course Phy 231 wbnl assignment #017
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19:50:46 `q001. Note that this assignment contains 5 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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RESPONSE --> The Impulse-Momentum Theorem where mass is constant is: Fave * `dt = m * `dv Fave = m * `dv / `dt Fave = 10kg * (5m/s - 3m/s) / 0.03s Fave = 667N confidence assessment: 3
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19:51:53 By the Impulse-Momentum Theorem for a constant mass, Fave * `dt = m `dv so that Fave = m `dv / `dt = 10 kg * (-2 meters/second)/(.03 seconds) = -667 N. Note that this is the force exerted on the 10 kg object, and that the force is negative indicating that it is in the direction opposite that of the (positive) initial velocity of this object. Note also that the only thing exerting a force on this object in the direction of motion is the other object.
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RESPONSE --> I had the final and initial velocities switched resulting in a positive change in velocity. self critique assessment: 2
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20:11:13 `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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RESPONSE --> The force of the first object on the second will be equal and opposite according to Newton's Third Law, so the Fave * `dt /m = `dv `dv = 667N = .03s/2kg = 10m/s. Since the 2kg object started at rest, the final velocity is 10m/s. confidence assessment: 3
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20:11:30 Since the -667 N force exerted on the first object by the second implies and equal and opposite force of 667 Newtons exerted by the first object on the second. This force will result in a momentum change equal to the impulse F `dt = 667 N * .03 sec = 20 kg m/s delivered to the 2 kg object. A momentum change of 20 kg m/s on a 2 kg object implies a change in velocity of 20 kg m / s / ( 2 kg) = 10 m/s. Since the second object had initial velocity 0, its after-collision velocity must be 10 meters/second.
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RESPONSE --> self critique assessment: 3
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20:34:56 `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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RESPONSE --> Before collision: The KE of the first (10kg) object is: .5 * 10kg * (5m/s)^2 = 125J The KE of the second (2kg) object is: .5 * 2kg * (0m/s)^2 = 0J After collision: The KE of the first (10kg) object is: .5 * 10kg * (3m/s)^2 = 45J The KE of the second (2kg) object is: .5 * 2kg * (10m/s)^2 = 100J The total KE of the system after collision (100J + 45J = 145J) appears to be greater than that of before the collision (125J), so no the total kinetic energy after collision does not seem to be less than or equal to the total kinetic energy before the collision. The change in KE in the first (10kg) object is: .5*10kg*[(3m/s)^2 - (5m/s)^2] = -80J The change in KE in the second (2kg) object is: .5*2kg*[(10mls)^2 - (0m/s)^2] = 100J confidence assessment: 2
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20:37:14 The kinetic energy of the 10 kg object moving at 5 meters/second is .5 m v^2 = .5 * 10 kg * (5 m/s)^2 = 125 kg m^2 s^2 = 125 Joules. Since the 2 kg object was initially stationary, the total kinetic energy before collision is 125 Joules. The kinetic energy of the 2 kg object after collision is .5 m v^2 = .5 * 2 kg * (10 m/s)^2 = 100 Joules, and the kinetic energy of the second object after collision is .5 m v^2 = .5 * 10 kg * (3 m/s)^2 = 45 Joules. Thus the total kinetic energy after collision is 145 Joules. Note that the total kinetic energy after the collision is greater than the total kinetic energy before the collision, which violates the conservation of energy unless some source of energy other than the kinetic energy (such as a small explosion between the objects, which would convert some chemical potential energy to kinetic, or perhaps a coiled spring that is released upon collision, which would convert elastic PE to KE) is involved.
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RESPONSE --> That seems to help explain the difference in the KE that I saw. self critique assessment: 2
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20:44:18 `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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RESPONSE --> The momentum before collision: Object #1: 10kg * 5m/s = 50kg*m/s Object #2: 2kg * 0m/s = 0kg*m/s 50kg*m/s + 0kg*m/s = 50kg*m/s The momentum after collision: Object #1: 10kg * 3m/s = 30kg*m/s Object #2: 2kg * 10m/s = 20kg*m/s 30kg*m/s + 20kg*m/s = 50kg*m/s The total momentum is equal. confidence assessment: 3
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20:44:28 The momentum of the 10 kg object before collision is 10 kg * 5 meters/second = 50 kg meters/second. This is the total momentum before collision. The momentum of the first object after collision is 10 kg * 3 meters/second = 30 kg meters/second, and the momentum of the second object after collision is 2 kg * 10 meters/second = 20 kg meters/second. The total momentum after collision is therefore 30 kg meters/second + 20 kg meters/second = 50 kg meters/second. The total momentum after collision is therefore equal to the total momentum before collision.
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RESPONSE --> self critique assessment: 3
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20:50:34 `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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RESPONSE --> Because the forces acting on each other are equal and opposite, the impulses are equal and opposite. Thus the momentum change of the system is always zero. confidence assessment: 3
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20:50:50 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.
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RESPONSE --> self critique assessment: 3
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