SP9 · Forces and their effectsTopic 9 — Forces and their effects
Resultant forces and interactions
Revise the key ideas
Interactions and contact forces
Objects interact by exerting forces on each other. A force is a vector with magnitude and direction, measured in newtons (N).
Contact forces require physical contact between objects. Examples include normal contact force, friction, tension, drag and upthrust from a fluid.
The normal contact force is the support force acting at right angles (perpendicular) to a surface. It acts upwards on a horizontal table and at right angles to the slope on a sloping surface.The perpendicular arrow rises leftwards because the slope rises rightwards.
Friction opposes relative sliding or the tendency to slide between surfaces. It can also provide useful grip, such as between shoes and the ground.
Tension acts along a taut string or cable, pulling the attached object. A string does not push an object along its length.
Air and water resistance are drag forces associated with relative motion through a fluid. Upthrust is an upward force from a fluid and does not require an object to be moving.
Newton’s third law: two interacting objects exert equal, opposite forces of the same type on each other. These act on different objects.
Earth attracts the Moon and the Moon attracts Earth with equal gravitational forces. Their different masses mean their accelerations are different.
Non-contact forces and fields
Non-contact forces act at a distance. Gravitational, electrostatic and magnetic interactions are represented using fields.
A field is a region in which an appropriate object experiences a force. It is not a material string connecting the objects.
All masses have gravitational fields and attract other masses. Weight is the gravitational force on an object in a gravitational field.
Charged objects have electrostatic fields. Like charges repel and unlike charges attract: two electrons repel; an electron and a proton attract.Charge signs determine attraction or repulsion.
Magnetic fields affect other magnets and magnetic materials such as iron, nickel and cobalt; steel can also be magnetic. Not all metals are magnetic.
Like magnetic poles repel; unlike poles attract. An initially unmagnetised magnetic material can be attracted as magnetism is induced in it.
A field can exist even when no test object is present. A force occurs when a suitable second object is placed in that field.
Free-body diagrams and balanced forces
A free-body diagram shows all the forces acting on one chosen object. Use labelled arrows pointing in the correct directions. Their lengths can show the sizes (magnitudes) of the forces.
For a book resting on a horizontal table, draw weight downwards and normal force upwards. If no other vertical force acts, these balance.
Weight and support on that book are not a third-law pair: both act on the book and are different interaction types. The partner forces act on Earth and the table.
For a car travelling at constant velocity on level ground, driving force balances drag/friction horizontally and support balances weight vertically.Only forces acting on the car are shown.
Zero resultant means no acceleration. This can describe rest or straight-line motion at constant velocity; it does not imply there are no forces.
An unbalanced resultant can change speed or direction. Even if perpendicular forces have equal sizes, they do not cancel because they are not opposite.
An object hanging from two angled strings has two tension forces and its weight acting on it. Each tension has a horizontal and vertical part (component). The horizontal parts can cancel while the vertical parts together balance the weight.
Combining vectors with scale drawings
Scalars such as mass, time, distance and speed have magnitude only. Force, weight, displacement and velocity have magnitude and direction and are vectors.
For forces in one straight line, add those in the same direction and subtract those in opposite directions, stating the resultant's direction.
For angled forces, choose a scale such as 1 cm = 2 N, draw accurate lengths and use a protractor for directions.
In the head-to-tail method, draw the second vector from the head of the first without rotating it. The resultant joins the first tail to the final head.Preserve each vector’s magnitude and direction when moving it head to tail.
In the parallelogram method, draw both forces from one point and complete the parallelogram. Its diagonal from that point is the resultant.Both construction methods give the same resultant.
Measure the resultant's length and direction on the drawing and convert length back to force using the chosen scale. Drawing thickness and protractor reading limit precision.
The equilibrant is a force the same size as the resultant but in the opposite direction. Adding it balances the forces, giving a zero resultant.
To resolve a force means to split it into two parts (components) at right angles. On a scale drawing, make the force the diagonal of a rectangle: its sides show the components. Together they have the same effect as the original force, but their lengths do not simply add to the diagonal’s length.The components form the sides; the original force is the diagonal.
A 3 N horizontal force plus 4 N vertical force has a 5 N diagonal resultant. A scale drawing also gives its direction, roughly 53° above the horizontal.
In equilibrium, forces form a closed head-to-tail polygon. Check both horizontal and vertical balance; cancelling one direction alone is insufficient.
Moments, levers and gears
A force can rotate an object about a pivot. Its moment = force × perpendicular distance from the pivot to the force’s line of action, measured in N m. The lever’s total length is not automatically the perpendicular distance.Distances are measured perpendicular to the force lines from the pivot.
For an object with no overall turning effect, total clockwise moment = total anticlockwise moment: rotational equilibrium. To stay completely at rest (static equilibrium), its resultant force must also be zero. Balanced moments alone do not stop it moving in a straight line.
A longer perpendicular lever arm gives a larger moment for the same force, so a long spanner can make a nut easier to turn. If the line of action passes through the pivot, the moment is zero.
A lever can give a larger output force by placing that force nearer the pivot than the input force. The input side then moves farther; the lever does not create extra energy.
Meshing gears transmit rotational effects. Two directly meshing gears turn in opposite directions; a small gear driving a larger one generally gives slower rotation and a larger torque, ignoring losses.
Ignoring losses, a gear with twice as many teeth turns at half the speed. For example, a 20-tooth gear driving a 40-tooth gear makes the larger gear turn at half the speed. This is an inverse relationship between rotation speed and number of teeth. Real gears also have friction and other losses.
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