Question

3. A toy rocket launcher contains a spring with a spring constant of 35 N/m. If the

toy has a mass of 100 g (look at units!) and the spring is compressed by 30 cm
(look at units!) what will be the initial acceleration of the rocket if fired
horizontally.

Answer 1

`a=105\ m/s^2`

Step-by-step explanation:

Spring Force

When a spring is compressed by a distance x, it exerts a force given by the law of Hooke:

`F=k.x`

Where k is the constant of the spring. If we know this force and the mass m of the object launched by the spring, we can compute its acceleration by using Newton's formula

`F=m.a`

`\displaystyle a=(F)/(m)`

Replacing the formula for the spring

`\displaystyle a=(kx)/(m)`

The values are

`k=35 N/m\\m=100 gr=0.1 kg\\x=30 cm=0.3 m`

Thus

`\displaystyle a=((35)(0.3))/(0.1)`

`\boxed{a=105\ m/s^2}`

The toy rocket will have an acceleration of
`105\ m/s^2`

Note: If the launch would have been vertical, then the acceleration of gravity should have been used in the calculations