P2aL4 Force and Acceleration

Key Words

Acceleration - change in speed divided by time.

Air resistance - drag experienced by moving through air

Directly proportional - a graph goes up in a straight line from the origin.

Force meter - instrument to measure force.

Friction - force opposing movement caused by surface rubbing against each other.

Inversely proportional - the graph is a 1/x graph, called a hyperbola.

Mass - amount of material in an object

Newton - unit of force.

Resultant force - force that occurs on an object when two or more forces are applied.

Ticker Timer - a machine that prints 50 dots a second onto a paper strip.  You can work out the speed from this.

Test Yourself

Homework
Physics GCSE
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Grade E

For a car, the forward force is the force from the engine.  The backwards forces are:

  • air resistance;

  • friction from the road, and the drive-train (gearbox, wheels, etc.).

When forces are balanced, the resultant force is zero.  A vehicle that has balanced forces acting on it will stay stationary, or at a constant speed.

If there is a resultant force, the vehicle will accelerate in the direction of the resultant force.  The acceleration will be dependent on the direction of the force:

  • If the force is in the same direction as the movement, the car will go faster.

  • If the force is in the opposite direction, the car will slow down.

  • If the force is at 90o to the direction of the movement, the car will go round a corner.

The bigger the force, the bigger the acceleration.

If we use the same force for different masses, the bigger the mass, the less the acceleration.

                                     

The van and the car have exactly the same engine and gives out exactly the same force.  The car accelerates a lot faster.

A common measure of acceleration is the "0 - 60 mph" figure (60 mph = 27 m/s).  That has now been changed to the "0 - 62 mph" figure, i.e. the 0 - 100 km/h figure.  For these two vehicles it is:

  • For the Mondeo, 10 s;

  • For the Transit Van, 15 s.

Grade C

We can investigate force and acceleration by pulling a physics trolley with a force meter, and measuring the acceleration with ticker tape.  It is not an easy experiment from which to get reliable data, and the working out of the data is tedious.  You can, of course, use a motion sensor with a computer.

What we do find is that:

 For a constant mass, the acceleration is directly proportional to the force.

This is shown in the graph:

The graph starts at the origin (zero force, zero acceleration).  If the force doubles, the acceleration doubles too.

This important finding is called Newton's Second Law of Motion.

a µ F

If we change the mass, and plot the data on a graph, we see that the graph is a hyperbola:

The graph shows that the acceleration is inversely proportional to the mass.  Double the mass, and the acceleration is halved.

So we can state that:

a µ 1/m

We can sum this up with the important equation:

Force (N) = mass (kg) × acceleration (m/s2)

In physics code:

F = ma

In triangle form:

The unit for force is Newton (N), which is defined as:

the force needed to accelerate a 1 kg mass at a rate of 1 m/s2

 

Grade A

On other planets the weight of an object changes.  A 1 kg mass on Earth weighs 10 N (remember that weight is a force, measured in Newtons).  On the Moon, it would weigh 1.6 N, while on Jupiter, it would weigh 32 N.  On Saturn, it would weigh 11 N.

We convert mass to weight  by the simple equation:

Weight (N) = mass (kg) × acceleration due to gravity (m/s2)

In Physics code:

W = mg

This is another way of stating Newton's Second Law.

We can also say that gravitational field strength is the same as the acceleration due to gravity.  The Gravitational field strength of the Earth is 10 N/kg.  N/kg is the same as m/s2.

Astronomers measure the acceleration due to gravity (or gravitational field strength) by moving a known mass with a known force.