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0.2 Force, momentum and impulse  (Page 24/35)

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Vector nature of momentum

As we have said, momentum is a vector quantity. Since momentum is a vector, the techniques of vector addition discussed in Chapter  [link] must be used to calculate the total momentum of a system.

Two billiard balls roll towards each other. They each have a mass of 0,3 kg. Ball 1 is moving at v 1 = 1 m · s - 1 to the right, while ball 2 is moving at v 2 = 0 , 8 m · s - 1 to the left. Calculate the total momentum of the system.

  1. The question explicitly gives

    • the mass of each ball,
    • the velocity of ball 1, v 1 , and
    • the velocity of ball 2, v 2 ,

    all in the correct units!

    We are asked to calculate the total momentum of the system . In this example our system consists of two balls. To find the total momentum we must determine the momentum of each ball and add them.

    p t o t a l = p 1 + p 2

    Since ball 1 is moving to the right, its momentum is in this direction, while the second ball's momentum is directed towards the left.

    Thus, we are required to find the sum of two vectors acting along the same straight line. The algebraic method of vector addition introduced in Chapter  [link] can thus be used.

  2. Let us choose right as the positive direction, then obviously left is negative.

  3. The total momentum of the system is then the sum of the two momenta taking the directions of the velocities into account. Ball 1 is travellingat 1 m · s - 1 to the right or +1 m · s - 1 . Ball 2 is travelling at 0,8 m · s - 1 to the left or -0,8 m · s - 1 . Thus,

    p t o t a l = m 1 v 1 + m 2 v 2 = ( 0 , 3 kg ) ( + 1 m · s - 1 ) + ( 0 , 3 kg ) ( - 0 , 8 m · s - 1 ) = ( + 0 , 3 kg · m · s - 1 ) + ( - 0 , 24 kg · m · s - 1 ) = + 0 , 06 kg · m · s - 1 = 0 , 06 kg · m · s - 1 to the right

    In the last step the direction was added in words. Since the result in the second last line is positive, the total momentum of the systemis in the positive direction (i.e. to the right).

Exercise

    1. The fastest recorded delivery for a cricket ball is 161,3 km · hr - 1 , bowled by Shoaib Akhtar of Pakistan during a match against England in the 2003 Cricket World Cup, held in South Africa. Calculate the ball's momentum if it has a mass of 160 g.
    2. The fastest tennis service by a man is 246,2 km · hr - 1 by Andy Roddick of the United States of America during a match in London in 2004. Calculate the ball's momentum if it has a mass of 58 g.
    3. The fastest server in the women's game is Venus Williams of the United States of America, who recorded a serve of 205 km · hr - 1 during a match in Switzerland in 1998. Calculate the ball's momentum if it has a mass of 58 g.
    4. If you had a choice of facing Shoaib, Andy or Venus and didn't want to get hurt, who would you choose based on the momentum of each ball.
  2. Two golf balls roll towards each other. They each have a mass of 100 g. Ball 1 is moving at v 1 = 2,4 m · s - 1 to the right, while ball 2 is moving at v 2 = 3 m · s - 1 to the left. Calculate the total momentum of the system.
  3. Two motor cycles are involved in a head on collision. Motorcycle A has a mass of 200 kg and was travelling at 120 km · hr - 1 south. Motor cycle B has a mass of 250 kg and was travelling north at 100 km · hr - 1 . A and B are about to collide. Calculate the momentum of the system before the collision takes place.
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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