Question

A constant force is applied to an object, causing the object to accelerate at 8 m/s2. What would the acceleration be if each of the following things happened (from the initial state)? (a) the force is doubled (b) the object's mass is doubled (c) the force and the object's mass are both doubled (d) the force is doubled and the object's mass is halved

Answer 1

(a) The acceleration doubles

According to Newton's second law, the acceleration of the object can be written as

`a=(F)/(m)`

where

F is the force exerted on the object

m is the mass of the object

Let's now analyze what happens when the force is doubled:

F' = 2F

In this case, the new acceleration is

`a'=(F')/(m)=(2F)/(m)=2(F)/(m)=2a`

So, the acceleration also doubles.

(b) The acceleration will halve

The initial acceleration is:

`a=(F)/(m)`

This time, the object's mass is doubled, so

m' = 2m

Therefore, the new acceleration will be:

`a'=(F)/(m')=(F)/(2m)=(1)/(2)(F)/(m)=(a)/(2)`

So, the acceleration will halve, since it is inversely proportional to the mass.

(c) The acceleration does not change

The initial acceleration is:

`a=(F)/(m)`

In this case, both the force and the mass are doubled, so:

F' = 2F

m' = 2m

So, the new acceleration is

`a'=(F')/(m')=(2F)/(2m)=(F)/(m)=a`

so, the acceleration has not changed.

(d) The acceleration will quadruple

The initial acceleration is:

`a=(F)/(m)`

In this case, the force is doubled and the mass is halved, so:

F' = 2F

m' = m/2

Therefore, the new acceleration is

`a'=(F')/(m')=(2F)/(m/2)=4(F)/(m)=4a`

so, the acceleration is quadrupled.