course Phy 201 ??????v?q???assignment #017
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05:38:22 `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 --> F = dp/dt F= 19.6N ( 9.8* 2kg ) / .03sec F= 653.3N confidence assessment: 1
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05:39:53 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 understand that you use the equation, Fave * `dt = m `dv and rearrange it to Fave = m `dv / `dt = to get the solution, 10 kg * (-2 meters/second)/(.03 seconds) = -667 N. self critique assessment: 2
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05:42:00 `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 --> Fave *dt= m dv therefore, -667N * .03sec = 2kg * dv =-667N * .03sec / 2kg = dv , dv = -10.01m/s^2 confidence assessment: 1
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05:44:59 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 --> I understand that the force exerted on the first object by the second has equal and opposite force of 667N, therefore, a momentum change equal to the impulse F `dt = 667 N * .03 sec = 20 kg m/s delivered to the 2 kg object and 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 therefore, the second object had initial velocity 0, its after-collision velocity must be 10 meters/second. self critique assessment: 2
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05:49:31 `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 the collison, KE = .5mv^2 = KE = .5*2kg*10m/s^2 =KE= 100kgm/s^2 and after the collison, KE = .5mv^2 KE= .5*10kg*-2m/s^2 ^2 KE = 20kgm/s^2 So, the after colision is less than the total kinetic energy before. confidence assessment: 1
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05:52:13 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 --> I understand that 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 and that 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 self critique assessment: 2
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05:54:30 `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 --> total momentum before is m*v = 10kg * 5m/s = 50 and after momentum is m*v = 2kg * 10m/s= 20 therefore, a difference of 30 confidence assessment: 1
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05:57:16 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 --> I understand that I did everything correctly, except I did not calculate the momentum of the first object after collision which was 10 kg * 3 meters/second = 30 kg meters/second so therefore, that + 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 and momentum of the second object after collision is 2 kg * 10 meters/second = 20 kg meters/second led to a total momentum after of 50kg m/s self critique assessment: 2
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05:58:23 `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 it is unchanging therefore making it equal to the total momentum before the collision. confidence assessment: 0
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05:59:16 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 --> I understand that since the changes in mometum are equal and opposite, that the total momentum is therefore zero. And that the momentum after the collision is equal to the mometum before the collision. self critique assessment: 2
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