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Jumping to the ground. A 75.0 $\mathrm{kg}$ man steps off a platform 3.10 $\mathrm{m}$ above the ground. He keeps his legs straight as he falls, but at the moment his feet touch the ground his knees begin to bend, and, treated as a particle, he moves an additional 0.60 $\mathrm{m}$ before coming to rest. (a) What is his speed at the instant his feet touch the ground? (b) Treating him as a particle, what are the magnitude and direction of his acceleration as he slows down if the acceleration is constant? (c) Draw a free-body diagram of this man as he is slowing down. (d) Use Newton's laws and the results of part (b) to calculate the force the ground exerts on him while he is slowing down. Express this force in newtons and also as a multiple of the man's weight. (e) What are the magnitude and direction of the reaction force to the force you found in part (c)?

a) $v_{y f}=7.79 \mathrm{m} / \mathrm{s}$b) $a_{y}=50.6 \mathrm{m} / \mathrm{s}^{2}$ upwardc) $\sum F=m g-N$ upward$N=4530 \mathrm{N}$ upward$N=6.16 \mathrm{mg}$

Physics 101 Mechanics

Chapter 4

Newton's Laws of Motion

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

05:10

Jumping to the Ground. A 7…

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A 75.0-kg man steps off a …

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11:18

A $65-\mathrm{kg}$ person …

08:07

When jumping straight down…

03:55

A Standing Vertical Jump. …

03:25

Figure $5-53$ shows a man …

02:57

11:41

08:21

A $78.0-\mathrm{kg}$ perso…

All right. So we have a platform that's 3.1 meters above the ground. Men of jumps of off of it so falls directly. Ah, and so gravity is the only thing acting on him really falls. And then he bounces back up for a bit and then falls back down again. This bed is point six meters. So we have to find of first the the velocity of the fall. And so this can be found from this equation of motion. Bossy squared equals initial velocity squared plus two times acceleration. That this is why direction times, ah times the distance fallen in the white direction. So velocity initially zero and so V why is just a square root of two times the acceleration due to gravity at times the distance? And so that would be two times. It's exciting. You're the gravity Also called she 9.8 meters per second squared times. Um, not times 3.1 meters isn't this distance. And so this velocity is 7.79 meters per second and that's it, for part prepared be. We're looking at this slight jump again. And so we use the same equation of motion. But now we want acceleration. Ah, and so acceleration sure will be equal to velocity squared minus initial velocity squared over two. Why these air? The wind direction. Why we? No, To your 0.6 meters. Ah, the final velocity is zero. So your initial velocity is just what we found here. Ah, so v zero. Why in this case is B y from part there? Ok, eso This gives you negative. 7.79 Eunice per second squared squared over two times 20.6 meters. All right on That gives you negative. 15.6 meters per second squared. And so, hero, when velocity was acting Ah, exacting downwards. And we got a positive number here for acceleration. We got a negative number of being set acceleration Must be acting up words Okay, s so try not to confuse yourself but the signed conventions here. But in this case, acceleration is upwards. Okay. Part C for this free body diagram you have you really have to force is ready your oven upward force Ah f nuova downward force the force of gravity of the weight of the person. And so what's happening here is that acceleration is acting upwards while velocity is acting downwards. All right, so so that's part ceiling and then party. Once you defined the force, the upward force knight a man of And so this would be from Newton's second law, Which is that the sum of forces? So here we're considering motion the Y direction. So forces why direction is mass times acceleration and why direction? It's the sum of forces of y direction from the three bodies. Diagram is just force minus the weight. Ah, this is she. And that's equal to mass times acceleration in the white direction. This would be the acceleration we found here. So in part B so this gives us that f equals mass. Take mass common times acceleration plus acceleration due to gravity and mass. As we know a 75 kilograms acceleration, it's 15.6 meters per seconds. Crazy just found and session due to gravity is 9.8 meters per second squared now you might be confused as to why thiss acceleration is positive and not negative as it was in part B. This is because of in parts A and B are different upwards. Direction was negative and downwards direction was positive and so when it was a negative acceleration, it means it meant many was acting upwards. Ah, contrary to hear, we're actually switching that fuel and calling the upward direction to be positive and our direction or sorry, upward direction No to be negative and our direction positive. And so that is why this is a positive here and you work that out, you get that a put forces 4,530 newts. Compare that to the weight. So Wei is just mass times acceleration due to gravity. Um, this is about 75 times 9.8 and 7 35 are 7 35 Newtons is those is the weight of the man weighing 75 killer of the terrified cure mass from So what we do is we take a ratio retake ratios of F ratio of after w upward forced to wait. And so that's 45. 30 over 7 35 And that gives you six points 16 meaning that upward force is over six times the weight. All right, and finally compartment Do ah, always doing is using Newton stirred law which says that action and reaction force is equal and opposite selves. So that means the reaction force. Ah, reaction floors fourth recalls 45 30 mutants, as we found in part. See? Ah, acting downwards. And so this this force contracts are completely balances. Thie upward force be calculated here by Newton. Stirred Law bounces around. And this is a force of the man pushing on the ground because this upward force here was a force of the ground pushing on the man, and that's it.

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