Balanced forces and changes in motion

Balanced does not mean stopped

Two forces on the same object balance when they have equal strengths and opposite directions. Both individual forces still act. Their combined effect does not change the object’s straight-line motion

1. 1Initially at rest If all forces balance, an object at rest stays at rest
2. 2Already moving If all forces balance, an object keeps moving at the same speed in the same direction
3. 3Everyday stopping A real rolling cart usually slows because resistance acts. Motion itself does not need an ongoing unbalanced forward push

Read two states of one cart

The next display compares a cart’s initial state with an observation at a selected time. Solid arrows show individual cable forces. Dashed cues show travel direction, not force or speed

1. 1Read the units Time is in seconds (s), position in metres (m), and speed in metres per second (m/s). A steady speed of 2 m/s covers 2 metres each second
2. 2One track scale Both tracks show the cart centre on the same fixed 0–10 m scale. Position tells where it is; the separate speed and direction tell how it is moving
3. 3The model Cable pulls stay constant. Horizontal resistance is neglected. Gravity and support balance and are not drawn. Both pull settings use the same cart mass
4. 4Compare separate runs Each pull setting starts from the same initial state. Switching settings does not change a force partway through a run
5. 5Selected observations The time control selects a state; it is not a live animation. Track limits are scale limits, not walls that the cart hits

A cart is already moving right when equal opposite pulls act on it. With all other forces balanced, what do you predict?

Force direction and travel direction

Unequal opposite forces have a stronger combined effect in one direction. This changes motion. Compare that direction with the object’s current travel direction

1. 1With current motion A stronger effect in the travel direction makes the object speed up
2. 2Against current motion An opposing effect initially makes the object slow down while still travelling the same way. It does not reverse instantly
3. 3From rest An unbalanced effect can start an object moving in that direction

With equal pulls, compare 0 s, 2 s and 4 s. Then select the stronger left pull and compare 1 s, 2 s and 3 s. Each setting is a separate run with constant pulls. Gravity and support balance; horizontal resistance is neglected

With the stronger left pull selected, why can the cart still move right at 1 s?

This cart is moving left. The equal cable pulls continue. Gravity and support balance; ignore horizontal resistance. What happens next?

Start with its current leftward motion. Balanced forces do not change it

This cart is moving right. The left pull is stronger. Gravity and support balance; ignore horizontal resistance. Before it has time to stop, how does its motion change?

Separate current travel from the direction of the unbalanced effect

What happens at the stop?

With a 4 N left pull and a 2 N right pull, the cart stops at 2 s. The left pull is still stronger. At 3 s the cart is moving left: stopping for an instant did not make the forces balance

1. 1Principle Unbalanced forces change motion, including when an object is momentarily at rest
2. 2Evidence The left pull remains stronger at the stop. No collision or new force has been introduced
3. 3Prediction If these pulls continue, the cart begins moving left rather than remaining at rest
4. 4If the pulls change Suppose instead that the pulls become equal before the cart stops. It then keeps the speed and direction it has at that moment. It neither stops automatically nor returns to an earlier speed

A cart that was moving right is stopped for an instant. These unequal pulls continue. Gravity and support balance; ignore horizontal resistance. What happens just after this instant?

The motion cue describes one instant. Check whether the forces have also become balanced

A cart is slowing while moving left. Before it stops, its cable pulls are made equal and then held equal. Gravity and support balance; ignore horizontal resistance. What happens after this change?

A ball has left a hand and is still travelling upwards. Ignore air resistance. The diagram shows the only force acting on it. Before it reaches its highest point, how does its motion change?

Predict a change, not just a direction

First identify the current motion. Then compare all forces in the stated model. Balanced forces preserve speed and direction. An unbalanced effect with the motion speeds it up; one against it initially slows it down

1. 1Keep the time in mind A continuing opposing effect can slow an object, stop it for an instant and then reverse its motion. If forces change, make a new prediction from the current state
2. 2Explain your prediction Explain why the released rising ball slows: state the force principle, identify the downward force and upward travel, then connect them to decreasing upward speed
3. 3Scope These idealised examples hold the mass fixed. Next we compare how the same force affects objects with different masses