Grade by Grade
D. Structures and Mechanisms · Form and Function

Describing Forces: Magnitude, Direction, Point and Plane of Application

D2.3 A1.2 A1.5About 45 minutes
Learning goals
  • I can describe a force on a structure by its magnitude, direction, point of application and plane of application.
  • I can calculate the approximate weight of an object in newtons from its mass.
  • I can explain how changing the point or plane of application changes a force's effect on a structure.

Words to know

force
A push or a pull. Forces are measured in newtons (N).
magnitude
The size or strength of a force, measured in newtons (N).
direction
The way a force pushes or pulls: up, down, sideways or at an angle.
point of application
The exact spot where a force acts on a structure.
plane of application
The surface or side of a structure that a force acts on, such as the top, the front face or the edge.
newton (N)
The unit for force. On Earth, gravity pulls on each kilogram with about 9.8 N.

Hook: same push, different result

Push a door open with one finger near the handle. Easy! Now push with the same finger right beside the hinges. Very hard!

Your push was the same size and in the same direction. The only thing that changed was where you pushed. To describe a force completely, engineers need four pieces of information.

A white door standing half open, with three metal hinges on one edge and a lever handle on the other edge.
The handle is placed as far from the hinges as possible. Pushing there, the same force turns the door much more easily. AI-generated image

Remember from earlier grades

In Grade 4 you met the newton (N), the unit for force. In Grade 5 you sorted the forces on structures into internal and external forces. In Grade 6 you learned that weight is the pull of gravity, about 9.8 N for each kilogram on Earth (almost 10 N).

In Grade 7 you will describe any force on a structure with four characteristics.

The four characteristics of a force

  1. Magnitude: how big the force is, in newtons (N). A small apple weighs about 1 N. A 50 kg student weighs about 490 N.
  2. Direction: which way the force acts: down (like gravity), up, sideways (like wind), or at an angle (like a person leaning on a wall).
  3. Point of application: the exact spot where the force acts, like the middle of a shelf or the very end of a diving board.
  4. Plane of application: the surface or side of the structure the force acts on, like the top of a table, the broad front face of a sign, or the narrow edge of a board.

Change any one of these and the force can have a very different effect on the structure.

magnitude: 50 Ndirection: rightboxpoint: the dot · plane: the shaded left face
A force described completely: a 50 N push (magnitude), to the right (direction), at the dot (point of application), on the box's left face (plane of application). In a diagram, the arrow's length shows the magnitude.

Working out magnitude from mass

When a load is an object resting on a structure, its force is its weight:

weight (N) ≈ mass (kg) × 9.8

For quick estimates, many engineers round 9.8 to 10.

  • A 2 kg bag of flour: 2 × 9.8 = 19.6 N (about 20 N), pointing down.
  • A 30 kg bag of rock salt: 30 × 9.8 = 294 N (about 300 N), pointing down.

Why point and plane matter

  • Point: a load at the middle of a long shelf makes it sag much more than the same load right beside a bracket. A diver standing at the tip of a diving board bends it far more than one standing near the fixed end.
  • Plane: lay a plastic ruler flat across two books and press the middle: it bends easily. Stand the ruler on its edge across the books and press with the same force on the top edge: it barely bends. Same force, same direction, different plane of application.
  • Wind pushing on the broad face of a road sign has a huge surface to push on. The same wind hitting the sign's edge has almost nothing to push.
same pushsame pushruler flat: bends a lotruler on its edge: barely bends
Same force, same direction, same point: only the plane of application changed. The ruler standing on its edge is much stiffer.
Worked example

Let's describe a force completely

A 5 kg box of books sits in the middle of the top of a wooden shelf. Describe the force it puts on the shelf.

  1. Magnitude: weight = 5 × 9.8 = 49 N (about 50 N).
  2. Direction: gravity pulls straight down.
  3. Point of application: the middle of the shelf.
  4. Plane of application: the shelf's top surface.

A force of about 49 N, acting straight down, at the middle of the shelf, on its top surface.

Worked example

Let's compare two forces

Wind pushes with 200 N on a backyard fence. In case A, it hits the broad face of the fence boards. In case B, the same 200 N wind push hits the fence from the end, along its length. Which is more likely to push the fence over? Use the four characteristics.

