World-class sprinters can accelerate out of the starting blocks w...

Question

World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 m/s2. How much horizontal force must a 55-kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

Accepted Answer

welcome back everybody. We have a sprinter running a race now in these races there's this little mechanism called a sprinter block that essentially pushes on our sprinter at the start of the race to get him propelled forward. Now we are told that this sprinter as he is propelled forward, achieves an acceleration of 14. m per second squared. And we are also told that the mass of this sprinter is 58 kg and we are asked to find out two different things here. A We need to figure out the total force that the sprinter is exerting on this block right here and be we need to figure out what object is causing a force to propel this sprinter forward. Is it going to be himself or will it be the block? So let's go ahead and start with part A. Here, starting with part A. I got to know Tate something really important here. We know that by Newton's third law of action reaction, the sprinter is pushing on the block and as the result, the block is pushing back on the sprinter. So, our summation of forces by the sprinter is equal to our summation of forces by the block. Now, this of course, according to Newton's second law, is just going to be the mass times acceleration. So let's go ahead and plug in our values here, we have 58 kg times the acceleration of 14.5 m per second squared. Which when you plug into your calculator, you get 841 Newtons. So now moving on to Part B, is this motion right here, Is he being propelled forward by a force from himself or the block? Well, we said by Newton's third law that the sprinter is pushing on the block and the block is pushing back, We'll notice how the blocks force is going in the same exact direction as the sprinters running direction. Therefore, it is the force from the block that is propelling the sprinter forward. So we have answered part B, and we have answered part A. What is the magnitude of that force? And this corresponds to answer choice. D Thank you guys so much for watching. Hope. This video helped. We will see you all in the next one.

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