Forces 101

Forces 101

A force is a push or a pull. Forces make things speed up, slow down, change direction or change shape, and nothing in mechanics happens without one. They are measured in newtons (N), with a newtonmeter, and they always have a direction. That makes a force a vector, which is why we draw forces as arrows: the length shows the size and the way it points shows the direction. Almost every mistake in this topic comes from forgetting that second half. A force with no direction attached is only half an answer.

Contact and non-contact

Forces divide into two families, and the test is simply whether the two objects have to be touching:

Label the forces

Four forces act on this box. Drag each label onto the correct arrow: the one pulling it down, the one pushing up from the surface, the applied push, and the force opposing the push.

Acting across a gap

Select ALL THREE situations in which a NON-CONTACT force is doing the work.

• A compass needle swings round when a current flows in a nearby wire
• A dropped ball speeds up as it falls
• A balloon rubbed on a jumper clings to the wall
• A book rests on a table without falling through it
• An open parachute slows a skydiver
• A rope holds up a child on a swing

Which force is acting?

Scalars and vectors

Every quantity in physics is one or the other, and which one it is decides whether a direction belongs in your answer:

Two fives

Two forces of 5 N each act on a box. Why can you not simply say the resultant is 10 N?

• Because force is a vector: 10 N only follows if both point the same way, and if they oppose each other the resultant is 0 N
• Because forces are always subtracted rather than added
• Because 5 N forces are too small to combine
• Because the mass of the box has not been given

Weight is a force

Weight is the force of gravity acting on an object, and like every force it is measured in newtons: W = m g, weight in N = mass in kg x gravitational field strength g, which is 9.8 N/kg on Earth Mass is the amount of matter in something, measured in kilograms, and it is a scalar that does not change wherever you take it. Weight is a vector, it points downwards, and it changes whenever g does. So an astronaut who travels to the Moon has the same mass they set off with, and weighs about a sixth as much. Everyday speech treats the two words as interchangeable; physics does not, and exam questions are built on the difference.

Work out the weight

A bag has a mass of 5 kg. Using W = m g with g = 9.8 N/kg, what is its weight, in newtons?

And on the Moon

An astronaut takes a toolkit of mass 2 kg to the Moon, where g is about 1.6 N/kg. What is the toolkit's weight there, in newtons?

Adding forces up

Several forces acting along one line can be replaced by a single resultant force with exactly the same effect. There are only three cases. Same direction: add them. 6 N right and 4 N right give a resultant of 10 N right. Opposite directions: subtract the smaller from the larger, and the resultant points the way of the larger. 6 N right and 4 N left give 2 N right. Equal and opposite: the resultant is 0 N. The forces are balanced, and the object carries on doing whatever it was already doing. Give the direction every time. A resultant of "2 N" is an incomplete answer, because the resultant is a vector and the direction is half of what it is.

Find the resultant

A box is pushed to the right with 10 N while friction acts to the left with 4 N. What is the SIZE of the resultant force, in newtons? (Its direction is to the right.)

Deadlock

Two people push a heavy crate from opposite sides, each with 200 N. What is the resultant force, and what happens to the crate?

• The resultant is 0 N: the forces are balanced, so the crate carries on doing whatever it was already doing
• The resultant is 400 N, because the two pushes add together
• The resultant is 0 N, so the crate must be stationary
• The resultant is 200 N, since only the stronger push counts

The force rules

A force is a push or a pull measured in _____, and it is a vector, so it always has a direction. Contact forces need the objects to be touching; gravity, magnetism and _____ forces act across a gap. Weight is found from weight = mass × gravitational field _____, so mass stays the same on the Moon while weight does not. When two forces act in opposite directions along a line you _____ them to find the resultant, and if they are equal the resultant is zero.