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You know forces can tie or have a winner. A force also has a direction, which is why it is called a vector. Dog A pulls a sled forward with 40 N, and Dog B pulls the same way with 30 N.
What is the resultant force on the sled?
Resultant Forces
Describe forces as vector quantities with both magnitude and direction, distinguish between balanced forces (zero resultant, no change in motion) and unbalanced forces (non-zero resultant, causes acceleration or deceleration)
What a learner can do afterwards
- Explains what a vector quantity is and why force is a vector
- Calculates the resultant force when two forces act in the same or opposite directions on an object
- Explains what happens to an object's motion when forces are balanced vs unbalanced
- Draws free body diagrams showing all forces on a stationary object (e.g. a book on a table)
1 · Read
A force isn't just how hard you push or pull. It also has a direction. Anything with both a size and a direction is called a vector quantity. Force is a vector, so a 5 newton push to the right is not the same as a 5 newton push to the left, even though the size is equal.
Try it together
Dog A pulls a sled forward with 40 newtons. Dog B pulls the same sled, same direction, with 30 newtons. Because both forces point the same way, you add them: 40 N + 30 N = 70 N forward. That total is called the resultant force.
Good to know
To find a resultant force: if the two forces point the same way, add them. If they point opposite ways, subtract the smaller from the larger. The resultant points in the direction of the bigger force.
Try it together
A book sits still on a table. Gravity pulls it down. The table pushes back up with a normal force of equal size. These two forces are balanced, so the resultant force is 0 N and the book doesn't move. If you then push the book sideways harder than friction can hold it, the forces become unbalanced and the book accelerates.
With three or more forces, add the ones pointing the same way first, then subtract the rest. You can also work backwards from the resultant. If an object stays still, the resultant is 0 N, so the forces must balance: a 16 N pull to the left needs a 16 N pull to the right to cancel it. If the resultant is not zero, the object accelerates the way the resultant points: 44 N to the right against 27 N to the left leaves 44 N - 27 N = 17 N to the right, so the object moves right.
Same-direction forces add together; opposite-direction forces subtract. A zero resultant means balanced forces and no change in motion; a non-zero resultant means unbalanced forces and acceleration.
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Take it off screen
Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
Then practise
28 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.