motion and energy

9. Distance – time graphs

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

10. Equations for uniform acceleration
11. First equation

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

12. Second equation

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

13. third equation

• s/ t = u + v/ 2

• = u + u + at / 2
• = 2u + at /2

• So, s = ut + 0.5 at2

14. 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

15. 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

16. Measuring g

• S = 0.5 gt 2
• G = 2s / t2

17. 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

18. 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

1. 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

2. 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

3. Newton’s second law

• Acceleration is directly proportional toforce an inversely proportional to mass
• Thus we get, F = kma ( k = constant of proportionality)
• One newton is deined as that force whih gives  a mass of 1 kg an acceleration of 1m/s2 
• Therefore, F=ma

4. Weight and gravity

• Weight of a body is the fore of gravity acting on it
• W=mg
• The greater the mass of a body, the greater is the force of gravity on it does not accelerate faster when falling because of its greater inertia.

5. Gravitational field

• The strength of this field is defined by the force acting on unit mass in the field
• There are 2 ways of considering g:  ------as acceleration for falling bodies

• ------as the earth’s gravitational strength

1. Newton’s third law

• If a body A exerts a force on body B, then body B exerts an equal but opposite force on body A
• The pair of equal and opposite forces do not act on the same body

2. Air resistance: terminal velocity

• When an object falls, the air resistance opposes its motion and reduces its acceleration
• Eventually, air resistance acting upwards equals the weight of the object acting downwards and thus the object falls with constant velocity, whose value depends on the object

Momentum

• Momentum = mass X velocity (vector)

3. Conservation of momentum

• When 2 or more bodies act one on another, as in a collision, the total momentum of the bodies remains constant, provided no external forces act. This is known as the conservation of momentum

4. Explosions

• Momentum is conserved in an explosion such as occurs when a rifle is fired

5. Rockets and jets

• In both, a high velocity stream of hot gas is produced by burning fuel and leaves the exhaust with large momentum

6. Force and momentum

• F=m(v- u)/t = mv – mu /t
• Also, Ft = mv – mu

• Impulse       final momentum           initial momentum

7. Sport: impulse and collision time

• Impulse is a smaller force which is usually applied over a longer time to remove the ‘sting’

Kinetic and potential energy

19. Kinetic energy

• It is the energy a body has become of its motion
• k.e. = 0.5mv2

20. potential energy

• it is the energy a body has because of its position or condition
• p.e. = mgh
• ∆p.e. = mgh

21. Conservation of energy

• Loss of pe = gain of ke

22. Elastic and inelastic collisions

• The greater the proportion of ke lost, the less elastic is the collision i.e. the more inelastic it is
• In a perfectly elastic collision ke is conserved

23. Driving and car safety
24. Braking distance and speed

• Fs=0.5mv2
• Braking distance       Mass of object
• Steady braking force applied
• Braking distance is directly proportional to the square of the speed
• The thinking distane (i.e. the distance travelled while the driver is reacting before applying the brakes) has to be added to the braking distance to obtain the overall stopping distance
• Thinking distance depends on the driver’s reaction time and braking distance varies with both the road conditions and the state of the car

25. Car design and safety

• Crumple zones at the front and rear collapse in such a way that the ke is absorbed gradually. This extends the collision time and hence reduces the force and hence the potential for injury to the passengers
• Extensible seat belts exert a backwards force
• Air bags inflate and protect the driver from injury by the steering wheel
• Head restraints ensure that if the car is hit from behind, the head goes forwards with the body and not backwards over the top of the seat

Circular motion

26. 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

27. 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

28. Satellites

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