  1. The magnitude (200 N) is the same in both cases.
  2. The direction is different: in A, the wind pushes across the fence; in B, it pushes along it.
  3. The plane of application is different: in A, it is the broad face of the boards; in B, it is the narrow end of the fence.
  4. A fence is thin and easy to bend in the direction across its face, but the whole length of the fence resists a push along it.

Case A. The same-sized force on the broad face, pushing across the fence, is much more likely to push it over.

Hands-on activity

Ruler force lab

You need: a 30 cm plastic ruler, two equal stacks of books about 25 cm apart, a few coins or small identical washers, a small plastic bag, a piece of string, tape, two small clips (like binder clips), a second ruler to measure the sag.

  1. Plane test: lay the ruler flat across the two stacks. Put 10 coins in the bag and hang it from the middle of the ruler with a loop of string. Measure how far the middle sags (in mm).
  2. Now carefully stand the ruler on its edge (hold its ends with tape or a small clip so it doesn't tip). Hang the same bag from the middle. Measure the sag.
  3. Point test: lay the ruler flat again. Hang the bag at the middle, then 5 cm from one end. Measure the sag each time.
  4. Keep the same coins each time so the magnitude stays the same. That makes it a fair test: you change only one thing at a time.
  5. Record your results in a table and write a conclusion using the words magnitude, direction, point of application and plane of application.

What to look for: the ruler sags much less on its edge (different plane) and much less near a support (different point), even though the magnitude and direction (down) stayed the same.

Just for fun

Why are door handles put far away from the hinges?

Because nobody wants to push with all their might just to get to the snacks. (Thanks, point of application!)

Your turn

1

Name the four characteristics used to describe a force on a structure.

2

What unit is used for magnitude?

3

About how much does a 10 kg bag of potatoes weigh in newtons?

4

A person leans on a wall. What is the direction of their force?

5

What is the point of application when you stand at the very end of a diving board?

6

Wind blows against the front of a billboard. What is the plane of application?

7

Why is a door easier to push open near the handle than near the hinges?

More practice: warm-up

1

What does magnitude mean?

2

Which direction does gravity pull?

3

About how much does a 1 kg bag of sugar weigh?

4

Snow sits on top of a roof. What is the plane of application?

5

In a force diagram, what does a longer arrow show?

More practice: on your own

1

Describe completely the force of a 4 kg cat sitting on the end of a shelf.

2

Two people each push a heavy box with 150 N. One pushes on the side near the bottom, the other on the side near the top. What characteristic is different, and what might happen?

3

A hockey puck hits the boards of a rink. Which characteristics of the force would an engineer want to know to design the boards?

4

Explain why a wooden board laid flat as a bridge bends more than the same board turned on its edge.

5

A 60 kg adult stands on a balcony. Estimate the force on the balcony to the nearest 10 N.

Challenge

1

A sign hangs from a pole. On a calm day, the only force is the sign's weight, 80 N, straight down. On a windy day, wind pushes 300 N on the sign's face. Compare the two forces using all four characteristics.

2

A bookshelf is 1 m long and held up only at its two ends. Where should you put a heavy 15 kg box of books so the shelf sags the least? Explain using the characteristics of a force.

3

Design a fair test to find out whether the plane of application changes how much a strip of cardboard bends. What will you change, keep the same and measure?

Check your understanding

Quiz

1.

Which characteristic tells how big a force is?

2.

About how much does a 3 kg bag of apples weigh on Earth?

3.

Wind hits the front face of a road sign. The front face is the...

4.

Pushing a door near the hinges instead of near the handle changes the...

5.

A ruler bends less when a load is placed on its edge than on its flat side. Which characteristic changed?

6.

Which describes the direction of a snow load on a flat roof?

For parents and teachers

Big idea (D2.3): Students identify the magnitude, direction, point of application and plane of application of forces on a structure. They also connect mass to weight (about 9.8 N per kg, from Grade 6).

How to help: Use everyday moments: "How big is the force of your backpack on the hook? Which way? Where? On which surface?" Try the door-near-the-hinges test together.

Common difficulties:

  • Mixing up point and plane. The point is the spot; the plane is the surface or side the spot is on.
  • Writing kilograms instead of newtons. Mass is in kg; force (including weight) is in N. Multiply by 9.8 (or about 10 for estimates).
  • Fair tests: remind your child to change only one thing at a time in the ruler lab (A1.2).