K323 / 2027
Dynamics overview

Topic 2 of 7

Forces on one body

Draw the forces on the chosen body, then combine them to find the resultant force.

A force comes from an interaction, such as a string pulling or a surface pushing. Review force types and weight if you need help naming the forces.

A free-body diagram shows the forces acting on one selected body. Represent the body with a dot or a simple outline. Draw labelled arrows from it: the arrowhead gives direction, and the length can represent magnitude using a chosen scale.

  1. Choose the body: for example, the book, rather than the book and table together.
  2. Identify its interactions: Earth attracts the book, and the table pushes on it.
  3. Draw only forces on that body: the book's force on the table belongs on a different diagram.
  4. Check the directions and labels: weight is downwards; the normal contact force is perpendicular to the table.

Forces on a stationary book

Selected body: book

Forces on a stationary bookThe selected body is a book at rest on a horizontal table. The table pushes the book upwards and Earth pulls it downwards. The two forces have equal magnitudes and act on the same book. They are not an interaction pair.Supportby tableWeightby Earth

These forces balance on the same body.

Forces on a stationary book on a horizontal table. The upward support and downward weight balance. Both arrows are forces on the book.

The resultant is the single force equal to the vector sum of all the forces on the body. Along one line, forces in the same direction add; forces in opposite directions subtract. Keep their directions in the answer.

Balanced forces do not require the object to be at rest

Forces are balanced when their resultant is zero. The body's acceleration is then zero, so its velocity stays constant. A body already at rest remains at rest; a moving body continues at the same speed in the same direction.

Balanced forces on a moving trolley

Selected body: 2.0 kg trolley

The trolley is moving right along a horizontal track.

Balanced forces on a moving trolleyThe selected body is a 2.0 kg trolley moving right. Support by the track is 20 N upwards and weight by Earth is 20 N downwards. The string pulls with 3 N to the right and the track exerts 3 N resistance to the left. All force arrows use the same scale. The resultant is zero, so the velocity stays constant.20 NSupportby track20 NWeightby Earth3 NResistanceby track3 NPullby string

Zero resultant: constant velocity. The trolley need not be at rest.

A 2.0 kg trolley moves along a straight level track at a constant 2 m/s. The string pulls forwards with 3 N and the track resists with 3 N. Its 20 N weight and 20 N support also balance.

The trolley has forces acting on it, but their resultant is zero. The string's forward pull balances the resistance. If resistance were absent, a forward pull would no longer be needed to maintain the same velocity.

An unbalanced force changes velocity

A non-zero resultant force produces acceleration in its direction. Since velocity includes direction, several changes are possible:

  • An object at rest can start moving.
  • A resultant in the direction of motion can increase its speed.
  • A resultant opposite to its motion can reduce its speed.
  • A resultant can turn its motion. An object following a curved path has changing velocity even if its speed stays constant.

For example, increasing the trolley's string pull to 7 N while resistance remains 3 N gives a resultant of 4 N forwards. Its velocity now changes. We calculate how quickly it changes in resultant force and acceleration.

Do not add a "force of motion". Motion is what the body does; each force must come from an interaction. If a separate velocity arrow helps, label it as velocity and keep it distinct from the force diagram.

The trolley's support equals its weight here because the pull is horizontal and there is no vertical acceleration. Do not assume support always equals weight when other vertical forces or vertical acceleration are present.

Optional check A trolley travels along a straight level track at a constant 2 m/s. What must be true about the forces on it?
A trolley travels along a straight level track at a constant 2 m/s. What must be true about the forces on it?