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Problem 47 Medium Difficulty

mmh An 81-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is 0.49. (a) What is the magnitude of the frictional force? (b) If the player comes
to rest after 1.6 s, what was his initial velocity?

Answer

390 $\mathrm{N}$
7.7 $\mathrm{m} / \mathrm{s}$

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Video Transcript

in this question. There are three forces acting on the player. The weight forced the normal force, alerted by the ground and the frictional force exerted by the ground too. And in the first item, we have to calculate what is the magnitude off. The frictional force knows that the player is already moving. It's sliding on the ground. Therefore, we can calculate the frictional force using the following equation frictional force. In that case, where the player is already moving, he's given by the genetic frictional coefficient times the normal force. But in the situation, the normal force is exactly counterbalanced by the weight force. Therefore, what we have here is that the frictional force Zico student kinetic friction coefficient times The weight force with the weight force is given by the mass off the player times acceleration off gravity. Remember that acceleration of gravity is approximately 9.8 meters per second squared near the surface off the earth. Therefore, the fictional force is given by 0.49 times into one times 9.8, which gives us a frictional force off approximately 300 19 new times. So this is the answer for the first item on the second night and we have the following. The player started his light and then after a time off 1.6 seconds, it comes to rest. So the final velocity is he close to zero? Then what? Waas his initial velocity. To answer that question, we can use the following equation the velocity as a function off time. Is it close to the initial velocity plus the acceleration things that interval of time, then the final velocity is zero. So zero is it close to the initial velocity plus the acceleration times 1.6, which is the time it took for the velocity to become zero Then the initial velocity is because to minors acceleration times 1.6. Then how can we calculate acceleration? We can use Newton's second law for that you don't Second Law tells us that that force is the coast. The mass times acceleration. We we were applying Newton's second law over the horizontal axis, which I choose to be pointing to the right. Then the net force on that access is the frictional force. We just pointing to the left So miners fictional force is there close to the mass off that player times its acceleration then minus 390 is he goes to 81 times acceleration finally minus 390. Divided by a 21 is the acceleration off the player. Then the initial velocity is eco's too. 390 times 1.6 divided by 8 to 1. What happened to the minus sign? Well, there is a minor sign here and the minus sign here. So minus sign times a minus sign is a plus sign. This is why the minus sign Don't appear here and then the initial velocity is approximately 7.7 meters per second and this is the answer for the second item.