Question

A Force of 15 N accelerates an object by 2m/s2. what force is needed to give the same object an acceleration of 6m/s2?

Answer 1

The force is `=45N`

Explanation:

According to Newton's Second Law of motion

`vecF=mveca`

The force is `F=15N`

The acceleration is `a=2ms^-2`

Therefore,

The mass is `m=F/a=15/2=7.5kg`

The new force is `F_1=?`

The new acceleration is `a_1=6ms^-2`

Therefore,

`F_1=ma_1=7.5*6=45N`

Answer 2

`45" N"`

Explanation:

By Newton's Second Law, the acceleration of an object is directly proportional to the size of the net force acting on it. As a result, the ratio `\frac{F}{a}` should be a constant.

That is: `a \prop \sum F`

Assuming that the `15 N` is the only force acting on the object, so the net force `\sum F=15" N"`.

`\frac{F_1}{a_1}=\frac{F_2}{a_2}`

Multiply both sides by `a_2`:
`F_2=F_1 \cdot \frac{a_2}{a_1}=15"N"\cdot \frac{6m\cdot s^(-2)}{2m\cdot s^(-2)}=45"N"`

So the force you need would be `45` Newtons, precisely three times the initial force acted upon the object.