course PHY 121 1/4 018. `query 18*********************************************
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Given Solution: ** We treat the vertical and horizontal quantities independently. We are given vertical displacement and initial velocity and we know that the vertical acceleration is the acceleration of gravity. So we solve the vertical motion first, which will give us a `dt with which to solve the horizontal motion. We first determine the final vertical velocity using the equation vf^2 = v0^2 + 2a'ds, then average the result with the initial vertical velocity. We divide this into the vertical displacement to find the elapsed time. We are given the initial horizontal velocity, and the fact that for an ideal projectile the only force acting on it is vertical tells us that the acceleration in the horizontal direction is zero. Knowing `dt from the analysis of the vertical motion we can now solve the horizontal motion for `ds. This comes down to multiplying the constant horizontal velocity by the time interval `dt. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I skipped a step or two but I understand. ------------------------------------------------ Self-critique rating: ---- ********************************************* Question: `qQuery class notes #17 Why do we expect that in an isolated collision of two objects the momentum change of each object must be equal and opposite to that of the other? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Because the objects are isolated, that means that nothing else is interfering with the system. Whatever one force an object exerts on another, the second object exerts the opposite force. So in terms of momentum, the initial momentum of the objects is equal to the final momentum of the objects assuming no other influences. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: Briefly, the force exerted on each object on the other is equal and opposite to the force exerted on it by the other, by Newton's Third Law. By assumption the collision is isolated (i.e., this is a closed system); the two objects interact only with one another. So the net force on each object is the force exerted on it by the other. So the impulse F_net `dt on one object is equal and opposite the impulse experienced by the other. By the impulse-momentum theorem, F_net `dt = `d ( m v). The impulse on each object is equal to its change in momentum. Since the impulses are equal and opposite, the momentum changes are equal and opposite. **COMMON ERROR AND INSTRUCTION CORRECTION: This is because the KE change is going to be equal to the PE change. Momentum has nothing directly to do with energy. Two colliding objects exert equal and opposite forces on one another, resulting in equal and opposite impulses. i.e., F1 `dt = - F2 `dt. The result is that the change in momentum are equal and opposite: `dp1 = -`dp2. So the net momentum change is `dp1 + `dp2 = `dp1 +(-`dp1) = 0. ** STUDENT QUESTION: Are impulses the same as momentum changes? INSTRUCTOR RESPONSE : impulse is F * `dt momentum is m v, and as long as mass is constant momentum change will be m `dv by the impulse-momentum theorem impulse is equal to change in momentum (subject, of course, to the conditions of the theorem) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating: ---- ********************************************* Question: `qWhat are the six quantities in terms of which we analyze the momentum involved in a collision of two objects which, before and after collision, are both moving along a common straight line? How are these quantities related? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are two masses to consider, as well as the initial velocities and post velocities of each mass or object. The quantities form the relationship m1 v1 + m2 v2 = m1 v1 ' + m2 v2 ', where m1 and m2 are the masses, v1 and v2 are the initial velocities, and v1’ and v2’ are the final velocities. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** We analyze the momentum for such a collision in terms of the masses m1 and m2, the before-collision velocities v1 and v2 and the after-collision velocities v1' and v2'. Total momentum before collision is m1 v1 + m2 v2. Total momentum after collision is m1 v1' + m2 v2'. Conservation of momentum, which follows from the impulse-momentum theorem, gives us m1 v1 + m2 v2 = m1 v1' + m2 v2'. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating: ---- ********************************************* Question: `1prin phy and gen phy 6.47. RR cars mass 7650 kg at 95 km/hr in opposite directions collide and come to rest. How much thermal energy is produced in the collision? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 95km/hr * 1000m/km *1hr/60min * 60s/1m = 26.4m/s. KE = .5(m)(v^2) = .5(7650kg)(26.4m/s)^2 = 2665872 J per car. Adding the cars together, the total KE is 5,331,744 J. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: There is no change in PE. All the initial KE of the cars will be lost to nonconservative forces, with nearly all of this energy converted to thermal energy. The initial speed are 95 km/hr * 1000 m/km * 1 hr / 3600 s = 26.4 m/s, so each car has initial KE of .5 m v^2 = .5 * 7650 kg * (26.4 m/s)^2 = 2,650,000 Joules, so that their total KE is 2 * 2,650,000 J = 5,300,000 J. This KE is practically all converted to thermal energy. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I wasn’t really sure how to determine how much is converted to thermal energy. The only thing I can come up with is since they both collide and come to rest, that momentum has gone somewhere. But I know you said earlier that PE/KE weren’t exactly related to momentum. ------------------------------------------------ Self-critique rating: "