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One 110-kg football lineman is running to the right at 2.75 m/s while another 125-kg lineman is running directly toward him at 2.60 m/s. What are (a) the magnitude and direction of the net momentum of these two athletes, and (b) their total kinetic energy?
(a) $P_{x}=m_{A} v_{A x}+m_{B} v_{B x}=(110 \mathrm{kg})(2.75 \mathrm{m} / \mathrm{s})+(125 \mathrm{kg})(-2.60 \mathrm{m} / \mathrm{s})=-22.5 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ The netmomentum has magnitude $22.5 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ and is directed to the left.(b) $K=\frac{1}{2} m_{A} v_{A}^{2}+\frac{1}{2} m_{B} v_{B}^{2}=\frac{1}{2}(110 \mathrm{kg})(2.75 \mathrm{m} / \mathrm{s})^{2}+\frac{1}{2}(125 \mathrm{kg})(2.60 \mathrm{m} / \mathrm{s})^{2}=838 \mathrm{J}$
Physics 101 Mechanics
Chapter 8
Momentum, Impulse, and Collisions
Section 1
Momentum and Impulse
Moment, Impulse, and Collisions
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problem. 8.5 way have thes two football lineman running towards each other, the masses and speeds shown. And we want to know. First of all, what is the net momentum of the system formed by these two alignment running at each other? And then what is the net kinetic energy? Uh, from you know, they're having some mass and speed, so we'll call this the positive X direction are just the positive direction, since this is one dimensional. Doesn't call this, but let's call it six. So the momentum is going to be the momentum of this lineman who, since he's running in the direction of called Positive, this would be positive and it's going to be his mass times. The speed when I didn't 10 kilograms times two point. So I mean, it's per second. And then this lineman is running in the negative extraction. So let's attract his momentum from from that of the first day over here, and that this is going to be 100 and 25 kilograms times two points, six meters per second. And then if you, uh, do all of your asthma tick here, this will work out to be negative, 22.5. That's Graham meters per second. So this is the direction negative X direction with and then this is a magnitude. Now we'd like to do is find out what the net kinetic energy of all this is. And similarly, we just add up the kinetic energy of each part of the system. That'll tell us how much we're dealing with. So recalled it. It's 1/2 and B squared. So 1/2 I'm sorry, 110 kilograms times five squared plus an hour Adding this because the spirit here is always going to be positive. So even if we were accounting for the fact we called were saying, This guy's running in the negative direction, this still ends up Being positive because we've squared is also technically a speed is is positive because it's the magnitude of the velocity. You know, we're using the bubble butt. This is 125 kilograms, and he's going slightly slower 2.6 meters per second, which we will spare and then going through the numbers here, you'll find this is 838 Jules. So this is the direction and magnitude of their mo mentum. So I'm going to the left is this guy's a little bit bigger and this is their total kinetic energy.
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