Question

A cart is pushed and undergoes a certain acceleration. Consider how the acceleration would compare if it were pushed with twice the net force while its mass increased by four. Then its acceleration would be?

Answer 1

Answer:

If the cart is pushed with twice the net force while its mass increases by four, its acceleration would be half the other acceleration.

Explanation:

Newton's second law relates the force (F) applied to an object with its acceleration (a) in the next way:

$a=\frac{F}{m}$ (1), with m the mass of the object (the cart in our case)

Note that the acceleration is directly proportional to the force applied and inversely proportional to the mass of the object, that means if we let m constant and increase the force the acceleration will increase too, and if we let F constant and increase m the acceleration will decrease, but if we increase the two quantities at the same time, we should analyze mathematically the situation to observe better the behavior of the acceleration. If $F_{1}=2F$ and $m_{1} = 4m$ the acceleration by Newton’s second law is now:

$a_{1}=\frac{F_{1}}{m_{1}}=\frac{2F}{4m}=\frac{1}{2}(\frac{F}{m})=\frac{a}{2}$

Note that $a_{1} = \frac{a}{2}$ so the acceleration would be half the initial acceleration