Motion, speed, acceleration and Energy

Motion, speed, acceleration and Energy 1. Motion 2. Forces at work 5. Movement means energy

1 On the Move Average speed , v, is measured in m/s (metres per second) = average speed (m/s) d = distance (m) t = time (s) This is sometimes written as ms-1. Average speed can be calculated from the formula:

To measure an average speed you must make certain measurements: The distance travelled must be measured and the time taken to cover that distance must also be measured. These values should then be used in the equation To find the average speed.

Example 1. If a baby can crawl over a distance of 20 metres in a time of 10 seconds, what is it’s average speed? Example 2 A sprinter in training has an average speed of 5m/s. How long does it take this sprinter to complete a 100m race?

The instantaneous speed is how fast that object is travelling at one particular point in time. To measure the instantaneous speed a very short period of time must be used If the driver of a car glances at their speedometer they are checking their instantaneous speed. The average speed of an object is not always the same as the instantaneous speed of the same object……..

Take the example of a car travelling through a busy town centre to reach a motorway with 70kms speed limit. When the car is in town it should be travelling at a maximum of 50 kms/h and the car will have to stop at various points such as traffic lights. When the car is stopped it has an instantaneous speed of 0 km/h. but it will have an average speed over the journey of maybe 15 km/h.

When the car is on a road with 70kms speed limit it will probably be travelling at a constant speed of 70 kms. This means that the instantaneous speed is always 70 kms. and for the time that the car is on the motorway the average speed is also 70 kms.

The acceleration of an object is defined as the rate of change of velocity of that object. i.e. acceleration is a measure of how much an object changes speed per unit time. As a formula: final speed (m/s) initial speed (m/s) Vf - Vi a= t acceleration (m/s2) time (s) N.B units of acceleration sometimes written as ms-2

Example 1 If a bus can accelerate from rest to 60 m/s in a time of 7 seconds. Calculate the acceleration of the bus . Solution: Vi=0 Vf=60 m/s t=7s a=?

Example 2 A sports car may be able to accelerate from rest to 100 km/h in 10 seconds. Find the acceleration of the car. Solution: Vi=0 Vf=100 km/h t=10s a=? The units of acceleration are different because speeds are measured in km/h not m/s.

Speed - time graphs A speed - time graph that shows a straight line of positive gradient shows the motion of an accelerating object. A speed - time graph that shows a straight line of zero gradient shows the motion of an object travelling at a constant speed. A speed - time graph that shows a straight line of negative gradient shows the motion of an decelerating object.

You must be able to use speed - time graphs to find accelerations. Example: Vi=10 m/s At time = 0s, the speed, Vi=10 m/s

You must be able to use speed - time graphs to find accelerations. Example: Vi=10 m/s At time = 9s, the speed, Vf=64 m/s Vf=64 m/s

You must be able to use speed - time graphs to find accelerations. Example: Vi=10 m/s Vf=64 m/s a = 6ms-2

You can also calculate distance from a speed - time graph. The distance travelled is equal to the area under the graph. e.g. 3 1 4 2 Step 1: split graph into manageable areas.

You can also calculate distance from a speed - time graph. The distance travelled is equal to the area under the graph. e.g. 3 1 1 4 2 Area 1 = 1/2 x 10 x 5 = 25

You can also calculate distance from a speed - time graph. The distance travelled is equal to the area under the graph. e.g. 3 1 4 2 2 Area 1 = ½ x 10 x 5 = 25 Area 2 = 5 x 2 = 10

You can also calculate distance from a speed - time graph. The distance travelled is equal to the area under the graph. e.g. 3 3 1 4 2 Area 1 = ½ x 10 x 5 = 25 Area 3 = 7 x 12 = 84 Area 2 = 5 x 2 = 10

You can also calculate distance from a speed - time graph. The distance travelled is equal to the area under the graph. e.g. 3 1 4 4 2 Area 1 = 1/2 x 10 x 5 = 25 Area 3 = 7 x 12 = 84 Area 4 = 1/2 x 4 x 12 = 24 Area 2 = 5 x 2 = 10

You can also calculate distance from a speed - time graph. The distance travelled is equal to the area under the graph. e.g. 3 1 4 2 Area 1 = 25 Area 2 = 10 Area 3 = 84 Area 4 = 24 Total Area = distance = 25 + 10 + 84 + 24 = 143 m

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2. Forces at Work A force can have any of the following effects: change the speed of an object, change the direction of an object or, change the shape of an object. Take the example of someone punching someone else in the face.

When the punch lands: The persons head will move – speed and direction has changed. The persons face will also change shape. Maybe permanently! These effects are all due to the force being applied by the punch.

One way of measuring a force in the laboratory is to use a Newton balance. (Sometimes called a spring balance) The balance has a spring inside which stretches more when a heavier object is placed on the end. To use a Newton balance the object should be placed on the hook at the bottom of the balance. The balance should then be held steady and the reading read from the scale on the balance. This reading would be the objects weight. Weight is a force and is therefore measured in Newtons (N).

