Resultant force
Definition
Resultant force
Resultant force is the single force that has the same effect as all the forces acting on an object, after their sizes and directions have been taken into account.
- A force is a vector quantity, so its direction matters as well as its size. Forces acting in the same direction are added. Forces acting in opposite directions are subtracted.
- For forces along one line, the direction of the larger total determines the direction of the resultant force. For example, 700 N700\ \text{N}700 N forwards and 250 N250\ \text{N}250 N backwards give 450 N450\ \text{N}450 N forwards.
- If forces are equal in size and opposite in direction, the resultant force is 0 N0\ \text{N}0 N. The forces are balanced, but forces are still acting on the object.
Example
Balancing forces
- A car travels at constant velocity. Its engine provides a driving force of 1800 N1800\ \text{N}1800 N forwards.
- Constant velocity means the resultant force is 0 N0\ \text{N}0 N.
- Therefore driving force−resistive force=0\text{driving force}-\text{resistive force}=0driving force−resistive force=0.
- Substitution gives 1800 N−resistive force=0 N1800\ \text{N}-\text{resistive force}=0\ \text{N}1800 N−resistive force=0 N.
- The resistive force is 1800 N1800\ \text{N}1800 N backwards.
Newton's first law
Definition
Newton's first law
Newton's first law states that an object remains at rest or continues to move at constant velocity unless a non-zero resultant force acts on it.
- A constant velocity means constant speed in a constant direction. Motion at constant speed around a bend is not constant velocity because the direction changes.
- Newton's first law does not say that a moving object needs a forward resultant force. A resultant force is needed to change velocity, not to maintain a constant velocity.
- A bicycle slows when the rider stops pedalling because friction and air resistance provide a resultant force opposite to its motion. If no resultant force acted, it would continue at constant velocity.
Zero resultant force
Definition
Balanced forces
Balanced forces are forces whose vector sum is zero, so they produce no change in velocity.
- When the resultant force is zero, acceleration is zero. An object can therefore remain at rest or move at constant velocity.
- A book at rest on a table has weight acting downwards and an equal normal contact force acting upwards. The two forces balance, so the book remains at rest.
- A vehicle moving at constant velocity has a driving force forwards equal to the total friction and drag backwards. The forces balance, so its speed and direction remain constant.
- A falling object at terminal velocity has weight downwards equal to air resistance upwards. Its resultant force and acceleration are zero, so it continues downwards at constant speed.
Exam technique
Explaining balanced motion
- Link the force condition to the motion: the forces are balanced, so the resultant force is zero, therefore the object remains at rest or moves at constant velocity.
- Do not write that there are no forces. State that the forces are equal and opposite or that their resultant is zero.
- When a value and direction are required, include both, such as 450 N450\ \text{N}450 N forwards.
Non-zero resultant force
Definition
Acceleration
Acceleration is the rate of change of velocity.
- When the resultant force is not zero, the object's velocity changes. The acceleration is in the same direction as the resultant force.
- A resultant force in the direction of motion makes the object speed up. A resultant force opposite to the direction of motion makes it slow down.
- A resultant force at an angle to the motion changes the direction of the velocity. The speed can stay constant while the velocity changes.
Example
Using an unbalanced force
- A car has a driving force of 4200 N4200\ \text{N}4200 N forwards and resistive forces totalling 3000 N3000\ \text{N}3000 N backwards.
- The resultant force is 4200 N−3000 N=1200 N4200\ \text{N}-3000\ \text{N}=1200\ \text{N}4200 N−3000 N=1200 N forwards.
- The resultant force is non-zero, so the car accelerates.
- The resultant force acts in the direction of motion, so the car speeds up.
Common Mistake
Common force errors
- Zero resultant force does not mean zero individual forces.
- Constant speed only proves zero acceleration if the direction is also constant.
- Do not say that a force is used up. Forces act on objects and can change their velocity.
Self review
- State Newton's first law.
- Explain why an object moving at constant velocity has a resultant force of zero.
- Calculate the resultant force when 650 N650\ \text{N}650 N acts forwards and 280 N280\ \text{N}280 N acts backwards.
- Explain why zero resultant force does not mean that no forces are acting.
- Describe how a non-zero resultant force changes an object's velocity.
