Add forces on a force diagram and predict how motion changes

Learning goal: Describe motion relative to a reference point, add the forces acting on an object to find the net force, draw and read a force diagram, and use balanced or unbalanced forces to predict whether an object's speed or direction will change, including the effects of kinetic friction and drag.

Motion is measured from a reference point. Before asking what changes an object's motion, decide what its motion is. The motion of an object is always measured with respect to a reference point. A pencil resting in your hand is at rest relative to you, but to an observer in a car driving past, the pencil is moving backward at the car's speed. A passenger walking toward the front of a moving train is moving slowly relative to the train and quickly relative to the platform. None of these descriptions is wrong; each names a different reference point. In this lesson, unless stated otherwise, the reference point is a fixed spot on the ground.

Forces can be added. A force is a push or a pull, and every force has a size, called its magnitude, and a direction. When several forces act on one object, their combined effect is what influences the object's motion. The net force on an object is the sum of all the forces acting on it, taking direction into account. Two forces in the same direction add: pulls of 30 N and 20 N to the right combine to 50 N to the right. Two forces in opposite directions partly cancel: a 50 N pull to the right and a 20 N pull to the left combine to 30 N to the right, because 50 minus 20 leaves 30 in the direction of the larger force. Two forces cancel to a net force of zero only when they are equal in strength and act in opposite directions; with three or more forces, what matters is that the sum in each direction is zero. The newton, N, is the unit of force used on the diagrams; at this grade it is used only to compare and add forces, not in equations.

Balanced and unbalanced. If all the forces on an object cancel, the forces are balanced and the net force is zero. A balanced object maintains its current motion, both speed and direction. That has two cases that students often treat as one. If the object is stationary, it stays stationary: a book on a table has gravity pulling it down and the table pushing it up with equal force, so it does not move. If the object is already moving, it keeps moving in the same direction at the same speed: a puck gliding on an air-hockey table with almost no friction travels in a straight line at a steady speed with no one pushing it. When the net force is nonzero, the forces are unbalanced and the object's motion will change: its speed, its direction, or both. A nonzero net force in the direction of motion makes the object speed up; a net force opposite to the motion makes it slow down; a net force that points toward one center while the object is moving sideways to it makes the path curve, which is how a moon can orbit a planet or a ball on a string swings in a circle.

The sustained-force misconception. Many people believe an object needs a continuing force to keep moving. Everyday experience seems to support it: stop pushing a box and it stops. But the box stops because kinetic friction is still acting on it after the push ends, so the net force is now unbalanced and opposite to the motion. Where friction is very small, as for the puck or a cart on a smooth level track, an object keeps moving with nothing pushing it. A force is needed to change motion, not to maintain it. Some textbooks name this idea Newton's first law; the name is less important than the reasoning.

Friction and drag. Kinetic friction is a force that opposes sliding between two surfaces that are in contact and moving relative to each other. It acts on the sliding object in the direction opposite to the object's motion relative to the surface. Drag is a similar force that opposes the motion of a solid object moving through a fluid, a gas or a liquid: air resistance on a cyclist, water resistance on a swimmer. Kinetic friction and drag affect the motion of objects and can bring moving objects to a stop unless another force is exerted in the direction of motion. Drag grows as an object moves faster, which is why a falling skydiver eventually stops speeding up: drag increases until it balances the pull of gravity and the speed then stays constant. Friction is sometimes helpful, letting shoes grip a floor and brakes stop a bicycle, and sometimes a nuisance, warming a bearing and wasting effort; engineers change surfaces, lubricants and shapes to increase or reduce it.

Force diagrams. The forces acting on an object can be modeled by a force diagram: an isolated picture of the object with one arrow for each force acting on it. Each arrow starts at the object, points in the direction of the force, and has a length proportional to the magnitude of the force. Only forces on the object appear; the object's own push on the floor belongs on the floor's diagram, not this one. From the diagram you can identify the direction and relative size of the net force and predict its effect. At this grade, diagrams may have forces in both the horizontal and vertical directions, but the forces will be unbalanced in only one of those directions at a time.

A worked model. The diagram shows a crate on a level table with four forces: a push of 6 N to the right, kinetic friction of 2 N to the left, gravity of 10 N downward, and the table's upward support of 10 N. Add the vertical forces: 10 N up and 10 N down cancel, so the crate neither rises nor sinks. Add the horizontal forces: 6 N right and 2 N left give a net force of 4 N to the right. The net force is nonzero and points in the direction of the push, so the crate speeds up toward the right. If the push is reduced to 2 N, the horizontal forces balance and the crate, if already sliding, continues at a steady speed; if the push stops entirely, only the 2 N friction remains and the crate slows to a stop. Which of these happens depends only on the sum, not on how many arrows there are.

