Additional Physics Topic 4 - Forces and Free Fall

Free fall is what happens when you let go of an object, and let it fall.  It falls because of the force of gravity, which gives the object weight.  It is really important to understand what weight means.

Weight

It is important to know the difference between weight and mass.

• Mass is the amount of material in an object.  It is measured in kilograms.

• Weight is the force on a mass due to gravity.  It is measured in Newtons.

Weight is a force and is measured in Newtons.  (Repeat after me:  Weight is a Force, measured in Newtons.) It is depressing how many students still write weight in kilograms.

Think about a cosmonaut in a spaceship.  He may have a mass of 75 kg.  On the Earth that means he has a weight of 750 N.  His weight is 120 N on the Moon.  In deep space it is zero.  That doesn't mean he doesn't have material in his body.  There is simply zero gravity, so he would have zero weight.

The relationship between weight and mass is given by:

weight (N) = mass (kg) × gravitational field strength (N/kg)

In Physics Code:

W = mg

In triangle form: On the Earth g, the gravitational field strength is 9.81 N/kg.  At GCSE it is perfectly acceptable to quote g as 10 N/kg, which is the value we will use in these notes.  The gravitational field strength is also the acceleration due to gravity, 10 m/s2.

1 kg = 10 N

 Question 1 How much will our 75 kg cosmonaut weigh on Jupiter, where g = 32 N/kg? Gravity makes objects accelerate.  All objects accelerate towards the Earth at 10 m/s2, regardless of their mass.  A canon-ball and a watermelon dropped together at the same time will fall together. You can demonstrate this for yourself.  Drop two objects of different mass at the same time, and you should notice that they hit the ground at the same time.  Another common demonstration is to allow a feather and a ball bearing to drop in a tube that has a vacuum in it.  Both fall at the same rate.

Viscous Drag

Air is a fluid. A fluid is any liquid or gas; it can flow around objects. Drag arises because:

• particles of the fluid have to be pushed out of the way;

• particles rub along the object.

Both of these contribute to the phenomenon of viscous drag.

As the speed gets higher, the drag gets bigger because more particles need to be pushed out of the way every second, and the friction of them rubbing against the sides get bigger too. Also some fluids have higher densities.

Water makes much more drag than air, so boats tend to be much slower than say cars or even bicycles. A power boat manages to get to a high speed because it is designed to lift out of the water and to plane or skim along the surface of the water. Therefore there is only a little drag from the water, and air resistance.

An eight oared racing shell is about 18 metres long but only 50 cm wide. It is very streamlined and can cut through the water at quite high speed, about 6 m/s. Other faster moving objects are streamlined.

Viscous drag results in terminal velocity when objects undergo free fall

Terminal Speed

If you drop a ball bearing through thick treacly (viscous) oil, you will see that the ball bearing falls slowly at a constant speed.  It does not change speed.  This is because the weight downwards is balanced by the upwards drag force.  This constant speed is called terminal speed.  It is encountered whenever objects fall through fluids (liquids or gases).

Air is a fluid because it's a gas.  So a feather falling through air will have a terminal speed of 10 cm/s.  A sky diver falling through air has a terminal speed of about 60 m/s (about 230 km/h).    If he hits the ground at that speed, he will be killed.  To reduce the terminal speed he opens a parachute which increases the surface area (and the drag) which slows him down to about 5 m/s.

Think about sky divers jumping from a plane: Picture by Dinanna 1, Wikimedia Commons

• The sky divers accelerate at 10 m s-2 as they leave the aeroplane.

• As their speed increases, viscous drag increases.

• The drag is in the opposite direction to the weight, so the acceleration decreases.

• Then the drag (upwards force) balances the downward force (weight)

• Therefore there is no acceleration and the speed is constant.  This is terminal speed.

• For the sky divers in the picture above, the terminal speed is 60 m s-1.

This animation shows the idea: A speed time graph of a parachutist would look like this: Question 2 Explain what is happening in this speed time graph. The graph is a simplified version of what would happen in reality.

 Question 3 Answer the interactive fill-in-the-spaces exercise. Terminal velocity is a similar situation to the maximum speed of a car.  Newton I and Newton II apply.

 How do Newton's First and Second Laws apply to a free fall object? 