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I wrote:
Newton' second law:
F = dp/dt= mdv/dt + vdm/dt
In the third term, what is v?
Justin Parke
Oakland Mills High School
Columbia, MD
Dan replied
F = dp/dt = d(mv)/dt = m dv/dt + v dm/dt
This is the chain rule applied to momentum p = mv.
v is velocity throughout
regards,
Dan M
Consider a flatcar on a train track rolling at speed v without dissipative forces and loaded with sand. As the car rolls sand is shoveled off to the side at a rate of c, thrown perpendicular to the direction of motion. Will the speed of the car change as a result of the decrease in mass?
I suspect the answer is no because the force exerted on the sand, and hence the force exerted *by* the sand on the car has no component along the direction of motion.
F = mdv/dt + vdm/dt = m (0) + v (-c)? This suggests that an outside force is necessary to maintain a constant speed. What is wrong with my reasoning?
Justin Parke
Oakland Mills High School
Columbia, MD