Question

Four objects are projected from a spring gun. Their masses and velocities are given in the following table: 7. Velocity (m/s) 10 4 Object Mass (kg) 2 4 8 2 Rank these objects by their momentum from greatest to least. A light-weight bowling ball has a mass of about 3 kg. A standard ping-pong ball has a mass of 0.003 kg. Assume that these balls have the same momentum, p 0.3 kg*m/s. a. Which ball requires a greater Impulse to stop? 8. b. Which ball has the greater velocity?

Answer 1

NOTE:

Momentum is defined as  

Momentum�is defined as p = mv, Where, m is the mass and v is the velocity of the object. And Impulse�is defined as Impulse = Change in momentum From the given table: Momentum of object A is P_A = 1 times 10 = 10 kg.m/s Momentum of object B is P_B = 2 times 4 = 8 kg.m/s Momentum of object C is P_C = 4 times 3 = 12 kg.m/s Momentum of object D is P_D = 8 times 2 = 16 kg.m/s Hence, P_D > P_C > P_A > P_B According to the question, both the balls have same momentum i.e.�p = 0.3 kg.m/s. (a)�If both the balls are going to stop then the change in momentum in both the case will be same (as both balls have same momentum). And we know that: Impulse = Change in momentum = 0.3 kg.m/s (for both cases) Hence both ball

Where, m is the mass and v is the velocity of the object. And

Impulse is defined as

  

(7) From the given table:

Momentum of object A is

  

Momentum of object B is

Momentum of object C is

  

Momentum of object D is

Hence,

(8) According to the question, both the balls have same momentum i.e. p = 0.3 kg.m/s .

(a) If both the balls are going to stop then the change in momentum in both the case will be same (as both balls have same momentum). And we know that :

   (for both cases)

Hence both ball will require same impulse to stop.

(b) Given,  

Mass of bowling ball = 3 kg

Mass of ping - pong ball = 0.003 kg

Momentum of both the balls = 0.3 kg.m/s

Now, we know that

Momentum = Mass x Velocity

or, Velocity = Momentum / Mass

So, Velocity of bowling ball = 0.3 / 3 = 0.1 m/s

And, velocity of ping - pong ball = 0.3 / 0.003 = 100 m/s

Hence, the ping - pong ball has greater velocity.

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