Classical Mechanics "variable mass" linear motion problem in one dimention.

[cemtu]

Homework Statement

A truck with empty mass m0 starts to move under a constant force F0 in a rainy weather. Assuming that the rate of change of the mass of the truck starts to move from rest. a) Find the mass m(t) of the truck, b)Find the speed v(t) of the truck, c)find the distance taken x(t) by the truck; all at time t..

Relevant Equations

F=m*dv/dt
P=(dm/dt)*v +m*(dv/dt)

Please help please

 

[TSny]

Hello, @cemtu. Welcome to PF!

As a newcomer, please take a look at the Homework Guidelines here. Note in particular item #4.

You can edit your first post so that you can show us how you are thinking about the problem and any work that you have done so far on the problem.

Please proofread your statement of the problem. The second sentence seems to be missing some words.

Also, the second equation in your post cannot be correct. The dimensions on the left and right sides don't match.

 

[haruspex]

P=(dm/dt)*v +m*(dv/dt)

You mean dp/dt=(dm/dt)*v +m*(dv/dt), but that equation should be struck out from all textbooks and course notes. While it is true in an obvious sense, when properly interpreted it turns out not to be that useful. The issue is, what exactly is p the momentum of here? If it is of a rigid body then dm/dt=0.
It is tempting to then write F=dp/dt, but that leads to the impression that somehow applying a force leads to a change in mass!
If the mass of the system is varying then either matter is being added or removed, and it may bring/take momentum with it as it does so.

 

[cemtu]

Also, the second equation in your post cannot be correct. The dimensions on the left and right sides don't match.

yes thanks for warning. However the site does not allow me to edit the homework equations.There was also a mistake in the question. I am reposting here:

• A truck with empty mass m0 starts to move from rest under a constant force F0 in a rainy weather. Rain fills the back of the truck. Assuming that the rate of change of the mass of the truck is a constant α.

a) Find the mass m(t) of the truck,
b)Find the speed v(t) of the truck,
c)find the distance taken x(t) by the truck;
all at time t..

Homework Equations:
F = dP/dt = d(mv)/dt = (dm/dt)*v +m*(dv/dt)

 

[PeroK]

yes thanks for warning. However the site does not allow me to edit the homework equations.There was also a mistake in the question. I am reposting here:

• A truck with empty mass m0 starts to move from rest under a constant force F0 in a rainy weather. Rain fills the back of the truck. Assuming that the rate of change of the mass of the truck is a constant α.

a) Find the mass m(t) of the truck,
b)Find the speed v(t) of the truck,
c)find the distance taken x(t) by the truck;
all at time t..

Homework Equations:
F = dP/dt = d(mv)/dt = (dm/dt)*v +m*(dv/dt)

How far can you get without any help?

 

[cemtu]

How far can you get without any help?

I think I solved it. Can you check please?

 

[PeroK]

I think I solved it. Can you check please?

Post your answers if you want.

 

[cemtu]

Post your answers if you want.

of course thank you Iwas preparing my answer right now:

 

[cemtu]

I think I solved the problem can anyone please check it?

 

[PeroK]

Looks good to me. There was a much quicker way to do part b), by integrating the momentum.

For part c) you could expand the log function using Taylor series and check what you have makes sense. Especially if ##\alpha = 0##.

Note that the log function can be simplified to something of the form ##\ln(1 + \alpha t/m_0)##.

Good work!

 

[cemtu]

Looks good to me. There was a much quicker way to do part b), by integrating the momentum.

For part c) you could expand the log function using Taylor series and check what you have makes sense. Especially if ##\alpha = 0##.

Note that the log function can be simplified to something of the form ##\ln(1 + \alpha t/m_0)##.

Good work!

Thank you so much mister PeroK! now that at least my solution is approved, I can give this solution to my teacher without concern! thank you!

 

[haruspex]

There was a much quicker way to do part b), by integrating the momentum.

I think you meant, by integrating the force to get the momentum.