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Problem 1 Medium Difficulty

(a) What is the magnitude of the momentum of a $10,000-k g$ truck whose speed is 12.0 $\mathrm{m} / \mathrm{s} ?$ (b) What speed would a $2,000-\mathrm{kg}$ SUV have to attain in order to have (i) the same momentum? (ii) the same kinetic energy?

Answer

a. $1.20 \times 10^{5} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$
b. (i) $60$ m/s (ii)26.8 $\mathrm{m} / \mathrm{s}$

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Video Transcript

in this question. We have a truck that is moving safe, the right with velocity off 12 m per second on the mass off the truck is 10,000 kg. Given that we have to calculate the magnitude off the momentum for that, we can use this expression which tells us what is the magnitude off the momentum. According that expression, the magnitude off the momentum is given by the product off the mass which is 10,000 by the velocity which is 12. We can write the mass as 10 to the fourth on the velocity as 1.2 times 10 on these results in the momentum off 1.3 times 10 to the fifth kilograms, times meters per seconds. On this is the answer to the first item off this question. In the second item, an SUV is moving with some unknown velocity V to the right, say on it has a mass off 2000 kg. In the first item off the second item, we have to calculate what should be the velocity off the SUV. In order for this momentum to be equal to the momentum off the truck so we can use the equation for the magnitude of the momentum. P is equals to the mass off the SUV times the velocity off the SUV. We want the momentum off the SUV. Toby equals to the momentum off the truck. These results in the following 1.2 times stand to the fifth should be equal to the mass off the SUV, which is 2000 times its velocity. Then the velocity of the SUV is equals to 1.2 times 10 to the fifth, divided by 2000, which we can write as two times 10 to the third, and then we just have to do the calculation. So we cancel out three turns off 10. So we're left with them to the second in the numerator. Then you simplify here. So we have 0.6 under reform. The velocity is 0.6 times stand to second or 60 m per second on this is the answer for the first item off the second item. Now, for the second item off the second item, we want Signet IQ energy off the SUV to be the same as the kinetic energy off the truck that is moving with 12 m per second off velocity with the mass off 10,000 kg. So remember that expression for the kinetic energy is this one. The kinetic energy is half m times V squared. What do you want? Is that the kinetic energy off the S E V to be the same as the kinetic energy off the truck? So these results in the following the mass off the SUV times the velocity off the S U V, which will calculating this item divided by two and the velocity squared should be equals to the mass off the truck times the velocity off the truck squared, divided by two. These results in the following 2000 kg times the velocity off the SUV. Let me call this V s Divided by two should be equals to the mass off the truck, which is 10,000 kg times its velocity 12 squared, divided by two. Then, as you can see, we can already get rid of these factors off to. And then we solve this equation for the velocity off the SUV. By doing that to get the following the velocity of the S. U V squared is given by 10,000 times 12 squared, divided by 2000, we can simplify 10,000 with 2000. And this is very easy because this division results in five. The reform The velocity off the S U V is equal to the square it off five times 12 squared. This is the square root off five times the square root off 12 squared the square root off 12 squared is 12 off course and then we have the square root off five and then we can approximate the square root off five so that the final result is a velocity off approximately 26.8 m per second on this is the answer to the second item off the second item.

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