Problem 17 - University Physics with Modern Physics

Question

A rocket works by expelling gas (fuel) from its nozzles at a high velocity. However, if we take the system to be the rocket and fuel, explain qualitatively why a stationary rocket is able to move.

Step-by-Step Solution

Answer

Question: Explain qualitatively why a stationary rocket is able to move. Answer: A stationary rocket is able to move due to Newton's third law of motion and the conservation of momentum. As the rocket expels fuel, it creates action and reaction forces between the rocket and the expelled gas, causing the rocket to gain momentum and accelerate in the opposite direction. The conservation of momentum ensures that the rocket continues to gain momentum and move forward as long as it expels fuel.

Step 1: Understand Newton's Third Law of Motion

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. When a rocket expels gas (fuel) from its nozzles, it pushes the gas in one direction while the gas pushes the rocket in the opposite direction. This action and reaction forces between the expelled gas and the rocket will cause the stationary rocket to move.

Step 2: Define Force, Mass, and Acceleration

Force is the product of mass and acceleration, which means that it measures the strength of the push or pull acting on an object, causing it to change its velocity. Mass refers to the amount of matter in an object, and acceleration is the rate at which the object's velocity changes over time. In the context of rocket propulsion, the force exerted on the rocket depends on the mass of expelled fuel and the acceleration of the fuel coming out of the nozzles.

Step 3: Examine the Conservation of Momentum

The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. When the rocket expels fuel, the momentum of the expelled fuel is equal and opposite to the momentum gained by the rocket. As the rocket expels more fuel, it continues to gain momentum, which causes the rocket to accelerate and move forward.

Step 4: Relate Newton's Law and the Conservation of Momentum to the Rocket

The conservation of momentum and Newton's third law of motion work together to explain the motion of a stationary rocket. When the rocket expels fuel, it creates a force on the rocket and the fuel, making them gain equal and opposite momentum. The momentum gained by the rocket propels the stationary rocket upward and causes it to accelerate. In conclusion, the stationary rocket moves due to the action and reaction forces between the expelled gas and the rocket, following Newton's third law of motion, and the conservation of momentum ensures that the rocket continues to gain momentum and accelerate as long as it expels fuel.