Transcript
UNIT 4TOPIC 1: FURTHER
MECHANICS
Part 1: MOMENTUM
Prepared by: Pn Siti Fatimah Saipuddin INTEC
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OBJECTIVES
Able to express equation p = mv Apply the principle of conservation of
momentum, m1u1 + m2u2 = m1v1 + m2v2
Special cases in collisions and energy, explosions
Apply the concept of impulse, Ft = mv-mu and force
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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]
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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: m1u1 + m2u2 = m1v1 + m2v2
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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]
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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 6
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. [v1 = 2.0 ms-1 and v2 = 8.0 ms-1] 7
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 ]
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T
S
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]
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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)
tFt = 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]
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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]11
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, Fs = μsR
The limiting static friction, Fs between two surfaces just before relative motion occurs.
Independent of the surface area of contact
Kinetic friction, Fk = μkR 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: μk < μs
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SUMMARY Momentum, p = Mass, m x Velocity, v Principle of conservation of momentum states that: m1u1 + m2u2 = m1v1 + m2v2
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, Fs = μsR Kinetic friction, Fk = μkR μk < μs
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ONE-DIMENSIONAL COLLISION
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ELASTIC COLLISION PERFECTLY INELASTIC COLISION
TWO-DIMENSIONAL COLLISION
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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
16θ = 53.1°vf = 15.6 ms-1
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