Resultant force and vectorsIB MYP Physics: Revision notes
Section 1
Scalars and vectors
A scalar quantity has size (magnitude) only. A vector quantity has size and direction.
| Scalar | Vector |
|---|---|
| distance | displacement |
| speed | velocity |
| mass | weight (a force) |
| time, energy | force, acceleration |
Distance is the total length of the path you travel. Displacement is the straight-line distance from start to finish, in a stated direction. If you walk 3 km east and then 3 km back west, your distance is 6 km but your displacement is 0 km.
Mass is the amount of matter in an object (kg) and does not change. Weight is the force of gravity on the object (N), acting downwards, and it depends on the strength of gravity.
Mass and weight are not the same. Mass is in kg and is a scalar; weight is a force in N and is a vector.
Section 2
Adding forces along a line
Forces are drawn as arrows. The resultant force is the single force that has the same effect as all the forces acting together.
- Forces in the same direction: add them. 40 N + 30 N = 70 N in that direction.
- Forces in opposite directions: subtract the smaller from the larger. 50 N right and 20 N left give 30 N to the right.
The resultant always points in the direction of the larger force.
Choose one direction as positive (say right) and the opposite as negative. Then add all the forces and the sign gives the direction.
Section 3
Balanced and unbalanced forces
When the forces on an object are balanced, the resultant force is zero. A stationary object stays at rest, and a moving object keeps moving at constant velocity (same speed, same direction).
When the forces are unbalanced, there is a non-zero resultant force. The object accelerates in the direction of the resultant: it speeds up, slows down or changes direction.
A car moving at a steady 20 m/s along a straight road has balanced forces, even though it is moving.
A moving object does not need a resultant force to keep moving. Only a change in velocity needs a resultant force.
Section 4
Perpendicular forces: Pythagoras and scale drawing
Forces at right angles cannot just be added. Two ways to find the resultant:
1. Pythagoras. The resultant is the hypotenuse of a right-angled triangle: R² = F₁² + F₂².
Worked example: a boat is pulled 3.0 N north by a rope and 4.0 N east by the current. R = √(3.0² + 4.0²) = √(9 + 16) = √25 = 5.0 N.
2. Scale drawing. Choose a scale (for example 1 cm = 1 N). Draw the first force as a line, then draw the second force from its end at 90°. Draw the resultant from the start of the first line to the end of the second, measure its length and convert it back using the scale. Measure the angle with a protractor to give the direction.
The resultant of two perpendicular forces is always smaller than their sum, so check your answer is less than F₁ + F₂.
Section 5
Equilibrium
An object is in equilibrium when the forces on it are balanced, so the resultant force is zero.
- A book on a table: weight acts down, the normal contact force from the table acts up. They are equal, so the book stays at rest.
- A hanging mass of 2 kg (weight 20 N, taking 10 N/kg): the cable pulls up with 20 N.
With three or more forces, equilibrium means the forces cancel out in every direction. In the ring investigation, the third force equals the resultant of the other two but acts in the opposite direction.
Must know
- Scalars have size only; vectors have size and direction.
- Distance, speed and mass are scalars; displacement, velocity, force and weight are vectors.
- Same direction: add forces. Opposite directions: subtract.
- Balanced forces: resultant zero, no change in motion.
- Unbalanced forces: acceleration in the direction of the resultant.
- Perpendicular forces: R = √(F₁² + F₂²) or a scale drawing.
- Equilibrium means a resultant force of zero.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Resultant force and vectors
- A delivery cyclist in Nairobi rides 6 km east along a straight road, then turns and rides 8 km north to reach a school. The whole journey takes 40 minutes.Explain why the size of the cyclist's displacement is different from the distance she travels.2 marks
- Two workers in a warehouse in Lagos push a heavy crate along a smooth floor. Friction between the crate and the floor is so small that it can be ignored. One worker pushes to the right with a force of 300 N and the other pushes to the left with a force of 220 N.A third worker joins and also pushes to the left, with a force of 80 N. The crate is moving to the right at that moment. Calculate the new resultant force and describe how the crate's motion now changes.2 marks
- A student in Seoul is finding out how two forces at right angles combine. She fixes a small metal ring to a flat board. Two newton meters pull the ring at right angles to each other, and a third newton meter pulls in the opposite direction to the resultant of the first two so that the ring stays at rest.She pulls the ring with forces of 6.0 N and 8.0 N at right angles to each other. Calculate the reading on the third newton meter when the ring is at rest.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).