Same amount of work implies what relationship for the relative momentum ?In summary, the question compares the kinetic energy and momentum of a lighter bobsled pushed for 5 meters by a team to that of heavier bobsleds. The second question changes the distance to a fixed time of 5 seconds. Using the work-energy theorem, the final kinetic energy of the light sled will be greater than that of the heavier sleds, while using the impulse-momentum theorem, the final momentum of the light sled will also be greater. This is because the lighter sled will have a greater velocity due to its smaller mass. The same principle applies for the fixed time scenario. The questions highlight the relationship between force, energy, and momentum, and how
  • #1
Feodalherren
605
6

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 o_O.
 
Last edited:
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  • #2
Feodalherren said:

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 o_O.
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?
 
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  • #3
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...
 
  • #4
Feodalherren said:
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.
 
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  • #5
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!
 
  • #6
Feodalherren said:
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 ?
 

FAQ: Conceptual Energy vs Momentum question

What is the difference between conceptual energy and momentum?

Conceptual energy is a measure of the potential and kinetic energy of a system, while momentum is a measure of the motion and inertia of an object. In simpler terms, energy is the ability to do work, while momentum is the quantity of motion an object possesses.

Why do we need both energy and momentum in physics?

While energy and momentum may seem similar, they serve different purposes in physics. Energy helps us understand how objects interact and change over time, while momentum helps us understand how objects move and behave in collisions.

How are energy and momentum related?

Energy and momentum are related through the principle of conservation of energy. This principle states that the total energy in a closed system remains constant, meaning that energy can be transferred from one form to another but cannot be created or destroyed. Momentum is also conserved in a closed system, meaning that the total momentum of the system remains constant.

Can an object have energy but no momentum?

Yes, an object can have energy without having momentum. This can occur when an object has potential energy, such as a ball sitting at the top of a hill. The ball has energy due to its position, but no momentum because it is not moving.

What real-life examples demonstrate the difference between energy and momentum?

A good example of the difference between energy and momentum is a rollercoaster ride. As the rollercoaster car climbs up the first hill, it gains potential energy due to its height. As it goes down the hill, this potential energy is converted into kinetic energy, giving the car momentum. However, as the car reaches the top of the next hill, it loses momentum but still has potential energy. This demonstrates how energy and momentum are separate but related concepts in physics.

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