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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?
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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.
More to read
5.1 Forces
A force is a push or a pull. It has both magnitude (size) and direction. That makes it a vector. Vectors are added differently than regular numbers. You must consider direction. A force of 10 N to the right plus 10 N to the left gives a net force of zero. A force of 10 N right plus 10 N right gives 20 N right.
How to Find Net Force: 9 Steps (with Pictures)
The resultant force is the single force that has the same effect as all the forces acting together. To find it, add all the forces as vectors. Forces in the same direction add. Forces in opposite directions subtract. Forces at angles use the parallelogram rule or add components. If the resultant force is zero, the forces are balanced. The object does not accelerate. If the resultant force is not zero, the forces are unbalanced. The object accelerates in the direction of the resultant force.
5.3 Newton's Second Law
A free-body diagram shows all the forces acting on an object. Draw the object as a dot or box. Draw arrows for each force. The length of the arrow shows the magnitude. The direction of the arrow shows the direction. Label each force: weight, normal force, friction, tension, applied force. Then add the forces to find the resultant. If the object is not accelerating, the forces are balanced and the resultant is zero.
Newton's first law
When forces are balanced, the net force is zero. The object stays at rest or moves at constant velocity. When forces are unbalanced, there is a net force. The object accelerates. Acceleration = net force / mass. A book on a table has weight down and normal force up. These are equal and opposite, so they are balanced. The book does not move.
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Where it sits
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