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Object A has mass mA = 8 kg and initial momentum pA,i = < 15, -8, 0 > kg · m/s, just before it strikes object B, which has mass mB = 11 kg. Just before the collision object B has initial momentum pB,i = < 2, 7, 0 > kg · m/s.
A) Consider a system consisting of both objects A and B. What is the total initial momentum of this system, just before the collision?
B) The forces that A and B exert on each other are very large but last for a very short time. If we choose a time interval from just before to just after the collision, what is the approximate value of the impulse applied to the two-object system due to forces exerted on the system by objects outside the system?
C) Therefore, what does the Momentum Principle predict that the total final momentum of the system will be, just after the collision?
D) Just after the collision, object A is observed to have momentum pA,f = < 13, 4, 0 > kg · m/s. What is the momentum of object B just after the collision?

Respuesta :

Answer:

A)

<17, - 1, 0>

B)

0 Ns

C)

<17, - 1, 0>

D)

<4, - 5, 0>

Explanation:

A)

[tex]p_{A,i}[/tex] = initial momentum of object A = 15 i - 8 j + 0 k

[tex]p_{B,i}[/tex] = initial momentum of object B = 2 i + 7 j + 0 k

Total initial momentum of the system is given as the sum of initial momenta of A and B , hence

[tex]p_{i}[/tex] = [tex]p_{A,i}[/tex] + [tex]p_{B,i}[/tex]

[tex]p_{i}[/tex] = (15 i - 8 j + 0 k) + (2 i + 7 j + 0 k)

[tex]p_{i}[/tex] = 17 i - j + 0 k

B)

[tex]F_{ext}[/tex] = Net external force on the two objects = 0 N

[tex]t[/tex] = duration of the collision

[tex]I[/tex] = Impulse

Impulse is given as

[tex]I = F_{ext} t \\I = (0) t \\I = 0 Ns[/tex]

C)

[tex]p_{f}[/tex] = final momentum of the system

we know that the Impulse is nothing but change in momentum of the system of objects, hence

[tex]I = p_{f} - p_{i}\\0 = p_{f} - p_{i}\\p_{f} = p_{i}[/tex]

[tex]p_{f}[/tex] = 17 i - j + 0 k

D)

[tex]p_{A,f}[/tex] = final momentum of object A = 13 i + 4 j + 0 k

[tex]p_{B,f}[/tex] = final momentum of object B = ?

Total final momentum of the system is given as

[tex]p_{f} = p_{A,f} + p_{B,f}[/tex]

17 i - j + 0 k = ( 13 i + 4 j + 0 k ) + [tex]p_{B,f}[/tex]

[tex]p_{B,f}[/tex] = 4 i - 5 j + 0 k

So final momentum of the object is <4, - 5, 0>

adefioyelaoye

The total initial momentum of this system just before the collision is 17 i - j + 0 k.

What is Impulse?

This is defined as a term which quantifies the overall effect of a force acting over time.

  • Total initial momentum of this system just before the collision:

Initial momentum of A = 15 i - 8 j + 0 k

initial momentum of B = 2 i + 7 j + 0 k

Total = sum of initial momentum of A and B

= (15 i - 8 j + 0 k) + (2 i + 7 j + 0 k)

= 17 i - j + 0 k

  • The approximate value of the impulse

Impulse = Ft where F is force and t is time

Net external force on the two objects = 0 N

Impulse = (0)t

              = 0Ns

  • The final momentum of the system

Impulse = change in momentum

= 17 i - j + 0 k

  • The momentum of object B just after the collision

Final momentum of object A = 13 i + 4 j + 0 k

Final momentum of object B = ?

Total final momentum = Final momentum of object A + Final momentum of object B

17 i - j + 0 k = ( 13 i + 4 j + 0 k ) + Final momentum of object B

= 4 i - 5 j + 0 k

Read more about Momentum here https://brainly.com/question/402617

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