Mass, qualitatively. The same net force does not change every object's motion by the same amount. From earlier grades: for a given net force, an object with more mass changes its motion less, and for a given object a larger net force produces a larger change. That relationship is stated in words here; the equation that makes it exact is developed in high school physics and is not part of this grade.

Investigation: a tug-of-war on a cart. Materials: a low-friction cart or a smooth wooden block on a smooth table, two spring scales or two identical elastic bands, string, safety glasses (an elastic band can snap). Steps: attach one string to each end of the cart; have two students pull gently in opposite directions and read both scales while the cart stays still; then have one student pull slightly harder and note which way the cart starts to move; finally pull with both scales in the same direction and compare the start of motion with a single pull. Record scale readings, the direction of motion and whether it started, sped up or stayed still. A result that supports the claim: the cart stays put when the readings are equal and starts to move toward the larger reading when they differ. What the model cannot show: the scales read the pulls but not the friction on the cart, so a small difference in readings may not start motion; the diagram must include the friction arrow to explain that.

Worked example 1 — sled on packed snow. A sled is pulled with a 50 N force to the right while kinetic friction on the runners is 20 N to the left. Gravity and the snow's upward support are equal and cancel. Horizontal net force: 50 N minus 20 N leaves 30 N to the right. The net force is nonzero and points along the motion, so the sled speeds up. If the puller lets go, only the 20 N friction remains, pointing opposite to the motion, so the sled slows down and eventually stops; it does not stop instantly, because a force changes motion over time rather than switching it off.

Worked example 2 — balanced but moving. A box is sliding across a floor while a student pushes it with 8 N to the right and kinetic friction on it is 8 N to the left. Gravity of 15 N down is balanced by the floor pushing up with 15 N. Every pair cancels, so the net force is zero and the forces are balanced. The box therefore keeps its current motion: it continues sliding at the same speed in the same direction. A balanced object is not necessarily at rest; balanced means "motion unchanged", which includes steady motion.

Worked example 3 — two teams pulling a rope. Team A pulls a rope with 300 N to the left and Team B with 300 N to the right. The two horizontal forces are equal and opposite, the net force on the rope is zero, and the rope's motion does not change. If Team B increases its pull to 340 N, the net force is 40 N to the right and the rope starts to move toward Team B. A rope at rest starts to move toward the larger force (a rope already moving would have its motion change toward that side); what decides it is the larger force, not whichever team is pulling "harder than before".

Worked example 4 — reading a diagram with vertical and horizontal arrows. A lamp hangs from a cord: gravity 12 N down, cord pull 12 N up, and a brief sideways gust pushes it with 3 N to the left with no horizontal force opposing it. At the instant the gust acts, the vertical forces balance, so the lamp's vertical motion does not change: it was hanging still, so it stays at that height for now. The horizontal net force is 3 N to the left, so the lamp begins to swing left. The forces are unbalanced in only the horizontal direction, and the prediction follows from that one direction alone; as the lamp swings, the cord's pull changes direction, so the diagram describes only that first instant.

Representation task: draw four force diagrams. For each situation, draw the object as a box, add one labeled arrow per force with lengths in proportion, and write the net force with its direction: (a) a book at rest on a table; (b) a puck gliding on an air-hockey table where friction is small enough to ignore; (c) a cyclist moving at a steady speed on a level road, where the road pushes the bike forward through the turning back wheel (draw this as the forward push) while drag and friction act backward; (d) a ball just after it leaves a thrower's hand, moving upward, with drag ignored. Under each diagram, state whether the object's speed, its direction, both or neither will change, and why.

Independent performance: predict, test and explain. Choose a small object (a toy car, a block or a cart) and a level surface. Predict, with a force diagram, what happens when it is (1) pushed once and released, (2) pushed steadily so that it moves at constant speed, and (3) pushed steadily harder than in (2). Carry out the three trials, keeping the same object and surface, and record what you observed: started, sped up, steady, slowed, stopped. Success criteria: each diagram includes gravity, the surface's upward support, friction opposite the motion (kinetic friction for a sliding block; for a wheeled car, friction in the axles and rolling resistance, which also act opposite to the motion) and any push; each prediction names the direction of the net force and the resulting change; the write-up explains why the object in trial (1) slowed and stopped without anyone pushing it backward, and states one thing the diagram cannot show (for example, how quickly the change happens).