# 03Non-zero force changes speed

Mo03PN of the Motion topic
• ## 01 Changing motionsMo03PNnugget01 Introduction

### The ice-skater

Imagine that you are watching an ice-skater. She stands motionless in the centre of the ice before pushing off and gliding out towards the edge of the rink. At first she is stationary and she ends up moving at more-or-less constant speed. Somewhere in between she must have speeded up (or accelerated) and it is this changing motion that we are interested in here. Everyday experience offers countless examples of changing motion, for example the sprinter accelerating out of their blocks; a football being kicked from the penalty spot; a train slowing down as it enters the station. We're sure you'll be able to add many to the list.

The basic condition for an object to be speeding up or slowing down is summarised in Newton's first law of motion:

If an object is either speeding up or slowing down, there must be a resultant force acting on it.

In other words, if the forces acting on an object do not all add to zero, then the object has a changing motion.

Forces do not add to zero  → motion will change.

• ## 02 Forces acting and changing motionMo03PNnugget02 Exposition

### Forces for speeding up and slowing down

Consider an object moving on a horizontal surface, maybe a pencil case that you are pushing across the table. For such examples the essential forces to consider are the forward driving force (your push) and the retarding force acting in the opposite direction (due to friction between the pencil case and the table). Let's look closely at these two forces:

• If the driving force is greater, the object will speed up.
• If the retarding force is greater, the object will slow down.
• If the forces are the same size, then the object continues at a constant speed (it's in equilibrium).

It is the driving force which starts the object moving. As long as the driving force is greater than the retarding force, the object will speed up. If the driving force is removed, the retarding force will continue to act on the object until it eventually comes to rest (the pencil case soon comes to a halt if you stop pushing it).

### The cyclist

The forces acting on a cyclist moving at constant speed add to zero. As soon as the cyclist stops pedalling, the driving force disappears. The frictional forces (drag and slip forces) continue to act and the effect of these retarding horizontal forces will be to slow down the cyclist.

Resultant force  → change in motion.

• ## 03 Floating and sinkingMo03PNnugget03 Exposition

### Buoyancy forces cause things to rise in fluids

Here are four situations where a non-zero resultant force predicts a change in motion:

• Hold some balsa wood underwater. The buoyancy force will be greater than the gravity force. Remove the force applied by your hands. The block rises.
• Hold a helium filled balloon and its tether. The buoyancy force is again greater than the pull of gravity, so if you release the tether the balloon will rise.
• Hold a stone below the water. The buoyancy force is less than the pull of gravity. Release the stone and it will sink.
• Hold a tennis ball in air. The buoyancy force is less than the pull of gravity. Release the ball and it will sink.

In all cases the resultant force determines the change in motion: from rest to moving off in the direction determined by the sum of the forces.

A volume of warmer air or warmer water can take the place of the balsa wood or the helium filled balloon. The buoyancy forces on it are greater than the gravity forces, so it starts to rise. Similarly a volume of colder fluid will sink, as the gravity force will be greater than the buoyancy force.

These are convection currents.

Are convection currents important? Yes! Convection streams dominate our global environment, appearing in ocean currents and the winds and driving both plate tectonics and the dynamo that produces the Earth's magnetic field.

### Convection currents: volumes of warmed fluid moving around

In the process of convection, volumes of already warmed liquids and gases move around. Convection works by convection currents. These are streams of liquids and gases which carry warm volumes from a hot place to cooler parts of the system. So, as with conduction, convection still relies on particles to shift the energy (SPT: Energy topic). The crucial difference from conduction is that in convection there is mass movement of the particles.

How do convection streams get started, and what drives them? It's all a matter of floating and sinking.

Energy shifted from the thermal store associated with the hot object (such as the radiator in our example) to the thermal store of a volume of particles warms that volume (the air above the radiator). This process is conduction: the pathway is heating by particles. The volume of air expands, but still contains the same number of particles (in other words its density is reduced). This air then rises, floating up through the cooler, denser air around it. As the air moves it takes a quantity of energy away with it. It's not a case of heat rising, but of the warmed air floating up through the surrounding cooler air.

As the warm air rises, cool air moves in to take its place. The process is continuous, with a rising stream of air moving away from the hot radiator. This upward movement is a clear pointer to distinguish convection from conduction. Although the mechanism of convection has been described here in relation to the warm air rising from the radiator example, precisely the same processes occur when convection currents are set up in liquids.

