Wednesday, December 23, 2009

How would a change of mass of an object affect the velocity?

if a truck with a shipment of items was traveling at a constant velocity, and the cables securing the payload(STS specific term?) broke allowing the items to start falling out, would the velocity change?How would a change of mass of an object affect the velocity?
F = dP/dt = d(mv)/dt = m(dv/dt) + v (dm/dt)





dv/dt = [F - v (dm/dt)]/m





F is traction force, m is instantaneous mass function at t and dv/dt is acceleration.How would a change of mass of an object affect the velocity?
It depends on whether you are accounting for friction.





If there is no friction (an ideal model) then the change in mass has no effect on a truck with constant velocity.





If you are accounting for friction then the truck is using a force F to counter friction exactly and if the truck loses mass then it will also decrease friction and so will accelerate.
if the truck delivers a constant force, then yes the velocity would change. It would increase actually.





force = mass x (velocity / time) = (mass x velocity) / time = momentum / time





mass is inversley proprotionate to velocity therefore the lower the mass, the higher the velocity


(at a constant force, which the truck is at).
Assuming the force moving the truck remained the same, the velocity would increase as the mass was reduced. But otherwise, mass has nothing to do with velocity. Velocity is simply a rate of motion (speed) in a certain direction.

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