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1. Know that a force is measured in newtons (N).

The unit for force is newtons.

1. Describe how forces may change the size, shape, and motion of a body.

When an external force acts on a body, it may change the direction it moves in, its speed, or cause it to start moving from rest (like when you kick a ball). Sometimes, the force might cause a rearrangement of the molecules making up the body, causing it to change in size or shape (e.g., crushing a can, stretching a spring).

1. Plot extension-load graphs and describe the associated experimental procedure.

When an object increases in length, it undergoes extension.

When it decreases in length, it undergoes compression.

One experiment we can use to measure the relationship between force and extension is the following:

Hooke’s Law Experiment

Aim: To measure to the relationship between the force applied on and the resulting extension of a spring.

Hypothesis: The greater the force, the greater the extension. In other words, force is directly proportional to extension.

Apparatus:

• 2 clamps
• 1 ring stand
• 1 meter stick
• 1 spring with a hooked end
• Weights of known masses, e.g., use masses of 200g each.
• 1 electric balance

Procedure:

1. Set up all apparatus except the known mass as shown in the diagram.
2. Measure and record the initial length of the spring against the meter stick. At this length, the extension is 0 cm.
3. Weigh the first 200g mass on an electric balance and record its mass.
4. Add the mass to the end of the spring and record its new length. Calculate and record its extension by subtracting the initial length from the new length.
5. Weigh and record the mass of another 200g mass on an electric balance.
6. Add this to the spring and record its new length. Calculate and record its extension by subtracting the initial length from this length.
7. Repeat steps 5 and 6 until all the masses are hanging from the end of the spring.
8. To calculate the load on the spring at each stage, use the formula W=mg, where W is weight (or in this instance, the load on the spring), measured in N; m is the total mass the spring is carrying at that stage, measured in kg; and g is the acceleration of free-fall, which is approximately 9.81m/s2.
9. Plot a graph of extension (cm) against load (N). Draw a line of best fit.

The graph usually ends up looking like one of these:

Looking at the above graphs, you can see that the best fit line is an upwards slanting straight line (at least, for the first part of the second graph). This shows that, until a certain point, force and extension share a strong positive correlation – the extension of an object is directly proportional to the force acting on it.

Notice that in the second graph, after a certain point, instead of the line remaining straight, it curves up. This is because so much weight is added to the spring that it becomes damaged. The spring has been stretched beyond its elastic limit.

Elastic limit is the maximum extent to which a solid may be stretched without permanent alteration of size or shape.

Objects with high elastic limits (e.g. springs and rubber bands) are called elastic.

Objects with very low elastic limits (e.g., rocks or glass) are said to behave like a ‘plastic.’

Once elastics are stretched beyond their elastic limit, they tend to behave like plastics too.

Sometimes, when an elastic is stretched beyond its elastic limit, and the load is taken off it, it will automatically compress again, but not to its original length – it will be slightly longer:

In the graph, the dotted line shows the extension of the spring as you reduce the load on it after it’s been stretched beyond its elastic limit.

1. State and use Hooke’s Law and recall and use the expression:

force = constant x extension (F=kx)

Hooke’s Law states that within the elastic limit, the extension (x) of an object is directly proportional to the force (f) that causes the extension.

When written mathematically, it is F ∝ x.

That means, for any value of x, if you multiply it by a certain number, you’ll get F. That certain number is called a constant because the number does not change no matter the value of x or F. For this specific equation, the symbol we use to denote the constant is usually k.

This means that mathematically written, Hooke’s Law is F=kx.

Different materials have different constants of elasticity, because they may have different extensions for the same force. Generally, the greater the constant of elasticity of a material, the harder it is to stretch.

1. Recognise the significance of the term ‘limit of proportionality’ for an extension-load graph.

‘Limit of proportionality’ is another phrase for ‘elastic limit’. They mean the same thing.

The point at which the graph goes from being a straight line to a curved line is the limit of proportionality.

1. Recall and use the relation between force, mass and acceleration (including the direction): F=ma

This point describes Newton’s second law of motion: “For a constant mass, force equals mass times acceleration.”

Note that this is only true for the overall force acting on a mass. For example, if there were two forces, of equal sizes, acting on the same mass but in opposite directions, the two forces cancel each other out, resulting in an overall force of 0N. Therefore, the object will have an acceleration of 0m/s2. You can test this using any object you like – pick up a ball and push on its opposite sides using both your hands. Exert the same amount of force with both hands. You will notice that the ball doesn’t move in either direction.

1. Find the resultant of two or more forces acting along the same line.

If two or more forces are acting along the same line, they are either acting in the same direction or in opposite directions.

Look at the diagram to the left if you’d like some examples.

The number in red denotes its magnitude (size). Notice that, in this case, a force that points towards the right-hand side or upwards is taken as positive, and a force facing left or down is taken as negative. For your convenience, you can choose any direction you like as the positive direction, and the opposite direction will thus be negative. You must be consistent though – do not confuse your positive and negative direction or your calculations will be messed up.

Once you know the magnitude and direction (positive or negative) of the forces, you simply add them together, as shown above.

1. Explain how a system is in equilibrium when there is no resultant force.

When a system (e.g., an object or group of objects) is in equilibrium, the resultant force is 0N. This either means that there are no forces acting on the system, or all the forces acting on it cancel each other out. Thus, the acceleration of the system will be 0 – the system will be at rest (it’s not moving), or it will be in a constant state of motion (it will be travelling at a constant speed without changing direction – in other words, it will be travelling at a constant velocity.)

If you look at the above diagram, you’ll notice that in the second diagram, forces equal to 5N and -5N add up to equal a resultant force of 0N. So if those are the only two forces acting on a system, then that system will be in equilibrium.

Notes submitted by Sarah