0625 · 1.5Forces

Effects of forces and motion

0:00A seesaw can balance even when the children sitting on it have different weights. A moving bicycle can travel steadily even while several forces act on it. A spring can stretch without moving from its support. These situations connect through one idea. Forces can change an object’s shape, change its motion, or produce a turning effect. In this video, we will connect those effects rather than learn them as separate rules.

0:23You will learn how to investigate stretching, combine forces, explain circular motion, and calculate turning effects. We will also find the centre of gravity of an irregular object. Finally, we will explain why some objects topple more easily than others. A force is a push or pull, measured in newtons. Its direction matters as much as its size. Speed describes how fast something moves, while velocity includes its direction. Acceleration is the change in velocity per unit time, so changing direction counts as acceleration even when speed stays constant.

Investigating spring extension

0:56Start with a spring hanging from a clamp. Adding a load pulls its lower end down and stretches it. Forces may produce changes in the size and shape of an object. Stretching a spring, compressing a sponge, and bending a ruler are examples of this effect. To investigate stretching, secure the spring beside a vertical ruler. Record its original length before adding the load. Add known loads in small steps, allowing the spring to settle before each reading.

1:21A pointer beside the ruler helps you read the same position consistently. Read the scale at eye level to avoid parallax error. Extension means the increase in length, not the spring’s total length. Calculate each extension by subtracting the original length from the loaded length. Record the applied force and corresponding extension in a table, including the starting reading with no added load. If you use hanging masses, their weights provide the loads.

1:47Convert those masses into forces using the mass and weight relationship from the earlier video. Repeat readings where practical to check consistency. Keep the stand secure, and avoid adding loads that could make the apparatus fall or the spring break.

Load-extension graphs and spring constant

2:00Plot extension on the horizontal axis and load on the vertical axis. Label both axes with quantities and units, and draw a suitable best fit line. For a spring that obeys proportional behaviour, the first section is straight and passes through the origin. Doubling the force then doubles the extension. That straight section tells us that force and extension are directly proportional. A sketch should show this relationship clearly, even without numerical scales.

2:26When plotting measurements, use sensible scales that spread your points across the graph. Do not force the whole graph into a straight line if the measurements clearly curve. We now reach Supplement content for Extended students. The limit of proportionality is the point beyond which load and extension are no longer directly proportional. Identify it where the graph stops following the initial straight line. Beyond it, equal increases in load no longer produce equal increases in extension.

2:53The spring constant is defined as force per unit extension. Spring constant equals force divided by extension, and its unit is newtons per metre. It describes how much force is needed for each metre of extension. A greater spring constant means a stiffer spring, requiring more force for the same extension. Suppose a spring extends by three centimetres under a force of six newtons, within its proportional region. First, convert three centimetres into zero point zero three metres.

3:22Next, divide six newtons by zero point zero three metres. The spring constant is therefore two hundred newtons per metre. For that spring, calculate the force needed for five centimetres of extension. Convert five centimetres into zero point zero five metres. Rearrange the relationship so that force equals spring constant multiplied by extension. 200 × 0.05 gives ten newtons, provided the spring remains within its proportional region. On our graph, spring constant is the gradient of the straight section.

3:54This follows because gradient is the change in force divided by the change in extension. A steeper line therefore represents a stiffer spring. Always check the axes. If they are swapped, the gradient is no longer the spring constant.

Resultant force and circular motion

4:08Now we return to Core content and move from changing shape to changing motion. Several forces can act on an object at once. Their combined effect is represented by the resultant force. For forces along the same straight line, add forces acting in one direction and subtract those acting in the opposite direction. Our trolley has forces of ten newtons and five newtons acting to the right. Together, these provide fifteen newtons to the right.

4:33A force of nine newtons acts to the left. Subtracting nine from fifteen gives a resultant force of six newtons to the right. If opposite forces are equal, their resultant is zero. An object then either remains at rest or continues in a straight line at constant speed. This is why balanced forces do not necessarily mean an object is stationary. They mean its velocity is not changing. A resultant force may change velocity by changing speed or direction.

4:59It can make an object speed up, slow down, or turn. The important question is not simply whether forces exist. It is whether they combine to give a non-zero resultant force. A cyclist travelling steadily can have a driving force forwards and resistance backwards. If these forces balance, the cyclist continues at constant velocity. On an ordinary surface, a bicycle slows when the driving force stops because resistance remains. Motion itself does not require a resultant force, but changing motion does.

5:30Solid friction is the force between two surfaces that may impede motion and produce heating. It opposes sliding, or the tendency to slide, between the surfaces. Rubbing your hands demonstrates the heating effect. Friction also provides grip, so it is not always an unwanted force. Objects moving through liquids and gases also experience friction, called drag. Water resists a swimmer’s movement, and air resistance acts on a moving bicycle. Drag opposes an object’s motion relative to the surrounding fluid.

6:01These resistance forces help explain why a moving object often slows when no driving force balances them. Here is the next Supplement relationship. Resultant force equals mass multiplied by acceleration. The force must be the resultant, not just one selected force acting on the object. Acceleration is in the same direction as that resultant force. For the same mass, a larger resultant produces a larger acceleration. Consider a trolley of mass two kilograms, driven rightwards by ten newtons against four newtons of resistance.

6:32First, subtract four from ten to obtain a resultant of six newtons rightwards. Next, rearrange the equation so that acceleration equals resultant force divided by mass. Dividing six by two gives three metres per second squared, directed rightwards. For a given resultant force, a greater mass gives a smaller acceleration. This matches the experience of pushing an empty trolley and a loaded trolley. If the resultant acts opposite to the velocity, the object slows down.

