During a launch of the shuttle, fuel is being burned at a rate of 2000 kg every second. the exhaust from the burning of this fuel is expelled by the engines and can be seen during the launch. readings from instruments mounted on the space shuttle show that for the first 2 min after launch the thrust (force) provided to the shuttle is constant. yet during this time of constant applied force, the acceleration of the shuttle constantly increases? how is this possible?

thanks!

the mass of the shuttle is decreasing because fuel is being expelled

F = m a
same F
less m
more a

Same happens with your car, but so slowly it does not matter :)

During the first 2 minutes after launch, the thrust provided to the shuttle remains constant. However, the acceleration of the shuttle constantly increases due to the concept of Newton's second law of motion.

According to Newton's second law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as:

F = m * a

Where:
F = Net force
m = Mass of the object
a = Acceleration of the object

In the case of the space shuttle, the burning of fuel generates thrust, which acts as the net force on the shuttle. As more fuel is burned, the mass of the shuttle decreases due to the expulsion of exhaust gases. However, since the thrust remains constant, the net force acting on the shuttle remains the same.

With a constant net force and a decreasing mass, the acceleration of the shuttle increases. This is because the net force is divided by a smaller mass, resulting in a larger acceleration according to Newton's second law.

In other words, even though the thrust (force) applied to the shuttle remains constant, the decrease in mass causes the acceleration to increase during the first 2 minutes after launch.

This phenomenon is known as the rocket's increasing acceleration during constant thrust. To understand why this happens, we need to consider Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation for this is F = ma, where F represents force, m represents mass, and a represents acceleration.

In the case of a rocket launch, the force being applied is the thrust created by burning fuel. The mass of the rocket decreases as the fuel is burned, so the net force acting on the rocket remains constant as long as the rate at which fuel is being burned is constant. However, because the mass of the rocket is decreasing, according to the second law of motion, the acceleration of the rocket must increase to maintain a constant force.

Let's break it down with some numbers. If we assume the mass of the rocket at the start of the launch (including fuel) is M, and the rate at which fuel is being burned is 2000 kg/s, after a certain time t, the mass of the rocket will be M - 2000t.

So, the net force acting on the rocket is constant and equals the thrust, F = 2000t (since mass is decreasing linearly with time). Since force equals mass times acceleration, we can rewrite the equation as F = (M - 2000t) * a.

Now, if we substitute the value of F from earlier (F = 2000t), we get 2000t = (M - 2000t) * a. Solving for acceleration (a), we find a = 4000t / (M - 2000t).

As you can see, as time (t) increases, the acceleration of the rocket increases because the rocket's mass is decreasing as fuel is burned. This phenomenon allows the rocket to continue accelerating even though the applied force (thrust) remains constant during the first few minutes of the launch.

It's important to note that this increasing acceleration will eventually start to decrease as the amount of fuel decreases and the rate of mass loss slows down. At that point, the rocket will experience diminishing acceleration until there is no more fuel left.