“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)
You chose wisely!
When a net, or excess, force
is applied to an object, it will accelerate in the direction of
the 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. In this case, we say that the acceleration is
inversely proportional to the mass (as mass increases, the acceleration
decreases, and vice-versa).
We write this 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 the
rocket's acceleration if it moved HORIZONTALLY (we don’t want
to fight gravity yet), on some frictionless surface.
Solution: First we need to change
pounds of thrust into the metric equivalent of pounds…a unit
called Newtons. We do this by multiplying 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.
= (111.3 Newtons) ÷ (1.4 kilograms)
= 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 we fire the rocket vertically, its acceleration will be a bit
less since it will struggle against gravity. That calculation is:
Acceleration = Force ÷
If the rocket moves vertically, there are TWO forces:
the upward thrust of 25 pounds, or 111.3 Newtons, and 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).
= mass x gravitational force
= (1.40 kilograms) x (9.80 Newtons per kilogram)
= 13.7 Newtons
Let’s use the weight in the acceleration equation: