Question

What thrust does a $200g$model rocket need in order to have a vertical acceleration of $10m/s^2$

a. On earth?

b. On the moon, where g = $1.62m/s^2$?

Short answer

a. Acceleration due to gravity on Earth is $3.96N$

b. Acceleration due to gravity on Moon is$2.32N$

Step-by-step solution

Content Introduction

We have the forces acting on the rocket and we are given,

Mass of the model rocket $$\begin{gathered} m=200g \\ m=0.2kg \end{gathered}$$

vertical acceleration $a_y=10m/s^2$

Apply Newton's second law to calculate the thrust of the rocket.

localid="1648126460693" $$\begin{gathered} \sum _{f_y}=m{a}_y \\ F-mg=m{a}_y \\ F=m(a_y+g)........................\left(1\right) \end{gathered}$$

Explanation (Part a)

Acceleration due to gravity on Earth , $g=9.81m/s^2$,$m$is the mass, $a_y$is the vertical acceleration

By substituting numerical numbers in equation, the thrust on the rocket is computed.

localid="1648126441936" $$\begin{gathered} F=m(a_y+g) \\ F=(0.2kg)(10m/s^2+9.81m/s^2) \\ F=3.96N \end{gathered}$$

Explanation (Part b)

Acceleration due to gravity on Moon ,$g=1.62m/s^2$

By substituting numerical numbers in equation, the thrust on the rocket is computed.$\left(1\right)$

localid="1648126421788" $$\begin{gathered} F=m(a_y+g) \\ F=(0.2kg)(10m/s^2+1.62m/s^2) \\ F=2.32N \end{gathered}$$