Lesson_Text_3.5 - 1 Lesson 3.5 Impulse, Elastic and...

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1 Lesson 3.5 Impulse, Elastic and Inelastic Collisions. 1. Impulse : Impulse is a term that describes the effect of a force on an object. The impulse of a constant force on an object depends on how long the force has been acting on the object. For example, when you drive a nail down by a hammer, the nail goes down deeper if the hammer is in contact with the nail for a longer duration. Impulse is a vector and we will use I to represent it. Impulse of a force is measured as the product of the force and the time of action of the force. I = F t …(i) Here t is the time of action of the force. The unit of impulse is N.s But since force is the rate of change of momentum, we have: t p F = Therefore, Impulse I is given by p I t p t = ∆ = ∆ Impulse is a measure of the change in momentum. I = p …(ii) Impulse is given by the area under the graph of force versus time. impulse = area under F-t graph F t
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2 The average force during the interval t = t 2 – t 1 is given by: net I F t = ….(iv) Example 1 : When tossed upward and hit horizontally by a batter, a 0.2 kg softball receives an impulse of 4.0 N s. With what speed does the ball move away from the bat? Solution: A ball tossed upward has no initial horizontal velocity. Therefore, its initial horizontal momentum is zero. Let the horizontal velocity of the ball be v m/s after hitting. Its momentum after hitting = m v = 0.2 v kg m.s -1 The change in momentum of the ball = 0.2 v – 0 = 0.2 v kg m.s -1 We have, Impulse = change in momentum 4.0 N s = 0.2 v kg m.s -1 1 4.0 0.2 20 . N s m v s kg - = = Example 2: An automobile with a linear momentum of 3.2 × 10 4 kg.m.s -1 is brought to stop in 4.0 s. What is the magnitude of the average breaking force? Solution: Initial momentum of the automobile p 1 = 3.2 × 10 4 kg m.s -1 Its final momentum p 2 = 0 The change in momentum = p 2 – p 1 = -3.2 × 10 4 kg m.s -1 This is a measure of the impulse on the automobile. I = -3.2 × 10 4 kg m.s -1 4 3 3.2 10 8.0 10 4.0 net I F N t - × = = = - × F = -8.0 × 10 3 N 2. Elastic and Inelastic Collisions.
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3 When two or more objects collide, energy and momentum both are conserved. Although energy is conserved, the kinetic energy of the colliding objects may not always be conserved. For example, if the shape of one or more of the colliding objects is altered during collision, the internal potential energies of these objects have been changed. This change in potential energy has been achieved at the expense of the kinetic energies of the objects before collision. In such a case, the total kinetic energy after collision will be less than the total kinetic energy before collision. This means that in such cases, kinetic energy is not conserved. A collision in which both the kinetic energy and the
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Lesson_Text_3.5 - 1 Lesson 3.5 Impulse, Elastic and...

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