A small rocket burns 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1600 m/s. (a) What is the thrust of the rocket?

Verified step by step guidance

1. Identify the mass flow rate of the fuel, which is given as 0.0500 kg/s.
2. Recognize that the velocity of the ejected gas relative to the rocket is 1600 m/s.
3. Use the formula for thrust, which is given by the equation: Thrust = mass flow rate imes velocity of the ejected gas. This equation is derived from the conservation of momentum principle.
4. Substitute the values into the formula: Thrust = 0.0500 kg/s imes 1600 m/s.
5. Calculate the product to find the thrust of the rocket in newtons (N).

Key Concepts

Thrust

Thrust is the force exerted by a rocket or engine to propel it forward. It is generated by expelling mass (in this case, fuel) at high velocity. According to Newton's third law, for every action, there is an equal and opposite reaction; thus, the thrust produced is equal to the rate of change of momentum of the expelled gas.

Momentum

Momentum is the product of an object's mass and its velocity, representing the quantity of motion it possesses. In the context of rockets, the momentum change of the expelled fuel contributes to the thrust. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

Conservation of Momentum

The conservation of momentum principle states that in a closed system, the total momentum remains constant if no external forces act on it. For rockets, as fuel is burned and expelled, the momentum of the rocket and the expelled gas must balance, allowing the rocket to gain forward momentum while the gas moves in the opposite direction.