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START YOUR JOURNEY - LAWS OF MOTION

Newton’s Laws of Motion Challenge You chose : 2. The Law of Proportionality: “The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.” This can be expressed in equation form: Force = (Mass) x (Acceleration)

This choice is not the right one for the example.

However, it still applies to rocket flight! When a net (or excess) force is applied to an object, it will accelerate in the direction of that force. In physics we say that the acceleration is directly proportional to the force.

Of course, the more massive the object, the slower it will accelerate. For this case we say that the acceleration is inversely proportional to the mass (as mass increases, the acceleration decreases, and vice-versa).

We write the equation as:

Force (thrust) = Mass x Acceleration

Or we can write it as:

Acceleration = Force ÷ Mass

Example: The force is 25.0 lbs of thrust. The rocket has a mass of 1.400 kilograms. Calculate its acceleration during HORIZONTAL movement on some frictionless surface. (Let's not fight gravity yet.)

Solution: First, let's change pounds of thrust into the metric equivalent of pounds…a unit called Newtons. Multiply 4.45 Newtons per pound times the number of pounds of force. So…25.0 lbs x 4.45 Newtons/lb = 111.3 Newtons of metric force.

 Acceleration = (111.3 Newtons) ÷ (1.4 kilograms) Acceleration = 79.5 Newtons per kilogram = 79.5 meters per second each second

That means that the rocket’s speed increases by 79.5 meters per second every second.

If you fire the rocket vertically, its acceleration will be a bit less since it will struggle against gravity. That calculation is:

Acceleration = Force ÷ Mass

If a rocket moves vertically, there are TWO forces: (1) the upward thrust of 25 pounds, or 111.3 Newtons, and (2) the downward pull of gravity, which is the rocket’s weight.

First, what does the rocket weigh?
The rocket has a mass of 1.40 kilograms. Any object’s weight is found by multiplying its mass times the force of gravity. On the surface of the Earth, the force of gravity is 9.80 Newtons for every kilogram of mass (written as 9.8 N/kg).

So,

 Weight = mass x gravitational force Weight = (1.40 kilograms) x (9.80 Newtons per kilogram) Weight = 13.7 Newtons

Let’s use the weight in the acceleration equation:

 Acceleration = Force ÷ Mass Acceleration = (111.3 Newtons – 13.7 Newtons) ÷ (1.4 kilograms)

Notice we SUBTRACT the weight. It’s holding our rocket back!

Acceleration = 69.7 meters per second per second.

>> Try Again - Back to the thrust page

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