physics question

Question

Suppose a cart is being moved by a certain net force.

If the net force is increased by a factor of 7, by what factor does its acceleration change?

Answer 1

The key idea here is to consider Newton's second law of motion. Since the net force is directly proportional to the acceleration, an increase in the net force by any factor will also increase the acceleration by that same factor. For more detail, see below.

Let's call the initial force F_net, the mass of the cart m, and the initial acceleration a. Then Newton's second law tells us F_net = ma.

Then an increase to F_net by a factor of 7 means the new force will be F'_net = 7F_net. Let's call the new acceleration a'. Then the new version of the second law will be F'_net = ma'. We replace F'_net with 7F_net to find 7F_net = ma'. And now we recall from our first equation that F_net = ma. So, where we wrote 7F_net, we can write 7ma. Finally we have 7ma = ma'. We can cancel the m, since it appears on both sides leaving a' = 7a. The acceleration also increases by a factor of 7.