Topics

Forces and free-body diagrams

Covers AS91171

What a force is

A force is a push or a pull on an object. It is measured in newtons (N) and it is a vector.
A force is always exerted by one object on another — name both when you describe it.
A force can:
- change an object's speed,
- change its direction,
- change its shape.

The forces you meet at Level 2

Weight ( $F_w = mg$ $F_{w} = m g$ ) — the gravitational pull of the Earth on the object.
- Always acts vertically downward, from the centre of the object.
- $m$ is the mass in kg; $g = 9.8$ m s⁻².
- Mass and weight are not the same. Mass (kg) is the amount of matter and never changes; weight (N) is a force and depends on $g$ .
Normal force ( $N$ $N$ ) — the push of a surface on an object resting against it.
- Always acts perpendicular to the surface, not always vertically.
Tension ( $T$ ) — the pull of a string, rope or cable, along its length, away from the object.
Friction — opposes relative motion between surfaces, acting along the surface.
Air resistance / drag — opposes motion through a fluid, and grows with speed.
Applied force — a push or pull from a person, engine or machine.

Drawing a free-body diagram

A free-body diagram shows every force acting on one object, and nothing else.

Draw the object as a simple box or dot.
Draw an arrow for each force, starting at the object and pointing the way the force acts.
Make the length of each arrow roughly proportional to its size.
Label every arrow with a name and, where known, a value in newtons.
Include only forces acting on the object — never forces the object exerts on something else.

Things students wrongly add to free-body diagrams:
- a "force of motion" or "forward force" on a coasting object — a moving object needs no force to keep moving,
- a "centrifugal force" pointing outward in circular motion,
- the object's own push on the ground — that acts on the ground, not on the object.

Net force

The net force (or resultant, or unbalanced force) is the vector sum of all the forces on an object.
If the net force is zero, the forces are balanced: the object stays at rest, or keeps moving at constant velocity.
If the net force is not zero, the object accelerates in the direction of the net force.
Add forces in one dimension by choosing a positive direction and adding with signs:
- two forces the same way: add them,
- two forces in opposite directions: subtract, and the answer takes the direction of the larger.

Worked ExampleWeight, mass and normal force

A $12$ kg box rests on a horizontal floor. (a) Calculate its weight. (b) State the size and direction of the normal force. (c) A person then presses down on the box with a force of $40$ N. State the new normal force.

(a) Weight

$F_w = mg = (12)(9.8) = 117.6 \approx 118 \text{ N downward}$

(b) The normal force with nothing else acting

The box is not accelerating vertically, so the vertical forces must balance:

$N = F_w = 118 \text{ N upward}$

(c) With an extra $40$ N push downward

The floor must now support the weight and the push:

$N = 118 + 40 = 158 \text{ N upward}$

$F_w = 118 \text{ N}, \qquad N = 118 \text{ N}, \qquad N_{\text{new}} = 158 \text{ N}$

Worked ExampleNet force in one dimension

A $50$ kg crate is pulled to the right with a force of $220$ N while friction of $75$ N acts on it. Draw the free-body diagram in words, and find the net force.

Step 1 — List the four forces acting on the crate

Weight: $F_w = (50)(9.8) = 490$ N, downward
Normal force: $490$ N, upward (no vertical acceleration, so these two balance)
Applied force: $220$ N, right
Friction: $75$ N, left (opposing the motion)

Step 2 — Vertical direction

$F_{\text{net, vertical}} = 490 - 490 = 0$

The crate does not accelerate vertically, which is the check that the normal force was right.

Step 3 — Horizontal direction, taking right as positive

$F_{\text{net}} = 220 - 75 = 145 \text{ N to the right}$

$F_{\text{net}} = 145 \text{ N right}$

Forces and free-body diagrams

Covers AS91171

What a force is

A force is a push or a pull on an object. It is measured in newtons (N) and it is a vector.
A force is always exerted by one object on another — name both when you describe it.
A force can:
- change an object's speed,
- change its direction,
- change its shape.

