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Chapter 2: Problem 14

As a rocket ascends, its acceleration increases even though the net force on it stays constant. Why?

Short Answer

Expert verified
Answer: A rocket's acceleration increases while ascending due to its decreasing mass as it burns fuel and expels exhaust gases. With the net force remaining constant, the decreasing mass results in an increasing acceleration according to Newton's second law of motion (\(F = ma\)).

Step by step solution

01

Understanding the forces acting on a rocket

During flight, a rocket experiences two primary forces: thrust and gravity. The thrust force is generated by the rocket's engine, providing an upward force and accelerating the rocket. The gravitational force acts downward, pulling the rocket towards the Earth. The net force on a rocket is the difference between these two forces.
02

Explaining how rocket mass changes

A key feature of rockets is that their mass changes during flight. As the rocket engines burn fuel, the rocket loses mass in the form of expelled exhaust gases. Consequently, the rocket becomes lighter as it ascends and uses up more fuel.
03

Applying Newton's second law of motion

According to Newton's second law of motion, the net force acting on an object equals its mass multiplied by its acceleration (\(F = ma\)). If the net force remains constant, but the mass decreases, the acceleration of the object must increase to maintain this relationship.
04

Connecting decreasing mass to increasing acceleration

As the rocket's mass decreases due to burning fuel and expelling exhaust gases, its acceleration increases because the constant net force (\(F\)) is spread over a smaller mass (\(m\)). This is mathematically represented by the equation: \(a = F/m\). The decreasing mass results in the increasing acceleration while the rocket ascends.

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