Student Question

# How does the acceleration of a cart depend on the total mass if the net force is constant?

The answer above is correct: if the force is constant, the mass is inversely proportional to the acceleration. So if the mass increases, the acceleration decreases, and vice versa.

This comes from the second Newton's Law, that states that the net force equals mass times acceleration:

`F = m_1*a_1` , where `m_1` is...

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the original mass and `a_1` is the original acceleration.

If the mass and acceleration change, but the force remains the same, then

`F = m_2*a_2` , where `m_2` is the new mass and `a_2` is the new acceleration.

Combining the two equations, we get

`m_1*a_1 = m_2*a_2`

If we divide this equation by `m_1*a_2` , it becomes

`a_1/a_2 = m_2/m_1` ,

which means that the acceleration is inversely proportional to mass.

This is why mass is also called "the measure of inertia". Inertia is the tendency of an object to resist the change in its motion, or the change in how fast it moves. The objects with larger mass have larger inertia, so they are harder to accelerate.

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By Newton's Second Law, the acceleration of an object is proportional to the net force and inversely proportional to the mass:

a = Fnet/m

If Fnet is a constant, then as m increases a will decrease and as m decreases a will increase proportionally.  That is, doubling the mass cuts the acceleration in half.  Halving the mass doubles the acceleration.

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How does the acceleration of a cart depend on the net force acing on the cart if the total mass is constant?

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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