The Crate on the Table
A crate sits at rest on a table. Gravity pulls it down, and the table pushes up. Before any calculation we must decide exactly which forces act on the crate โ and which forces act on something else. Move the mass slider and watch the two forces that act on the crate.
weight $W = mg$ = 49.0 N ยท normal reaction $R$ = 49.0 N
The crate is at rest, so the resultant is zero and $R = W = mg$. Only these two forces act on the crate.
Try each in your head before clicking an answer โ this is a test, not a reveal. See how many you get first try. The clock starts on your first answer.
R1. The weight of a mass $m$ is given by:
R2. The unit of force is the:
R3. A vector quantity is completely described by its:
A force is a push or a pull that one body exerts on another. It is a vector, measured in newtons, so on a diagram it is drawn as an arrow: the length shows the magnitude and the arrowhead shows the direction.
| Quantity | Type | Unit |
|---|---|---|
| Force | vector | newton (N) |
| Mass | scalar | kilogram (kg) |
| Weight $W = mg$ | vector (a force) | newton (N) |
Every force belongs to one of two families:
| Family | Needs contact? | Examples |
|---|---|---|
| Contact | yes | normal reaction, tension, friction, thrust, air resistance |
| Non-contact | no | weight, magnetic force, electrostatic force |
Weight acts at a distance: the Earth pulls the body without touching it.
Draw the diagram for a single body and show only the forces acting on it.
The push the crate gives the table acts on the table, so it does not appear on the crate's diagram.
Use a name and, where known, a value. Worked example: a $5\ \text{kg}$ crate on a table has weight $W = 5\times 9.8 = 49\ \text{N}$ down and normal reaction $R = 49\ \text{N}$ up.
Groups of 4: tap a card to pick it up, then tap a zone to file it โ "โ Acts on the crate" or "โ Acts on something else". Discuss each card, then press Check cards. Six forces from a crate resting on a table.
Set the magnitude F and the direction theta of a single force. The arrow redraws live, with the components of the force shown as dashed lines. Move both sliders a few times, then answer the challenge below.
A lamp of mass $5\ \text{kg}$ hangs at rest from a single vertical wire. List the forces acting on the lamp and find the tension in the wire.
Only two forces act on the lamp: its weight (non-contact) and the tension (contact). At rest the two must balance.
Weight $W$ acting downwards (non-contact), and tension $T$ acting upwards along the wire (contact).
$W = mg = 5\times 9.8 = 49\ \text{N}$.
The lamp is at rest, so the resultant is zero: $T = W = 49\ \text{N}$ upwards.
A crate of mass $12\ \text{kg}$ rests on a horizontal table. A horizontal rope pulls it with a tension of $25\ \text{N}$, but the crate stays at rest. List the four forces acting on the crate and find the normal reaction.
The vertical forces are the weight and the normal reaction; the horizontal forces are the tension and friction. Resolve vertically to find the normal reaction.
Weight $W$ downwards; normal reaction $R$ upwards; tension $T = 25\ \text{N}$ horizontally; friction $F$ horizontally, opposing the pull.
$W = 12\times 9.8 = 117.6\ \text{N}$.
No vertical acceleration, so $R = W = 117.6\ \text{N}$.
Answer, then check. Options are shuffled every load. The clock starts on your first answer.
Q1. Which forces act on a crate resting on a table?
Q2. Which of these is a non-contact force?
Q3. A free-body diagram should include:
Q4. The weight of a $6\ \text{kg}$ mass is (take $g = 9.8$):
Work each on paper, then reveal the solution to check your working.
A book of mass $3\ \text{kg}$ rests on a horizontal desk. State the two forces acting on the book and find the normal reaction.
Reveal Solution
Weight $W = 3\times 9.8 = 29.4\ \text{N}$ downwards; normal reaction $R$ upwards. At rest $R = W = 29.4\ \text{N}$.
A block of mass $15\ \text{kg}$ hangs at rest from a single vertical rope. Find the tension in the rope.
Reveal Solution
$W = 15\times 9.8 = 147\ \text{N}$ downwards. At rest $T = W = 147\ \text{N}$.
A sign of mass $10\ \text{kg}$ hangs at rest from two vertical ropes. Find the tension in each rope.
Reveal Solution
$W = 10\times 9.8 = 98\ \text{N}$. By symmetry the two equal tensions share the weight: $T = 98\div 2 = 49\ \text{N}$ each.
A block of mass $5\ \text{kg}$ rests on a horizontal table. A rope pulls it with a force of $20\ \text{N}$ at $30^\circ$ above the horizontal, and the block stays at rest. State the four forces acting on the block.
Reveal Solution
Weight $W = 5\times 9.8 = 49\ \text{N}$ downwards; normal reaction $R$ upwards; the pull $20\ \text{N}$ at $30^\circ$; friction opposing the pull along the table. The pull has a vertical component, so $R = 49 - 20\sin 30^\circ = 39\ \text{N}$.
Box A of mass $3\ \text{kg}$ rests on box B of mass $5\ \text{kg}$, which rests on a table. State the forces acting on box A and the forces acting on box B.
Reveal Solution
On A: weight $29.4\ \text{N}$ down, normal reaction from B $29.4\ \text{N}$ up. On B: weight $49\ \text{N}$ down, the push from A $29.4\ \text{N}$ down, and the normal reaction from the table $78.4\ \text{N}$ up.
Exit Ticket
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