What thrust does a 200 g model rocket need in order to

Chapter 6, Problem 16E

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QUESTION:

Problem 16E

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

a. On earth?

b. On the moon, where g =1.62 m/s2?

Questions & Answers

QUESTION:

Problem 16E

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

a. On earth?

b. On the moon, where g =1.62 m/s2?

ANSWER:

Step 1 of 2

(a)

We need to find out the thrust needed by the rocket in order to have a vertical acceleration of \(10 \mathrm{~m} / \mathrm{s}\) on earth.

Using the Newton's second law we can write,

                                          \(F_{\text {thrust }}-F_{G}=m a\)

Implies,

                                        \(F_{\text {thrust }}=m a+F_{G}\)

                                        \(F_{\text {thrust }}=m a+m g\)

                                       \(F_{\text {thrust }}=m(a+g)\)

Mass of the rocket,

                                       \(m=200 \mathrm{~g}=0.200 \mathrm{~kg}\)

Acceleration,

                                     \(a=10 \mathrm{~m} / \mathrm{s}\)

Acceleration due to gravity,

                                      \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\)

So,

                                      \(F_{\text {thrust }}=(0.200)(10+9.8)\)

                                      \(F_{\text {thrust }}=3.96 \mathrm{~N}\)

The thrust needed by the rocket on the earth is \(F_{\text {thrust }}=3.96 \mathrm{~N}\)

 

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