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Lesson_3.5_Printable

# Lesson_3.5_Printable - Impulse of a force Impulse(I of a...

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Impulse of a force Impulse ( I ) of a force is the product of the force and duration of action of the force. If a force F N acts on an object for a time t , then I = F t But force is a measure of the rate of change of the rate of change of momentum. P F = P I = F t = × t = P Impulse of a force is a measure of the change in momentum it produces on an object. t t = t Impulse is measured in Ns which is the same a kgms -1 . When you drive a nail down, the longer the hammer stays in contact with the nail, the smoother will be the drive. 1

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When a 0.2 kg baseball is hit, its velocity changes from 25 ms -1 to -25 ms -1 . (a) What is the impulse delivered by the bat to the ball? (b) If the ball is in contact with the bat for 1.1 ms, what is average force on the ball? m = 0.2 kg, v i = 25 ms -1 , v f = -25 ms -1 , t = 1.1 ms = 1.1 × 10 -3 s P i = mv i = 0.2 kg × 25 ms -1 = 5 kgms -1 . P f = mv f = 0.2 kg × (-25 ms -1 ) = -5 kgms -1 . P = P f – P i = -5 kgms -1 – 5 kgms -1 = -10 kgms -1 . ave P (b) F = t (a) I = P = -10 kgms -1 . -1 -3 -10 kgms = 1.1 10 s × v i = 25 ms -1 v f = -25 ms -1 3 -9.1×10 N = -9.1 kN = 2
Elastic and inelastic collisions Momentum P is conserved in all types of collisions Kinetic energy K may or may not be conserved in a particular collision. If no energy is lost in deforming the objects then K will be conserved. A collision where momentum and energy both are conserved is called an elastic collision . For an elastic collision, P i = P f and K i = K f . For an inelastic collision , P i = P f but K f < K i If K f is not the same as K i , the collision is said to be inelastic. 3

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Let us consider an object of mass m 1 moving to the right with a velocity v 1i A second object of mass m 2 moves to the left with a velocity v 2i . m 1 v 1i m 2 v 2i v 1f v 2f They collide and object 1 moves away with a velocity v 1f The velocity of object 2 after collision is v 2f The momentum of object 1 before collision P 1i = m 1 v 1i The momentum of object 2 before collision P 2i = m 2 v 2i Total momentum before collision P i = m 1 v 1i + m 2 v 2i Total momentum after collision P f = m 1 v 1f + m 2 v 2f 4
Since momentum is conserved, P i = P f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f m 1 (v 1i – v 1f ) = m 2 (v 2f – v 2i ) ….(i) The initial kinetic energy of the two objects The total kinetic energy after collision 2 2 i 1 1i 2 2i 1 1 K = m v + m v 2 2 For an elastic collision, the kinetic energy is conserved.

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