Force and Newton's Laws

Mechanical Comprehension asks the same physics as General Science and asks it about equipment. This lesson is the foundation: what a force does, and what happens when several act at once.

Force and net force

A force is a push or a pull, measured in pounds or newtons, and it has a direction as well as a size.

The net force is what the forces add up to.

• Same direction: add them. Two people pushing a crate with 60 and 40 pounds in the same direction apply 100 pounds.
• Opposite directions: subtract. The same two pushing against each other give a net 20 pounds, in the direction of the larger.
• Equal and opposite: zero. Nothing changes.

Only the net force changes motion. That is the first law restated, and it is the most useful idea in this subtest.

Equilibrium

An object in equilibrium has zero net force, and it is either at rest or moving at a constant velocity.

Equilibrium does not mean stationary. A crate sliding at a steady speed across a floor is in equilibrium: the push forward exactly equals the friction backward. A question describing constant speed is describing balanced forces, whatever the speed is.

A book on a table is the simplest case: gravity pulls down, the table pushes up with an equal normal force, and the book stays put.

An elevator moving at constant speed is in equilibrium; an elevator accelerating is not, which is why a scale inside it reads differently.

The three laws, applied

First law - inertia. An object keeps doing what it is doing unless an unbalanced force acts. Inertia depends on mass, so a loaded truck is harder to start and harder to stop.

Second law - F = ma. More force gives more acceleration; more mass gives less. Rearranged, a = F / m, which is the form most questions need.

Third law - action and reaction. Every force has an equal and opposite partner acting on the other object.

The third law is the one this subtest asks about most, because machinery is full of it: a wrench pushes a bolt and the bolt pushes the wrench; a wheel pushes the ground back and the ground pushes the vehicle forward; recoil pushes a gun back as it pushes the bullet out.

They never cancel because they act on different things. A question suggesting they do is testing exactly that.

Tension in ropes and cables

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This is the highest-value idea in the lesson, because it is the one that is surprising.

Two cables supporting a load share it - but only when they hang straight down does each carry exactly half.

The wider the angle between them, the more tension is in each one. As the cables approach horizontal, the tension rises without limit, and it can far exceed the weight being held.

The reason: each cable's pull has a vertical part and a horizontal part. Only the vertical parts hold the load up. As the cable flattens, its pull is mostly horizontal, so it has to pull much harder for its shrinking vertical part to do the job.

A question showing the same load on cables at different angles wants that relationship, and the answer is always that the flatter arrangement has the higher tension.

The everyday version: a clothesline pulled tight will snap under a load that a sagging one holds easily, and a tow strap between two vehicles is most dangerous when it is nearly straight.

Common forces

Tension pulls; compression squeezes. A cable can only pull, which is why a crane's cables are in tension and its jib is in compression. That pairing is asked in the structures lesson too.

The four forces of flight

A jet engine works by Newton's third law: it throws gas backward and is pushed forward.

Terminal velocity is reached when air resistance grows to equal gravity. The net force is then zero, so the faller stops accelerating - a 150-pound skydiver at terminal velocity has a net force of 0 pounds. A parachute works by greatly increasing air resistance, which lowers that terminal speed.

Mass in slugs

In the US system, force is in pounds and mass is in slugs. F = ma still holds:

A cart accelerates at 5 feet per second squared under a 40-pound force. Its mass is 40 / 5 = 8 slugs.

More mass, more inertia: a loaded semi-trailer needs far more force than a car to accelerate at the same rate, and a heavy aircraft needs a longer runway. A tennis ball, at the other extreme, has very little.

What you can skip

Across the 87 questions on this topic in our bank:

• Metric force units. Newtons and kilograms never appear here. The questions use pounds, feet and slugs.
• Free-body diagram drawing never appears, and vector components come up once. Adding forces along one line, and the one right-angle case, is all that is asked.

Where people lose points

Thinking equilibrium means stationary. Constant velocity qualifies.

Thinking action and reaction cancel. Different objects.

Adding forces without regard to direction.

Assuming two cables always share a load equally. Only when symmetric, and the share is not half unless they hang vertically.

Thinking a flatter cable carries less. It carries far more.

Confusing mass and weight, as the General Science lesson covers.

Work one in under a minute

A 200-pound load hangs from two cables. In arrangement A the cables are nearly vertical; in arrangement B they are spread wide, close to horizontal. Which arrangement puts more tension in the cables?

Arrangement B, by a large margin.

In A, each cable's pull is almost entirely vertical, so each carries roughly 100 pounds.

In B, most of each cable's pull is horizontal and useless for holding the load up, so the cable must pull very hard for its small vertical component to reach 100 pounds.

Flatter means more tension, always, and the effect grows without limit as the cable approaches horizontal.

Where this leads

Every machine in this subtest is an arrangement of forces, and the tension idea reappears in pulleys and in structures.