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.
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?
wrong
a. The downward force of gravity on the rocket at blast-off can be calculated using the formula:
Force of gravity = mass of the rocket x acceleration due to gravity
Given:
Mass of the rocket (m) = 2.92 x 10^6 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Substituting the values into the formula:
Force of gravity = (2.92 x 10^6 kg) x (9.8 m/s^2) = 2.86 x 10^7 N
Therefore, the downward force of gravity on the rocket at blast-off is 2.86 x 10^7 N.
b. The unbalanced force on the rocket at blast-off is equal to the thrust of the engines minus the force of gravity.
Given:
Thrust of the engines = 3.34 x 10^7 N
Force of gravity = 2.86 x 10^7 N (from part a)
Unbalanced force = Thrust of the engines - Force of gravity
= (3.34 x 10^7 N) - (2.86 x 10^7 N)
= 4.8 x 10^6 N
Therefore, the unbalanced force on the rocket at blast-off is 4.8 x 10^6 N.
c. The acceleration of the rocket as it leaves the launching pad can be calculated using Newton's second law of motion:
Force (F) = mass (m) x acceleration (a)
Rearranging the formula, we get:
Acceleration (a) = Force (F) / mass (m)
Given:
Unbalanced force (F) = 4.8 x 10^6 N (from part b)
Mass of the rocket (m) = 2.92 x 10^6 kg
Substituting the values into the formula:
Acceleration (a) = (4.8 x 10^6 N) / (2.92 x 10^6 kg)
= 1.64 m/s^2
Therefore, the acceleration of the rocket as it leaves the launching pad is 1.64 m/s^2.
d. As the rocket travels upwards, the engine thrust remains constant, but the mass of the rocket decreases. The mass of the rocket decreases because the fuel is being burned and ejected as exhaust gases. This reduction in mass results in a decrease in the total inertia of the rocket, allowing it to accelerate more easily.
e. The acceleration of the rocket will decrease as the engines continue to fire. This is because as the rocket burns fuel and loses mass, its mass decreases while the thrust produced by the engines remains constant. According to Newton's second law of motion, if the force (thrust) remains constant and the mass decreases, the acceleration will decrease.
a. To find the downward force of gravity on the rocket at blast-off, we can use the formula:
Force of gravity = mass of the rocket x acceleration due to gravity
The mass of the rocket is given as 2.92 x 10^6 kg. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Substituting these values into the formula:
Force of gravity = (2.92 x 10^6 kg) x (9.8 m/s^2)
Force of gravity = 2.86 x 10^7 N
Therefore, the downward force of gravity on the rocket at blast-off is 2.86 x 10^7 N.
b. The unbalanced force on the rocket at blast-off can be calculated by subtracting the force of gravity acting on the rocket from the thrust of the rocket's engines:
Unbalanced force = Thrust - Force of gravity
The thrust of the rocket's engines is given as 3.34 x 10^7 N. We already calculated the force of gravity as 2.86 x 10^7 N.
Substituting the values into the formula:
Unbalanced force = (3.34 x 10^7 N) - (2.86 x 10^7 N)
Unbalanced force = 4.8 x 10^6 N
Therefore, the unbalanced force on the rocket at blast-off is 4.8 x 10^6 N.
c. The acceleration of the rocket as it leaves the launching pad can be found using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Force = mass x acceleration
Rearranging the formula to solve for acceleration:
Acceleration = Force / mass
We already know the unbalanced force on the rocket at blast-off (4.8 x 10^6 N) and the mass of the rocket (2.92 x 10^6 kg).
Substituting these values into the formula:
Acceleration = (4.8 x 10^6 N) / (2.92 x 10^6 kg)
Acceleration ≈ 1.65 m/s^2
Therefore, the acceleration of the rocket as it leaves the launching pad is approximately 1.65 m/s^2.
d. The mass of the rocket decreases as it travels upwards due to the consumption of fuel. The engines of the rocket burn fuel to produce thrust, and as the fuel is burned, the mass of the rocket reduces. This reduction in mass is due to the ejection of burnt fuel products.
e. The acceleration of the rocket remains the same as the engines continue to fire. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since the thrust of the engines remains constant and the mass of the rocket decreases, the net force on the rocket remains the same. Therefore, the acceleration of the rocket will also remain the same.