Linear Momentum/Kinetic Energy

[Alms]

Hey, I'm sorry to bombard you with questions, but I've been out of my Physics lecture due to lots of work from other classes, and I've got these 3 questions which I have no idea how to do. Our professor does not teach according to our textbook, and I'm too thick to understand these concepts. Any help would be very, very appreciated.

1. a. Two objects have masses of M and 3M, respectively. If both have the same kinetic energy, which one has the larger linear momentum and by what factor? Why?
b. If the two objects have the same linear momentum (magnitude), which will have the larger kinetic energy and by what factor? Why?

2. You drop a ball of mass 1 kg from a height of 2m. The collision with Earth lasts for about 10^-4 seconds and on bouncing the ball rises to a height of 1.5m. Is this collision totally elastic? Why?

3. A person of mass 50 kg is standing at the end of a plank of mass 100 kg and length 5m and the plank rests on a horizontal smooth, icy surface. If the person walks from one end to the other, by how much will the plank move? Why?



2. KE= 1/2m(p/m)^2=(p^2)/2m, (v1'-v2')=(v2-v1)=-(v1-v2)



3. (1) I'm really trying to understand 1, because I had thought that two objects with the same momentum, but different masses would have different kinetic energies. I don't think that I can really apply this, though.
(2) I'm thinking that it's not, because in an elastic collision, the KEs should be the same? On second thought, I don't know this at all, either.
(3) I don't know where to start with this.

I'm sorry for my idiocy.

 

[ehild]

In the first question, the two bodies have the same energy, but different momenta. The second question asks about a different situation, when the momentum is the same and the energy is different.

You wrote the correct relation between KE and linear momentum: KE=p^2/(2m). The two momenta are p_a and p_b, the masses are m_a=M, m_b=3M. Go ahead.

2. What do you know about the KE at the ground before and after impact, knowing the hight the ball fall from and the one it raised?

3. The plank and man is a closed system, only internal forces acting along the icy surface. What is the quantity conserved when there is no external force?

ehild

 

[Alms]

In the first question, the two bodies have the same energy, but different momenta. The second question asks about a different situation, when the momentum is the same and the energy is different.

You wrote the correct relation between KE and linear momentum: KE=p^2/(2m). The two momenta are p_a and p_b, the masses are m_a=M, m_b=3M. Go ahead.

2. What do you know about the KE at the ground before and after impact, knowing the hight the ball fall from and the one it raised?

3. The plank and man is a closed system, only internal forces acting along the icy surface. What is the quantity conserved when there is no external force?

ehild

2) Since KE in a total elastic collision should remain the same (I think), would this not be due to the fact that some KE is transferred to the ground, and so, since there is less Kinetic energy, the height on the way back up is less?

3) The forces from the man and the plank? mg? I'm not really sure.

Thanks so much for your help.

 

[ehild]

2) Since KE in a total elastic collision should remain the same (I think), would this not be due to the fact that some KE is transferred to the ground, and so, since there is less Kinetic energy, the height on the way back up is less?
.

It is true. But the ground stayed in rest so the mechanical energy was not conserved during the impact. The soil absorbed some of it, and transformed to other energies, deformation, sound, heat, and so on.

As for question 3: The same but opposite forces act between the man and the plank so the net force is zero. What happens with the centre of mass of the plank-man system if there is no external force?

 

[Alms]

It is true. But the ground stayed in rest so the mechanical energy was not conserved during the impact. The soil absorbed some of it, and transformed to other energies, deformation, sound, heat, and so on.

As for question 3: The same but opposite forces act between the man and the plank so the net force is zero. What happens with the centre of mass of the plank-man system if there is no external force?

If there is no external force, then velocity is constant and the system does not move?

 

[ehild]

If there is no external force, then velocity is constant and the system does not move?

If it did not move before the man walked from one side of the plank to the other, it will not move as a whole. The centre of mass stays in rest, while the man and the plank move relative to each other and relative to the ice.
See attached picture.

ehild

 

[Alms]

Thank you very much, you helped me a lot.