• ## 04 The motion changes for just as long as a resultant force is actingMo03PNnugget04 Exposition

### Speed changes require a resultant force to act

An important point to recognise in thinking about objects speeding up and slowing down is that the motion changes only for as long as a resultant force is acting on the object. Taking our first example of the ice skater, she speeds up only while she is pushing with her driving leg. As soon as she stops pushing, she stops speeding up. If she wants to gain a high final speed, she pushes with a big force and maintains her push for as long as she can.

If you hit a ball with a tennis racquet, the ball speeds up just as long as the strings are in contact with it. If you want the ball to fly away at top speed, you must hit it hard and for as long as possible. Expert tennis players achieve this by following through on their stroke (as do golfers, footballers and so on).

• ## 05 Different kinds of driving forcesMo03PNnugget05 Exposition

### Driving forces

Driving forces can be exerted by many different parts of the object's environment.

• Gravity is the driving force for an object falling towards the ground.
• A skate-boarder relies on the ground pushing on the sole of her shoe to drive her skateboard along.
• A shopper in the supermarket pushes against the ground as they walk and their hands provide the force which drives their trolley forward.
• A car, scooter or motorbike get going from a driving force through gripping the road surface.
• ## 06 Acceleration and decelerationMo03PNnugget06 Expansion – lead me deeper

### Acceleration

Please take care with acceleration. This note explains some concerns.

The word acceleration is used to describe motion which changes. It is common to use acceleration to mean speeding up and the word deceleration to mean slowing down. Strictly speaking, however, acceleration describes both types of motion. Speeding up might be referred to as positive acceleration and slowing down as negative acceleration. However, raising this point may confuse pupils at this level, with little addition to their understanding. Later in their studies of science, pupils will be introduced to a more formal definition of acceleration in terms such as:

acceleration = change in speedtime for change

(units of acceleration: metre / second in each second, or metre / second 2).

If they are introduced to an even more precise definition, it will be that acceleration is change of velocity each second. Pupils will also measure accelerations and resultant forces and relate them to each other. Sir Isaac Newton, in his second law of motion, saw that the greater the resultant force, the greater will be the resulting acceleration of a fixed mass. This finding is summarised in the relationship:

Fm = a

Where F is force in newton; m is mass in kilogram; a is acceleration in metre / second 2.

• ## 07 Terminal speed – the skydiver's storyMo03PNnugget07 Exposition

### The skydiver's story

The same ideas about resultant forces can be used to explain the motion of a skydiver falling through the air. The skydiver story is included here so you can check your own understanding. It is a challenge to follow the description of forces but getting to the end will provide you with a sense of achievement! The skydiver's story is told in four stages. Match the stages to the diagrams.

Skydiving stage 1 – the leap

Once committed, the skydiver leaps out of the plane and starts to descend. Gravity provides the downward force on the diver and as a result down they go. During this stage they speed up just as any falling object does. The downward force, the pull of gravity, is the dominant force. There is a drag force – as a result of moving through the air. During this first phase the driving force is larger than the retarding force. The resultant force is not zero. Here, the forces acting on the skydiver do not add to zero.

We'll say more about such non-zero resultant forces in episode 03.

Skydiving stage 2 – terminal speed

As the skydiver falls and speeds up, the air rushing past them exerts a greater drag force. At a certain, very high, speed the upward drag force is equal to the pull of gravity on them. Once this speed is reached there is no more speeding up. The skydiver continues to fall at this terminal speed. The resultant force on the skydiver is zero: equilibrium.

Skydiving stage 3 – the parachute opens

At a predetermined height above the ground the parachute is opened. The huge canopy area results in a much larger drag force, as the area of the falling object suddenly increases. The upward force acting on the skydiver increases. The diver will sense this sudden change. Their downward progress is slowed down due to the resultant force acting on them. As the diver slows down, the upward drag force reduces until…

Skydiving stage 4 – a new equilibrium

… at a new, much slower speed, the diver reaches a new equilibrium where the driving force is once again opposed by an equal but opposite retarding force. The diver continues to fall steadily to Earth under the action of these balanced forces.
• ## 08 When the resultant force is not zeroMo03PNnugget08 Summary

### Resultant forces change motion

• Most moving objects are acted upon by a driving force and retarding (often frictional) forces acting in the opposite direction to the motion.
• When these forces add to zero (the resultant force is zero), the object maintains a constant speed.
• When the forces do not add to zero (there is a non-zero resultant force), the object will either speed up, slow down or change direction.
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