The forces you meet at Level 2

Weight ( $F_w = mg$ $F_{w} = m g$ ) — the gravitational pull of the Earth on the object.
- Always acts vertically downward, from the centre of the object.
- $m$ is the mass in kg; $g = 9.8$ m s⁻².
- Mass and weight are not the same. Mass (kg) is the amount of matter and never changes; weight (N) is a force and depends on $g$ .
Normal force ( $N$ $N$ ) — the push of a surface on an object resting against it.
- Always acts perpendicular to the surface, not always vertically.
Tension ( $T$ ) — the pull of a string, rope or cable, along its length, away from the object.
Friction — opposes relative motion between surfaces, acting along the surface.
Air resistance / drag — opposes motion through a fluid, and grows with speed.
Applied force — a push or pull from a person, engine or machine.

Drawing a free-body diagram

A free-body diagram shows every force acting on one object, and nothing else.

Draw the object as a simple box or dot.
Draw an arrow for each force, starting at the object and pointing the way the force acts.
Make the length of each arrow roughly proportional to its size.
Label every arrow with a name and, where known, a value in newtons.
Include only forces acting on the object — never forces the object exerts on something else.

Things students wrongly add to free-body diagrams:
- a "force of motion" or "forward force" on a coasting object — a moving object needs no force to keep moving,
- a "centrifugal force" pointing outward in circular motion,
- the object's own push on the ground — that acts on the ground, not on the object.

Net force

The net force (or resultant, or unbalanced force) is the vector sum of all the forces on an object.
If the net force is zero, the forces are balanced: the object stays at rest, or keeps moving at constant velocity.
If the net force is not zero, the object accelerates in the direction of the net force.
Add forces in one dimension by choosing a positive direction and adding with signs:
- two forces the same way: add them,
- two forces in opposite directions: subtract, and the answer takes the direction of the larger.

Worked ExampleWeight, mass and normal force

(a) Weight

$F_w = mg = (12)(9.8) = 117.6 \approx 118 \text{ N downward}$

(b) The normal force with nothing else acting

The box is not accelerating vertically, so the vertical forces must balance:

$N = F_w = 118 \text{ N upward}$

(c) With an extra $40$ N push downward

The floor must now support the weight and the push:

$N = 118 + 40 = 158 \text{ N upward}$

$F_w = 118 \text{ N}, \qquad N = 118 \text{ N}, \qquad N_{\text{new}} = 158 \text{ N}$

Worked ExampleNet force in one dimension

A $50$ kg crate is pulled to the right with a force of $220$ N while friction of $75$ N acts on it. Draw the free-body diagram in words, and find the net force.

Step 1 — List the four forces acting on the crate

Weight: $F_w = (50)(9.8) = 490$ N, downward
Normal force: $490$ N, upward (no vertical acceleration, so these two balance)
Applied force: $220$ N, right
Friction: $75$ N, left (opposing the motion)

Step 2 — Vertical direction

$F_{\text{net, vertical}} = 490 - 490 = 0$

The crate does not accelerate vertically, which is the check that the normal force was right.

Step 3 — Horizontal direction, taking right as positive

$F_{\text{net}} = 220 - 75 = 145 \text{ N to the right}$

$F_{\text{net}} = 145 \text{ N right}$

Forces and free-body diagrams

What a force is

The forces you meet at Level 2

Drawing a free-body diagram

Net force

(a) Weight

(b) The normal force with nothing else acting

(c) With an extra 404040 N push downward

Step 1 — List the four forces acting on the crate

Step 2 — Vertical direction

Step 3 — Horizontal direction, taking right as positive

Forces and free-body diagrams

What a force is

The forces you meet at Level 2

Drawing a free-body diagram

Net force

(a) Weight

(b) The normal force with nothing else acting

(c) With an extra 404040 N push downward

Step 1 — List the four forces acting on the crate

Step 2 — Vertical direction

Step 3 — Horizontal direction, taking right as positive

(c) With an extra $40$ N push downward

(c) With an extra $40$ N push downward