Question

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

Answer 1

Answer:

$a=105\ m/s^2$

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

$F=m.a$

$\displaystyle a=\frac{F}{m}$

Replacing the formula for the spring

$\displaystyle a=\frac{kx}{m}$

The values are

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

Thus

$\displaystyle a=\frac{(35)(0.3)}{0.1}$

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

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