# motion and energy

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Introduction

Motion and energy

Speed velocity and acceleration

- Speed

- Average speed= distance moved / time taken

- Velocity

- Speed is a distance travelled in unit time ( scalar )
- Velocity is a distance travelled in unit time in a stated direction ( vector )
- Velocity = distance moved in a stated direction / time taken = displacement / time
- Velocity of a body is constatnt if it moves with steady speed in a straight line
- Distance moved in a stated direction is also known as displacement

- Acceleration

- It is the change in velocity in unit time
- Acceleration = change of velocity / time taken for change
- An acceleration is positive if the velocity increases and negative if it decreases. A negative acceleration is also called a deceleration or retardation

- Timers

- These are timers used to analyse motion

- Motion sensors

- They use the ultrasonic echo technique to determine the distance of the object from thee sensor

- Tickertape timer : tape charts

- One type has a marker which vibrates 50 times a second and makes dots at 1/50 s intervals on the paper tape being pulled through it
- 1/50 s is called a tick
- The distance between the successive dots equals the average speed of the object
- 1/5 s is called a tentick
- 5 tenticks = 1 second

- Photogate timer

- They are used to record time taken for a trolley to pass through a gate. If the length of the interrupt card is measured, the velocity can be calculated

Graphs and equations

- Velocity – time graphs

- Tape charts are velocity – time graphs which show the velocity changing in jums rather than smoothly.
- Motion sensors give a smoother plot
- The area under this graph measures the distance moved
- The slope or gradient of a velocity time graph shows the acceleration of a body

- Distance – time graphs

- The slope or gradient of this graph shows the velocity of the body

- Equations for uniform acceleration
- First equation

- a = v- u / t
- at = v – u
- V = u + at

- Second equation

- Average velocity = u + v /2
- s/ t = u + v/ 2
- s = (u + v /2) t

- third equation

- s/ t = u + v/ 2

- = u + u + at / 2
- = 2u + at /2

- So, s = ut + 0.5 at2

- Fourth equation

- V2 = ( u+ at)2
- V2 = u2 + 2uat + a2t2
- V2 = u2 + 2as

Falling bodies

- In air a coin falls faster than a piece of paper. This happens due to air resistance having a greater effect on light bodies than on heavy bodies

- Acceleration of free fall

- All the bodies falling freely under the force of gravity do so with uniform acceleration if air resistance is negligible
- This a is called the a of free fall and is denoted by g
- It is positive for falling bodies and negative for rising bodies

Middle

- Distance – time graphs

- The graph of s against t is a curved line
- The graph of s against t2 is a straight line from the origin since s is directly proportional to t2

- Projectiles

- The horizontal and vertical motions of a body are independent and can be treated separately

- The horizontal distance a projectile travels i.e. its range depends on the speed of projection and the angle of projection. Usually the range is maximum when the angle = 45

Force and acceleration

- Newton’s first law

- A body stays at rest, or if moving it continues to move with uniform velocity, unless an external force makes it behave differently
- The smaller the forces that are opposing the motion, the smaller are the forces needed to keep the body in motion

- Mass and inertia

- All matter has a built in opposition to being moved if it is at rest or, if it is moving, to having its motion changed. This property of matter is called inertia
- The larger the mass of a body the greater is its inertia i.e. the more difficult it is to move it when at rest and stop it when in motion. Thus the mass of a bosy measures its inertia

- Newton’s second law

- Acceleration is directly proportional toforce an inversely proportional to mass

Conclusion

Circular motion

- Centripetal force

- In the case of a whirling ball, the force is provided by the string pulling inwards on the ball. This force needs to be increased if the speed of the ball is increased, if the radius of the circle is decreased and if the mass of the ball is increased
- F=mv2/r
- This force which acts towards the centre and keeps a bosy moving ina circular path, is called the centripetal force. If this force is greater than the string can bear, the string breaks and the ball flies off with steady speed in a straight linealong the tangent

- Rounding a bend

- When a car rounds a bend a frictional force is exerted inwards by the road on the car’s tyres, so providing the centripetal force needed to keep it in the curved path
- If this frictional force is not large enough, skidding occurs

- Satellites

- For a satellite orbiting the earth , centripetal force is: F= mv2/r
- The orbital period: T=2r/v

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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