Force and Motion

Background Information

Speed

v (speed) = s (distance) / t (time)

The SI units are metres per second: m/s. (Note: 30mph = 13.5m/s.)

When measuring speed we measure the distance travelled in a certain time. This gives the average speed during that time period. The speed may have changed during that time period so the average speed does not give a complete picture, except for objects travelling at a constant speed. The smaller the time period we measure the closer the average speed is to the speed at any point (instantaneous speed).

A linear air track is almost frictionless, so the vehicle glides at a constant speed. A distance–time graph for the vehicle will show the same distance travelled in equal time intervals, and this gives a straight line. The gradient, or slope, of the line is the speed of the vehicle. The faster the speed the steeper the slope.

Acceleration

a (acceleration) = v (velocity) / t (time)

The SI units are metres per second per second, or metres per second squared: m/s/s or m/s². (Note: 0mph to 60mph in 5s = 5.4m/s/s and objects fall with acceleration of about 10m/s/s.)

The linear air track vehicle can be made to accelerate by attaching it to a weight via a pulley, so the weight pulls with a constant force, giving a constant acceleration. The distance–time graph of an accelerating object will be a curve. The increase in speed will show as an increase in gradient, so instead of a straight line the line will curve, becoming steeper. An object slowing down will curve to become less steep, but distance will always increase unless the object is reversing.

Gravity and Falling

Gravity is a force downwards which will accelerate all masses downwards at 10m/s² (actually 9.8m/s² although this is not a constant, and varies slightly between the poles and equator, due to the effect of the Earth’s rotation. It also varies with distance from the centre of the Earth, but only very slightly.)

A shuttle or satellite is kept in orbit by the force of gravity, as are the astronauts. Because they are all falling together (in free fall) the astronauts appear to be in zero gravity. This is how things would behave in regions of space where there is no gravity. (If the astronauts were really in zero gravity, or weightless, they would drift off into space and not stay in orbit.)

All masses are attracted by gravity with the same acceleration. A 1kg and a 2kg weight will fall with the same acceleration. However air resistance is a force which depends on the shape, size and speed of the object. Any difference in the speed of falling objects will be due to their different air resistance. In a vacuum, a feather and a ball bearing fall with the same speed. On the Moon, the gravity is less, only one sixth that of the Earth, because the Moon has less mass. However things will all fall at the same speed, because there is no air resistance.

Consider the case of a melon being dropped from the top of a 20m building. After one second it has accelerated from a speed of 0m/s to 10m/s and will have travelled 5m. Between one and two seconds it has accelerated from 10m/s to 20m/s and will have travelled 15m.