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course Phy 241
08/06 6:12 pm
" "Question: `q001. Note that this assignment contains 6 questions.
A mass of 10 kg moving at 5 meters/second collides with a mass of 2 kg which is initially stationary. The collision lasts .03 seconds, during which time the velocity of the 10 kg object decreases to 3 meters/second. Using the Impulse-Momentum Theorem determine the average force exerted by the second object on the first.
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Your solution:
F ave = m*dv/dt
F ave = 10 kg (-2 m/sec)/ (.03 sec)
F ave =- 667 Newtons
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Question: `q002. For the situation of the preceding problem, determine the average force exerted on the second object by the first and using the Impulse-Momentum Theorem determine the after-collision velocity of the 2 kg mass.
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Your solution:
F ‘ dt = 667 Newtons * .03 sec
F ‘ dt = 20 kg*m/sec
20 kg*m/s / 2 kg
= 10 m/s
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Question: `q003. For the situation of the preceding problem, is the total kinetic energy after collision less than or equal to the total kinetic energy before collision?
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Your solution:
KE = .5mv^2, m = 10 kg, v = .5 m/s
KE = .5 * 10 kg * (5 m/s)^2
KE = 5 kg * 25 m^2/s^2
KE = 125 J
m = 2 kg, 10 kg; v = 10 m/s, 3 m/s
KE = .5 * 2 kg * (10 m/s)^2 + .5 * 10 kg * (3 m/s)^2
KE = 100 J + 45 J
KE = 145 J
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Question: `q004. For the situation of the preceding problem, how does the total momentum after collision compare to the total momentum before collision?
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Your solution:
Before the collision
p = 10 kg * 5 m/sec
p = 50 kg*m/sec
After the collision
p = (10 kg*3 m/sec) + (10kg*2 m/sec)
p = 30 kg*m/sec + 20 kg*m/sec
p = 50 kg*m/sec
The momentum of the collision after is equal to the momentum before the collision.
confidence rating #$&*:
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Question: `q005. How does the Impulse-Momentum Theorem ensure that the total momentum after collision must be equal to the total momentum before collision?
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Your solution:
Since the force is exerted by the 2 objects on one another are equal and opposite, and since they act simultaneously, we have equal and opposite forces acting for equal time intervals. These forces therefore exert equal and opposite impulses on the two objects, resulting in equal and opposite changes in momentum.
Since the changes in momentum are equal and opposite, total momentum change is zero. So the momentum after collision is equal to the momentum before collision.
confidence rating #$&*:
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If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily. If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties.
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Question: `q006. A 2 kg mass moving at 6 m/s collides with a 3 kg mass, after which the 2 kg mass is moving at 4 m/s.
By how much did its momentum change?
By how much did the momentum of the 3 kg mass change?
How do the forces experienced by the two masses during the collision compare?
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Your solution:
(2 kg * 6 m/s) - (2 kg * 4 m/s)
= 12 kg*m/s - 8 kg*m/s
= 4 kg*m/s
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The change is final momentum - initial momentum, and is therefore negative.
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(3 kg * 0 m/s) - (2 kg * 6 m/s)
= - 12 kg*m/s
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The change in momentum of one mass is equal and opposite to that of the other.
Recommendation: Review the concepts of the above exercises.
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Since the 3 kg was not moving upon impact, it received a large amount of momentum to the other direction from its initial locations. As for the 2 kg mass, after the collision the 2 kg mass kept moving at the same direction but loss some momentum.
confidence rating #$&*:
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&#Your work looks good. See my notes. Let me know if you have any questions. &#