Question

A toy rocket is launched straight up by using a spring. The rocket is initially pressed down on the spring so that the spring is compressed by 9 cm. If the spring constant is 1050 N/m and the mass of the rocket is 50 g, how high will the rocket go? You may neglect the effects of air resistance.

Answer 1

8.68 m

Step-by-step explanation:

compression in spring, x = 9 cm = 0.09 m

Spring constant, K = 1050 N/m

mass of rocket, m = 50 g = 0.05 kg

Let it go upto height h.

Use conservation of energy

Potential energy stored in spring = potential energy of the rocket

`(1)/(2)kx^(2)=mgh`

0.5 x 1050 x 0.09 x 0.09 = 0.05 x 9.8 x h

h = 8.68 m

Thus, the rocket will go upto height 8.68 m.

Answer 2

Rocket will go to a height of 8.678 m

Step-by-step explanation:

Mass of the rocket m = 50 gram = 0.05 kg

Spring constant k = 1050 N /m

Spring is stretched to 9 cm

So x = 0.09 m

Work done in stretching the spring

`E=(1)/(2)kx^2=(1)/(2)* 1050* 0.09^2=4.2525J`

From energy conservation this energy will convert into potential energy

Potential energy is equal to
`E=mgh`, here m is mass, g is acceleration due to gravity and h is height

So
`0.05* 9.8* h=4.2525`

`h=8.678m`

So rocket will go to a height of 8.678 m