01 · A vertical resultant
Forces are 16 N up, 6 N down, 9 N left and 9 N right. Find the resultant.
Hint
Resolve along both axes.
Worked solution
Horizontal resultant is zero; vertical resultant is 16 − 6 = 10 N upward.
Understand · explore · practise
Force diagrams, resultants and equilibrium
Draw forces on one body, calculate a signed resultant and use Newton’s first law without confusing equilibrium with rest.
Before you startModelling in mechanics: force diagrams, vectors and motion signs.
01 / Choose one body before drawing its forces
Every arrow must name an interaction acting on that body.
A force diagram is not a motion diagram.
Include only forces exerted on the chosen body. Weight acts downward, contact reactions perpendicular to the surface, and tension along a taut string away from the body. A velocity or acceleration arrow can be drawn separately but must not be added to the force sum.
Forces on one particleExplore
The arrows represent forces acting on a single particle. Choose a case and resolve rightward and upward. The acceleration arrow is shown separately: it is not another force.
02 / Add signed forces along a chosen axis
Opposite arrows contribute opposite signs.
Forces are 18 N right, 7 N left, 12 N up and 12 N down.Worked example
Rightward resultant: 18 − 7 = 11 N
Take right as positive.
Upward resultant: 12 − 12 = 0 N
Vertical forces balance.
Resultant is 11 N to the right
This establishes acceleration direction, not the current velocity.
Watch: balanced arrows cancel in the resultant
Pause, replay or seek freely. The notes explain the same idea and stay in view.
02 · A negative component
Forces along a line are 5 N right and 13 N left. State the resultant using rightward positive.
Hint
Subtract the leftward magnitude.
Worked solution
Resultant = 5 − 13 = −8 N; equivalently 8 N left.
03 / Zero resultant means zero acceleration
Rest is one possible state of equilibrium.
Newton’s first law preserves velocity when the resultant is zero.
An object initially at rest remains at rest. An object already moving continues with the same velocity. Equilibrium does not imply that every individual force is zero.
03 · A supported book
A book has weight 8 N and rests on a horizontal table. With no other forces, find the normal reaction.
Hint
Its vertical acceleration is zero.
Worked solution
R − 8 = 0, so R = 8 N upward.
04 · A steadily moving object
A particle moves at a constant velocity of 3 m/s right. What is its resultant force?
Hint
Its velocity is not changing.
Worked solution
Zero resultant. A nonzero force is not needed to maintain constant velocity in this model.
05 · Individual forces
Can two nonzero forces act on a particle in equilibrium?
Hint
Consider equal opposite forces.
Worked solution
Yes. For example, 10 N right and 10 N left sum to zero.
04 / A resultant determines acceleration direction
It does not, by itself, tell you the direction of motion.
06 · Braking without reversing
A particle moves right while the resultant force points left. What happens to its speed initially?
Hint
Acceleration opposes its current velocity.
Worked solution
It initially slows down. It may still be moving right; a leftward force does not immediately imply leftward motion.
07 · Descending but slowing
A lift moves downward while its resultant force is upward. Describe its change in speed.
Hint
Velocity and acceleration have opposite directions.
Worked solution
Its downward speed decreases. Its acceleration is upward even though its current motion is downward.
08 · Turning at constant speed
A particle travels around a circle at constant speed. Must the resultant force be zero?
Hint
Velocity includes direction.
Worked solution
No. The changing direction means velocity changes, so acceleration and a nonzero resultant are required.
05 / Use equilibrium to find missing forces
Resolve independently in perpendicular directions.
09 · Unknown pull
A particle is in equilibrium under a 14 N rightward force and two leftward forces of 5 N and P N. Find P.
Hint
Set the horizontal resultant to zero.
Worked solution
14 − 5 − P = 0 gives P = 9 N.
10 · Two support ropes
A platform of weight 360 N is supported by two vertical ropes, each with the same tension, while moving at constant velocity. Find each tension.
Hint
The two upward tensions share the total load.
Worked solution
2T − 360 = 0, so each tension is 180 N. Constant velocity gives zero acceleration even while the platform moves.
11 · Reduced support
Both tensions in question 10 fall to 150 N. Find the resultant force and acceleration direction.
Hint
Add the two upward tensions, then subtract weight.
Worked solution
Upward resultant = 300 − 360 = −60 N, so the resultant and acceleration are downward. Without the initial velocity you cannot decide whether speed initially increases or decreases.
06 / Keep forces on other bodies out of this diagram
A force you exert is not automatically a force acting on you.
12 · Block and table
Should a diagram of forces on the block include the block’s downward push on the table?
Hint
Which object experiences that push?
Worked solution
No. That force acts on the table. The block’s diagram includes the table’s upward reaction on the block and the block’s weight, plus any other forces acting on it.
13 · Falling particle
A particle falls freely with air resistance neglected. Draw or describe its force diagram.
Hint
Do not add a force labelled “motion”.
Worked solution
There is one force: weight downward. Its downward velocity and acceleration are not extra forces.
07 / Read the surface and motion assumptions
A stated constant velocity can supply an equilibrium equation.
14 · Constant-speed car on a straight level road
In a particle model, a car has horizontal driving force 900 N and moves with constant velocity. Find total horizontal resistance, assuming no other horizontal force.
Hint
The horizontal resultant must be zero.
Worked solution
Resistance is 900 N backward. Vertical reaction balances weight if there are no other vertical forces or vertical acceleration.
For a smooth surface, omit friction. For a rough surface, include a resistance only with a direction justified by the motion or tendency to slide. Later lessons calculate acceleration from the resultant using mass.
08 / Resolve forces, then interpret the resultant
Keep force, velocity and acceleration distinct.
Name the body, draw the external forces acting on it and add their signed components. Zero resultant means constant velocity; a nonzero resultant gives acceleration in its direction. Use the current velocity as well when deciding whether the body is speeding up or slowing down.
Section 1 of 8 · Choose one body before drawing its forces