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Lesson_Text_3.3

# Lesson_Text_3.3 - 1 Lesson 3.3 Momentum 1 Linear Momentum A...

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1 Lesson 3.3 Momentum 1. Linear Momentum: A moving object has momentum. It is difficult to stop a moving object because it has momentum. The difficulty in stopping a moving object arises due to its (i) mass and (ii) its velocity. Therefore, momentum is determined by both these quantities. Momentum of a moving object is the quantity of motion it possesses and is measured as the product its mass and velocity. Momentum is represented by the letter p. If an object of mass m kg has a velocity v m.s -1 , its momentum p is given by p = m v ….(i) The unit for momentum is kg m.s -1 Momentum is a vector quantity and so all the rules of vector addition is applicable for adding vectors. For example a momentum 3.0 kg. m.s -1 i + 2.0 kg. m.s -1 i = 5.0 kg. m.s -1 i and 3.0 kg. m.s -1 i – 2.0 kg. m.s -1 i = 1.0 kg. m.s -1 i . 3 kg m/s i + = 2 kg m/s i 5 kg m/s i 3 kg m/s i -2 kg m/s i + = 1 kg m/s i Fig. 1 Similarly a momentum of 5.0 kg. m.s -1 at an angle 37 o can be written as: 5.0 cos 30 i + 5.0 sin 30 j

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2 5.0 cos 30 i 30 o 5.0 kg m/s 5.0 sin 30 j Fig. 2 Example 1 : A 0.5 kg ball is thrown in the x direction with a velocity 10 m.s -1 . It hits a wall and rebounds with the same speed. What is the change in momentum of the ball? Solution: The initial velocity of the ball = 10 m.s -1 i Therefore, initial momentum p i = 0.5 kg 10 m.s -1 i = 5.0 kg. m.s -1 i Because it rebounds with the same speed, its final velocity = -10 m.s -1 i Therefore, final momentum p f = 0.5 kg (-10 m.s -1 i ) = -5.0 kg. m.s -1 i The change in momentum = p = p f – p i = -5.0 kg. m.s -1 i – 5.0 kg. m.s -1 i p = -10 kg.m/s i . Example 2: A 0.5 kg ball is thrown against a wall at an angle of 53 o with a velocity of 10 m.s -1 and rebounds with the same speed and at an angle 53 o as shown in fig. 3a below. Find the change in momentum of the ball.
3 p = p f - p i Fig. 3a The ball hits the Fig. 3b. p1makes an angle Fig. 3c. p= p f p i wall at an angle of 53 o 127 o with the x-axis p f p f p f 53 o 53 o 53 o 127 o p i -p i Solution: The initial momentum of the ball p i = 0.5 10 = 5 kg. m.s -1 at and angle 127 o . (fig. 3b) The final momentum of the ball p f = 5 kg. m.s -1 at an angle 53 o . The change in momentum p = p f – p i = p f + -p i (fig. 3c) Remember, -p i is a vector of magnitude 5 at an angle –53 o . Therefore, -p i = 5 cos (-53) i + 5 sin (-53) j = 3.0 i - 4.0 j p f = 5 cos 53 i + 5 sin 53 j = 3.0 i + 4.0 j Therefore, change in momentum, p = p f + -p i = 6.0 i 2. Force and momentum : Only a force can bring about a change in momentum. We shall now see how the change in momentum is related to the force that causes the change in momentum. We have from the second law of motion: F = ma t v v a i f - = . Using this expression for a in F = ma gives: t p t p p t mv mv t v v m F i f i f i f = - = - = - = ) ( This leads us to conclude that: Force is a measure of the rate of change of momentum.

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4 P F t = 3. Kinetic energy and momentum : The kinetic energy K of a moving object can be expressed in terms of its momentum. We have: m p m v m mv K 2 2 2 1 2 2 2 2 = = = 2 2 p K m = …(ii) 4. Conservation of linear momentum: Consider a system of interacting objects. For example two balls colliding is a
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