How Forces Affect Motion · Lesson 2 of 8
Balanced and Unbalanced Forces
“Several forces can act together, but motion responds to their single combined result: the net force.”
• Identify multiple forces acting on an object. • Distinguish balanced forces from unbalanced forces. • Calculate net force for forces along one straight line. • Determine the direction of the net force. • Predict whether the velocity of an object can change.
A book resting on a table is being pulled down by the Earth, yet it does not fall through the table. A floating ball is pulled down by gravity, yet it remains at the water surface. These examples remind us that visible motion cannot be explained by naming only one force. The combined effect of all forces acting on the chosen object must be considered.
More Than One Force
When a box is pushed across a floor, the push acts forwards while friction acts backwards. At the same time, gravity pulls the box down and the floor pushes it up. Each force has its own source and direction. A force diagram becomes meaningful only after we clearly choose the object being studied and include forces acting on that object.
Net force is the single force that represents the combined effect of all the forces acting on an object.
Balanced Forces
Forces are balanced when their combined effect gives zero net force.
Two equal forces acting in opposite directions along the same line balance each other. A rope in tug of war remains at rest when the two teams pull with equal magnitude in opposite directions. A barbell held steadily by a weightlifter is another example: its downward weight is balanced by the upward force from the lifter.
Balanced forces do not mean that no forces exist. They mean that the forces present combine to give zero net force. This distinction is essential. Large forces can be balanced, just as small forces can be balanced. What matters is their combined magnitude and direction.
Unbalanced Forces
Forces are unbalanced when they combine to produce a non-zero net force.
If one tug-of-war team pulls harder, the two opposing forces no longer cancel. The rope has a net force towards the stronger team, so its velocity begins to change in that direction. An unbalanced force can start a stationary object, change the speed of a moving object, or turn its motion.
Forces In The Same Direction
When two forces act along the same line and in the same direction, their magnitudes add. If two people push a stalled car towards the east with forces of 120 N and 180 N, the net horizontal force is 300 N towards the east, provided other horizontal forces are being ignored.
Forces In Opposite Directions
When forces act along the same line in opposite directions, subtract the smaller magnitude from the larger. The net force points in the direction of the larger force. Direction is part of the answer; writing only the difference is incomplete.
Problem
Two people push a car towards the right with forces of 140 N and 210 N. Find the net force.
- 1.Choose the car as the object.
- 2.Check the directions: both forces point towards the right.
- 3.Add the magnitudes: 140 N + 210 N = 350 N.
- 4.Attach the common direction to the result.
- 5.The net force is 350 N towards the right.
Problem
A block is pulled with 10 N towards the right and 6 N towards the left. Find the net force.
- 1.Choose right as the positive direction.
- 2.Write the directed forces as +10 N and −6 N.
- 3.Combine them: +10 N − 6 N = +4 N.
- 4.The positive sign means the result points right.
- 5.The net force is 4 N towards the right.
Problem
A weightlifter holds a barbell stationary. The barbell weighs 294 N. What upward force acts on it if the forces are balanced?
- 1.The barbell remains steady, so its acceleration is zero.
- 2.Forces are balanced, so the net force is zero.
- 3.The downward force is 294 N.
- 4.An equal upward force is required to cancel it.
- 5.The lifter exerts 294 N upwards on the barbell.
Rotation As A Different Effect
Equal and opposite forces do not always prevent every kind of change. If they act at different points on an extended object, they may turn it. Equal opposite pushes on the ends of a handlebar can rotate it even though the total force is zero. A fuller study of rotational effect requires the turning effect of force, but the example shows why the points and lines of action can matter.
A Reliable Method For Net-Force Problems
First choose the object. Next list only the forces acting on that object. Draw arrows and select one direction as positive. Give forces in the opposite direction negative signs. Add the directed values. Finally, interpret the sign and write both magnitude and direction. This method prevents the common mistake of subtracting forces that actually point in the same direction.
Quiz
Which description best matches Net Force?
Which description best matches Balanced Forces?
Which term matches this description: Net force is the single force that represents the combined effect of all the forces acting on an object.
Which term matches this description: Forces are balanced when their combined effect gives zero net force.
Which statement is a key takeaway from this lesson?
Practice Problems
- A box experiences 18 N right and 18 N left. State the net force and whether the forces are balanced.
- A cart experiences 25 N east and 9 N west. Calculate the net force with direction.
- Two students push a trolley north with 40 N each. Ignore resistance and determine the net force.
- Explain why a floating ball may have forces acting on it even though it remains at rest.
Key Takeaways
• Motion depends on the net force, not on one selected force. • Balanced forces produce zero net force. • Unbalanced forces produce a non-zero net force. • Same-direction forces add. Opposite-direction forces subtract. • The net force points in the direction of the larger opposing force.
Friction is often the hidden force that changes an apparently simple push into a balanced or unbalanced situation.