How does the acceleration of a cart depend on the net force acing on the cart if the total mass is constant?
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Given Newton's second law of motion, acceleration and mass are proportional to force.
The net force is mass multiplied by acceleration.
If mass is constant, acceleration and net force will increase or decrease proportionally to each other; multiply or divide each by a similar factor.
Initially, Newton defined his second law of motion in terms of the rate of change in an object's momentum:
(Pf -Pi)/t = Fnet
Subsequently he developed the concept further to
(mVf - mVi)/t = Fnet or m(Vf - Vi)/t = Fnet
So, (Vf - Vi)/t = Fnet/m
by defining the rate of change in the velocity as acceleration we get the current form of the second law:
a = Fnet/m
From this we can see that if m is constant then a is directly proportional to Fnet. Increasing Fnet causes an increase in the acceleration.
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