Combining Force Vectors: Resultants
Representing forces as vectors — magnitude, direction, and scale
Forces - any straight-line push or pull
Myth or Fact ?
Forces include magnitude and ____ .
Is gravitational force constant or changing? Why?
Unit 1 - Forces
Push
Pull
A. Representing Forces
1. Units of force
a) lb. (English)
b) Newton (metric) — weight of 1 apple
2. Forces are VECTORS
Vector - Despicable Me
— described using:
— magnitude (size)
— direction 
Review - Scalar (magnitude only)
ex) time, distance
3. When solving problems and drawing pictures, forces are represented as arrows drawn to some selected scale
Scale: 1 cm = 10 N
*Length shows magnitude (size)
**arrow shows direction
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. What is a force?
2. Force is a vector. This means it is described by
3. Which of these is a scalar quantity?
4. Using a scale of 1 cm = 10 N, a force arrow pointing east is 4.0 cm long. What force does it represent?
5. Which is the metric unit of force, roughly equal to the weight of one apple?
Pulling a Stuck Canoe
A canoe is stuck in mud at the edge of a lake. Two campers tie ropes to the bow and pull horizontally. The forces they exert are shown in Table 1.
Table 1: Forces on the Canoe
| Camper | Force (N) | Direction |
|---|---|---|
| Ana | 120 | East |
| Ben | 80. | East |
What is the resultant of the two forces the campers exert on the canoe?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C2. Ben accidentally walks around the canoe and pulls west with 80. N while Ana still pulls east. What is the resultant?
C3. A student draws the resultant of the two campers’ forces (both pulling east) as an arrow using a scale of 1.0 cm = 25 N. Substitute numerical values into a mathematical representation that can be used to determine the length of the resultant arrow. Then calculate the length.
C4. A third camper, Dee, ties a rope to the stern and pulls west with 250 N while Ana and Ben both pull east. Taking east as to the right, choose the direction of the resultant of the three campers’ forces, and determine its magnitude.
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C5. Ben moves so his rope is at 90° to Ana’s. What is the magnitude of the resultant now?
C6. A fourth camper arrives to help free the canoe. Describe how all of the campers should direct their pulls to produce the largest possible resultant force, and explain your reasoning using vectors.