The weight of an object is a measure of the Earth`s pull on the object. Mass is a measure of how much substance makes up a body or object. Mass is measured in kilograms (kg). Weight is a force and is measured in Newtons (N). (Fw) Force of weight Fw = mg Where Fw = weight, (N) m = mass, (kg) g = gravitational field strength, (N/kg) The value of `g` on Earth is 10 N/kg

Gravitational field strength, `g` varies from planet to planet. `g` on the moon is less than it is on the Earth. This means that an object will have a smaller weight on the moon than it does on Earth. If a tin of beans was placed inside a rocket on Earth and the rocket was launched from Earth on a journey to the moon. The tin of beans would have weight on Earth – as the rocket gets further from Earth and goes into deep space, the weight of the beans would decrease until the weight = zero. As the rocket approaches the moon the weight would increase again but the final weight on the moon would be less than the weight on Earth. Note that the mass of the tin of beans does not change at all.

Friction is a force which always acts against the direction of motion. Direction of motion Direction of motion friction Friction is due to the rough surface of the tyres rubbing against the rough road surface. Friction is due to air resistance as the helicopter passes through the air. As the speed increases so does the air friction. friction

Friction is sometimes deliberately increased For example: A racing bike does not want to skid off of the track when it takes a corner – the tread on the tyre causes friction between the bike and the road and stops it skidding. A sky-diver does not want to hit the Earth at a large speed so when they approach the ground they open a parachute. When the parachute opens, air friction is increased and the falling person slows down.

Friction is sometimes deliberately decreased For example: A ten pin bowling alley is made as smooth as possible to make the bowls roll as smoothly and as quickly as possible. We use oil in engines to reduce the wear and tear on the rubbing pieces of metal. If oil is not used the engine will seize and stop moving.

2N 6N Mass 6N If two forces of the same size act in opposite directions on the same object we say the forces are balanced. These forces are then exactly the same as no forces at all! Mass This is applied in Newton’s First Law which states: An object will continue to travel in a straight line at a constant speed unless an unbalanced force acts upon it 2N

An example of Newton’s first law. If a passenger in a car is not wearing a seat belt and the car crashes, the passenger would continue to travel forward in a straight line at a constant speed. (The same speed that the car was travelling) If they had been wearing a seatbelt, the belt would have exerted a retarding (unbalanced) force on the passenger and would have prevented them from leaving the seat.

The acceleration of an object depends on two main factors: The Mass of the object and The Force applied to the object If the Mass is doubled, the acceleration is halved. If the Mass is trebled, the acceleration is divided by 3. If the Mass is halved, the acceleration doubles. If the Force is doubled, the acceleration doubles. If the Force is trebled, the acceleration trebles. If the Force is halved, the acceleration is also halved.

These rules all obey Newton’s Second Law which is normally remembered as: F=ma Force (N) acceleration (ms-2) mass (kg) Example 1 Calculate the force applied to a toy car of mass 0.1kg which accelerates at 2ms-2. Soln. F = ma F = 0.1 x 2 F = 0.2 N

Example 2 Calculate the acceleration of a small car (mass = 150 kg) that can produce an engine force of 1000N. Soln. F = ma 1000 = 150 x a a = 6.67 ms-2

Example 3 What is the mass of a car if it has a maximum acceleration of 20 ms-2 and the engine can produce a maximum force of 3500 N? F = ma 3500 = m x 20 m = 175 kg

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3 Movement Means Energy There are 8 different forms of energy: Electrical Heat Kinetic Potential Chemical Light Sound and Nuclear

The main energy transformations for a vehicle are as follows: For an accelerating vehicle Chemical energy (Fuel) > Kinetic energy. For a vehicle moving at a constant speed Chemical energy (Fuel) > Heat energy (due to friction) For a braking vehicle Kinetic energy > Heat energy For a vehicle climbing a hill Chemical energy > Potential Energy For a vehicle coming down a hill Potential energy > Kinetic energy

Work done is a measure of the energy transferred. The work done will double if the force applied doubles, The work done will also double if the distance doubles. This leads to the equation: EW = Fd Distance travelled (m) Work done (J) Force (N)

Example How much work is done by a manual worker in lifting a 2.5kg sledgehammer through a height of 1.5m? Soln. Ew = Fd Ew = mg x d Ew = (2.5 x 10) x 1.5 Ew = 37.5 J

Work done is measured in joules so it has to be ENERGY. • Example. • A dog drags a large bone 2.3m in a time of 12s, if the dog exerts a force of 3.7N on the bone find: • How much work the dog does, and • What power the dog develops. • Soln. a) Ew = Fd Ew = 3.7 x 2.3 Ew = 8.51 J b)

A change in gravitational potential energy is work done against/by gravity. A moving object’s Kinetic Energy (Ek) will increase if either it’s mass or it’s speed increases. Speed (m/s) Kinetic Energy (J) mass (kg)

Example How much kinetic energy does a helicopter of 6000kg have if it is travelling at 150ms-1? Soln. Ek = 0.5 x 6000 x1502 Ek = 3000 x 22,500 Ek = 67.5 x 106 J

To calculate how much potential energy an object has we use the equation: Ep = mgh height (m) Potential Energy (J) mass (kg) gravitational field strength (N/kg) Example How much potential energy does a 100g apple have when it is on a table 1.5m high? Ep = mgh Ep = 0.1 x 10 x 1.5 Ep = 1.5 J

If an object travels either up or down a slope Ek becomes Ep and vice – versa. Example A skateboarder leaves the top of a ramp (20m high), calculate his speed at the bottom of the ramp. Soln. Initial Ep = Final Ek mgh = 0.5 mv2 g x h = 0.5 v2 10 x 20 = 0.5 x v2 200 = 0.5 v2 400 = v2 v = 20 m/s

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Motion, speed, acceleration and Energy