Question

A fully loaded Saturn V rocket has a mass of 2.92 x 106 kg. Its engines have a thrust of 3.34 x 107 N.

Answer 1

Complete Question:

A fully loaded Saturn V rocket has a mass of 2.92 x 106 kg. Its engines have a thrust of 3.34 x 107 N. (8 marks)

a) What is the downward force of gravity on the rocket at blast-off?

b) What is the unbalanced force on the rocket at blast-off?

c) What is the acceleration of the rocket as it leaves the launching pad?

d) As the rocket travels upwards, the engine thrust remains constant, but the mass of the rocket decreases. Why?

e) Does the acceleration of the rocket increase, decrease, or remain the same as the engines continue to fire?

Answer:

a) $-2.8616 \times 10^{7} N$ is the downward force of gravity on the rocket at blast-off.

b) $4.784 \times 10^{6} N$ is the unbalanced force on the rocket at blast-off

c) $1.638 \mathrm{m} / \mathrm{s}^{2}$ is the acceleration of the rocket as it leaves the launching pad

d) Because the propellant here is burned up, hence the mass of the rocket seems to be varied (total mass of all its parts). Thereby, the mass decreases when the rocket moves upward.

e) The acceleration of the rocket increases when engines continue to fire

Explanation:

Given:

Mass (m) =  $2.92 \times 10^{6} \mathrm{kg}$

a) In physics, weight can be defined as the applied force on a body by gravity. It is the product of mass (m) and gravity $\left(g=9.8 \mathrm{m} / \mathrm{s}^{2}\right)$

  $\text { weight }(W)=m \times g=2.92 \times 10^{6} \times(-9.8)=28.616 \times 10^{6}=-2.8616 \times 10^{7} N$

The negative sign indicates the downward force of gravity.

b) To find the unbalanced force on the rocket at blast-off,

Accelerating force,

   $F_{a}=F+W=3.34 \times 10^{7}+\left(-2.8616 \times 10^{7}\right)=(3.34-2.8616) \times 10^{7}$

   $F_{a}=0.4784 \times 10^{7}=4.784 \times 10^{6} N$

c) Newton’s second law of motion states that the object’s acceleration depends on two variable:

• Directly proportionate to the object’s force existed
• Inversely proportionate to the mass of the objects

The equation can be given as below,

    $Force =m \times acceleration$

    $\text { Acceleration }=\frac{F_{a}}{m}=\frac{4.784 \times 10^{6}}{2.92 \times 10^{6}}=1.638 \mathrm{m} / \mathrm{s}^{2}$

d) The pushing of rocket upward will happen as long as the engine gets fired. The propellant here is burned up, hence the mass of the rocket seems to be varied (total mass of all its parts). Thereby, the mass decreases (taotal mass) when the rocket moves upward.

e) The acceleration of the rocket increases when engines continue to fire

Let consider $F_{a}$ is constant, mass gets decreasing, then the acceleration would be increasing (as mass and acceleration are inversely proportionate to each other) .