7:00The acceleration still points with the resultant, even though the object is travelling the other way. Circular motion is also Supplement content. Imagine a ball moving in a horizontal circle on a string. At each instant, its motion is along a tangent to the circle. The string pulls towards the centre, perpendicular to that instantaneous motion. The inward resultant continually changes the direction of the ball’s velocity. The ball can therefore accelerate while keeping a constant speed.

7:27Without the inward force, it would no longer follow the circle. It would move along the tangent rather than directly away from the centre. For this syllabus, you need three qualitative relationships rather than a circular motion equation. With mass and radius constant, greater speed requires a greater inward force. Equivalently, a greater force allows a greater speed along that same circular path. This compares different circular motions. The perpendicular force does not itself speed the object up.

7:55With mass and speed constant, a greater inward force produces a smaller radius. A tighter turn requires the direction to change more rapidly. With speed and radius constant, a greater mass requires a greater inward force. A more massive object needs more force to achieve the same change in velocity.

Moments and equilibrium

8:13We now return to Core content. Forces can also turn objects. A moment is a measure of the turning effect of a force about a pivot. A door turns about its hinges, and a spanner turns about the nut. Pushing farther from the pivot usually makes turning easier because the same force has a greater turning effect. Moment equals force multiplied by the perpendicular distance from the pivot to the line of action of the force.

8:37The line of action is the straight line along which the force acts. Perpendicular distance means the shortest distance, measured at a right angle. The unit of moment is the newton metre. Suppose a force of twenty newtons acts perpendicular to a spanner, zero point one five metres from its pivot. First, identify the force’s line of action and the perpendicular distance. Multiply twenty newtons by zero point one five metres.

9:03The moment is three newton metres, clockwise in this diagram. Use perpendicular distance, not automatically the length of the object. If the force acts at an angle, those distances can differ. A force whose line of action passes through the pivot has zero moment about that pivot. Its perpendicular distance is zero, even if the force itself is large. The principle of moments states that, for equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the same point.

9:33Think of these as competing turning effects. A smaller force farther from the pivot can balance a larger force closer to it. Equal moments do not require equal forces. A six newton force acts zero point four metres left of a pivot. Its anticlockwise moment is 6 × 0.4, giving two point four newton metres. A force on the right acts zero point three metres from the pivot and must produce the same moment.

9:58Dividing two point four by zero point three gives a balancing force of eight newtons. Extended students must also handle several forces on either side. Suppose left-side forces produce moments of two newton metres and one newton metre anticlockwise. A right-side force already produces one newton metre clockwise. Another right-side force must therefore provide two newton metres clockwise to make the totals equal. If that additional force acts zero point five metres from the pivot, calculate its size using the moment relationship.

10:30Divide the required moment of two newton metres by zero point five metres. The additional force is four newtons. Classify each force by its turning direction before adding moments, rather than simply grouping forces by their position. This experiment is also Supplement content. To demonstrate the principle experimentally, balance a uniform metre rule on a pivot at its centre of gravity. Hang known weights at measured distances on both sides.

10:55Adjust their positions until the rule remains horizontal and stationary. Measure each perpendicular distance from the pivot to the weight’s line of action. Calculate each moment, then add the clockwise moments and the anticlockwise moments separately. Repeat with different weights and positions, including several weights on each side. The totals should agree within experimental uncertainty. The rule’s own weight has no moment when its line of action passes through the pivot.

11:21An object is in equilibrium when there is no resultant force and no resultant moment. Balanced moments prevent a change in rotation, while balanced forces prevent a change in velocity. For our stationary beam, the upward support force balances all the downward weights. Checking moments alone does not establish complete equilibrium.

Centre of gravity and stability

11:40The centre of gravity is the point at which the weight of an object may be considered to act. This lets us represent the weight of an extended object using one downward force. For a uniform, symmetrical object, it is at the geometrical centre. An irregular object needs a different method. A plane lamina is a thin, flat sheet, such as a piece of cardboard. Make a small hole near its edge and suspend it freely from a pin.

12:05Hang a plumb line from the same pin and wait until both are still. Mark the vertical line shown by the plumb line onto the lamina. Suspend the lamina from a second point and mark another vertical line in the same way. Their intersection gives the position of the centre of gravity. A third suspension provides a useful check. The method works because the centre of gravity lies vertically below the suspension point when the lamina hangs in equilibrium.

12:29Stability describes how difficult it is to topple an object. Consider a block tilted about one bottom edge. If the vertical line through its centre of gravity falls inside its base, its weight tends to restore it. If that line falls outside the base, its weight produces a moment that topples it. A lower centre of gravity makes an object more stable because it must tilt farther before the weight’s line leaves the base.

12:53A wider base also increases stability. These features explain why tall, narrow objects topple more easily than low, broad ones. The key is the position of the weight’s line of action relative to the supporting base. Let us apply this to an exam-style question asking you to describe how to locate a lamina’s centre of gravity. Suspend the lamina freely from a point near its edge. Hang a plumb line from the same point and mark its vertical line.

13:18Repeat from another suspension point, and identify the intersection as the centre of gravity. A second question asks you to explain why lowering a vehicle’s centre of gravity improves stability. A lower centre of gravity means the vehicle can tilt farther before its weight’s line of action falls outside its base. When that line falls outside the base, the weight produces an overturning moment. Link the changed position to the turning effect, rather than simply saying the vehicle is better balanced.

13:46Keep four distinctions clear when answering questions. Extension is the increase in length, not total length. Zero resultant force means constant velocity, not necessarily zero velocity. Acceleration can involve a change of direction, while equilibrium requires both zero resultant force and zero resultant moment. The whole topic now fits together. Forces can deform objects, and load-extension graphs reveal how an elastic solid responds. A resultant force changes velocity, while a moment describes a turning effect.

14:19The centre of gravity locates the action of weight, helping us explain both balance and stability.