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I am confused because a changing momentum means an unbalanced force is acting down, yet the rocket has constant velocity so surely the forces acting on the rocket are balanced??? Hope someone can help, thank you. *adam*

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- Thread starter adamg
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I am confused because a changing momentum means an unbalanced force is acting down, yet the rocket has constant velocity so surely the forces acting on the rocket are balanced??? Hope someone can help, thank you. *adam*

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Originally posted by adamg

I am confused because a changing momentum means an unbalanced force is acting down, yet the rocket has constant velocity so surely the forces acting on the rocket are balanced??? Hope someone can help, thank you. *adam*

It would be helpful if you give a bit of a background on the level you are at (and this applies to everyone who posts school questions on here). For example, do you know a bit of calculus?

If you do, then assuming that this is a standard intro physics course, you should have known that a force is generally defined as the rate of change of momentum (which you have mentioned), but if you carry that through, you would have noticed an extra component to it, i.e.

F = dp/dt = d/dt (mv) = m dv/dt + v dm/dt

Now, in many instances, m is a constant in time, so dm/dt=0 and you only have

F = m dv/dt = ma

which is the familiar form of Newton's 2nd law. However, in YOUR case, m isn't a constant with time, only v is.... So dv/dt=0 and you have to rederive the force expression, i.e.

F = v dm/dt.

You are told how much the mass has changed in a certain time interval. Assume that this rate of change is uniform, you then know what dm/dt is, i.e. time rate of change of the mass. You then have enough information to find the force acting on the rocket.

Zz.

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Originally posted by adamg

I am confused because a changing momentum means an unbalanced force is acting down, yet the rocket has constant velocity so surely the forces acting on the rocket are balanced??? Hope someone can help, thank you. *adam*

There are two different forces at work here. There is the force of gravity and there is the force on the rocket due to the exhaust. The total force on the rocket is zero since the rocket is not accelerating. However the gravitational force is doing work on the rocket and that is equal to force times distance integrated over the distance traveled. The gravitational force is equal to the weight of the rocket and that weight is decreasing as a function of time.

That should get you started

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HallsofIvy

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HallsofIvy

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That is a net force: yes it unbalanced "Because it must be unbalanced to cause the change in momentum(?) " just as you say.

However, (once again!) "yet it must also be balanced because the velocity is constant(?)" is NOT true! That's only true when mass is a constant so that momentum is proportional to velocity. Force changes momentum (mass times velocity), not just velocity.

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HallsofIvy

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Newton's second law is often written as "f= ma". Stated that way it is incorrect. What Newton actually said was that "force is the rate of change of momentum"- that is, f= dp/dt which is, in fact, a perfectly good

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Over time, it disintegrates, and in 100 seconds, its mass has fallen to 45kg.

Because the mass has decreased, does that mean a force must be acting? What will happen to the object - will its velocity increase so that mv remains constant, or will it remain at the same speed, and therefore mv is reduced?

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Is this anywhere near the actual answer? Please correct me if i'm wrong.

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HallsofIvy

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Originally posted by adamg

Over time, it disintegrates, and in 100 seconds, its mass has fallen to 45kg.

Because the mass has decreased, does that mean a force must be acting? What will happen to the object - will its velocity increase so that mv remains constant, or will it remain at the same speed, and therefore mv is reduced?

No, since there is no external force, the

With no external force, d(mv)/dt= mdv/dt+ vdm/dt= 0.

The body has lost mass (actually, we ought to account for the momentum of every part that it loses but lets just assume it just disappears) of 5 kg in 100 seconds. Assuming that is a uniform loss, m(t)= 50- .05 t where m is measured in kg and t in seconds.

Now, momentum mv= (50- 0.05t)v(t) so d(mv)/dt= (50- 0.05t)dv/dt- 0.05v= 0. We can solve that differential equation for v:

It's separable. (50- 0.05t)dv/dt= 0.05v => dv/v= (0.05/(50-0.05t))dt. Integrating dv/v given ln(v). To integrate 0.05dt/(50-0.05t)dt, let u= 50- 0.05t so du= -0.05dt. The integral becomes -du/u which is -ln(u). We must have ln(v)= -ln(50-0.05t)+ C

or v= C/(50-0.05t). If the original velocity at t= 0 was v

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HallsofIvy

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Yes!

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(phew) thanks

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