The document discusses momentum, conservation of momentum, collisions, impulse, and friction. It defines momentum as mass times velocity and states that the total momentum before and after a collision remains the same if no external forces act, according to the conservation of momentum principle. It also distinguishes between elastic, inelastic, and completely inelastic collisions, and defines impulse as the change in momentum caused by a force over time. Static and kinetic friction are defined, with kinetic friction less than static friction. Examples and exercises demonstrate applications of these concepts.

1. UNIT 4 TOPIC 1: FURTHER MECHANICS Part 1: MOMENTUM Prepared by: Pn Siti Fatimah Saipuddin INTEC

2. OBJECTIVES Able to express equation p = mv Apply the principle of conservation of momentum, m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 Special cases in collisions and energy, explosions Apply the concept of impulse, Ft = mv-mu and force

3. LINEAR MOMENTUM The (linear) momentum of a body is defined by: Momentum = Mass x Velocity Exercise 2.1: A body A of mass 5 kg moves to the right with a velocity of 4 ms -1 . A body of mass 3 kg moves to the left with a velocity of 8 ms -1 . Calculate: The momentum of A [ +20 kg ms -1 ] The momentum of B [ -24 kg ms -1 ] The total momentum of A and B [ -4 kg ms -1 ]

4. CONSERVATION OF MOMENTUM Provided that no external forces are acting, it can be assumed that when collision happens between two bodies, the total momentum before collision is the same as that after collision. This means that: m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2

5. CONSERVATION OF MOMENTUM Exercise 2.2: A 2.0 kg object moving with a velocity of 8.0 ms -1 collides with a 4.0 kg object moving with a velocity of 5.0 ms -1 along the same line. If the two objects join together on impact, calculate their common velocity when they are initially moving In the same direction [ 6.0 ms -1 ] In opposite direction [ -0.67 ms -1 ]

6. COLLISIONS AND ENERGY Momentum is conserved in a collision. Total energy is also conserved but the kinetic energy might not be conserved. It can be converted to other forms such as sound, work done during plastic deformation, etc. In an elastic collision: Kinetic energy is conserved Linear momentum is conserved Energy is conserved In a non-elastic collision: Kinetic energy is not conserved Linear momentum is conserved Energy is conserved In a completely inelastic collision: The objects stick together on impact

7. COLLISIONS AND ENERGY Exercise 2.3: Calculate the KE converted to other forms during the collisions in (a) and (b) of Exercise 2.2 KE converted = [ 6J ] KE converted = [ 113J ] Exercise 2.4: A 2.0 kg object moving with velocity 6.0 ms -1 collides with a stationary object of mass 1.0 kg. Assuming that the collision is perfectly elastic, calculate the velocity of each object after the collision. [v 1 = 2.0 ms -1 and v 2 = 8.0 ms -1 ]

8. COLLISIONS AND ENERGY Example: Two particles S of mass 30g and T of mass 40g, both travel at the speed of 35 ms -1 in directions at right angles to each other. The two particles collide and stick together. Calculate their speed after the impact. [ 25.0 ms -1 ] T S

9. EXPLOSIONS An object explodes as a result of some internal forces. As the result, the total momentum of the separate parts will be the same as that of the original body, which is normally zero. Exercise 2.4: Figure below shows two trolleys A and B initially at rest, separated by a compressed spring. The spring is now released and the 3.0 kg trolley moves with a velocity of 1.0 ms -1 to the right. Calculate: The velocity of the 2.0 kg trolley [-1.5 ms -1 ] The total KE of the trolleys [3.75J]

10. IMPULSE AND FORCE If a force, F acts on a body of mass, m for a time, t so that the velocity of the body changes from u to v , then: F = (rate of change of momentum) = (mv-mu) t Ft = mv – mu = impulse Exercise 2.5: A stationary golf ball is hit with a club which exerts an average force of 80 N over a time of 0.025 s. Calculate: The change in the momentum [2.00 kg ms -1 ] The velocity acquired by the ball if it has a mass of 0.020 kg [ 100 ms -1 ]

11. IMPULSE AND FORCE Exercise 2.6: Figure below shows how the force acting on a body varies with time. The increase in momentum of the body, measured in Ns as the result of this force acting for four seconds is _________ [24 Ns]

12. FRICTION Friction is the force that opposes the relative motion between two solid surfaces which are in contact. The frictional force before relative motion between the surfaces occurs is known as static friction. Limiting static friction, F s = μ s R The limiting static friction, Fs between two surfaces just before relative motion occurs. Independent of the surface area of contact Kinetic friction, F k = μ k R The friction between two surfaces when there is relative motion between the surfaces Independent of the surface area of contact and the relative speed between the surfaces The value of coefficient: μ k < μ s

13. SUMMARY Momentum, p = Mass, m x Velocity, v Principle of conservation of momentum states that: m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 In an elastic collision: Kinetic energy, Linear momentum, and Energy are conserved In a non-elastic collision: Kinetic energy is not conserved Linear momentum and Energy are conserved Ft = mv – mu = impulse Limiting static friction, F s = μ s R Kinetic friction, F k = μ k R μ k < μ s

14. ONE-DIMENSIONAL COLLISION ELASTIC COLLISION PERFECTLY INELASTIC COLISION

15. TWO-DIMENSIONAL COLLISION

16. EXAMPLE: A 1500kg car traveling east with the speed of 25 ms -1 collides at an intersection with a 2500kg van traveling north at a speed of 20ms -1 . find the direction and the magnitude of the velocity of the wreckage after the collision, assuming that the collision undergoes perfectly inelastic collision θ = 53.1 ° v f = 15.6 ms -1