A rocket expels gas vertically downward at a constant velocity of 30 m/s. if the mass of the gas per unit time is 50 kg. Calculate the force exerted on the rocket to move it vertically upward?
To calculate the force exerted on the rocket to move it vertically upward, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum. In this case, the force exerted on the rocket is equal to the mass of the gas expelled per unit time multiplied by the change in velocity.
Given:
Velocity of the gas (v) = 30 m/s
Mass of the gas per unit time (m) = 50 kg/s
Since the gas is expelled downward, to determine the force exerted vertically upward, we need to consider the change in direction of both the gas and the rocket. The change in velocity is equal to twice the velocity of the gas, as both the gas and the rocket change direction.
Change in velocity (Δv) = 2 * 30 m/s = 60 m/s
Now, we can calculate the force exerted on the rocket using Newton's second law:
Force (F) = Mass (m) * Change in velocity (Δv)
F = 50 kg/s * 60 m/s
F = 3000 N
Therefore, the force exerted on the rocket to move it vertically upward is 3000 Newtons.