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Two rock climbers, Bill and Karen, use safety ropes ofsimilar length. Karen's rope is more elastic, called a dynamicrope by climbers. Bill has a static rope, not recommended forsafety purposes in pro climbing, (a) Karen falls freely about2.0 $\mathrm{m}$ and then the rope stops her over a distance of 1.0 $\mathrm{m}$ (Fig.60). Estimate how large a force (assume constant) she will feelfrom the rope. (Express the result in multiples of her weight.)(b) In a similar fall, Bill's rope stretches by only 30 $\mathrm{cm} .$ Howmany times his weight will the rope pull on him? Whichclimber is more likely to be hurt?

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a. 3.0 times her weightb. 7.7 times his weight, Bill is more likely to get hurt

Physics 101 Mechanics

Chapter 4

Dynamics: Newton's Laws of Motion

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Moment, Impulse, and Collisions

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October 23, 2020

A 420-kg piano is being unloaded from a truck by rolling it down a ramp inclined at 23 ?. There is negligible friction and the ramp is 11.0 m long. Two workers slow the rate at which the piano moves by pushing with a combined force of 1300 N parallel to t

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Lectures

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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.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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for the for this question, we should first find the final velocity right before they both hit the ground. Therefore, be final squared equals the initial squared, plus two times a delta y. In this case, a is going to be G. So we can say that the philosophy final would be equal to two g delta y all to the 1/2 power. Given that the initial velocities, of course zero, that term could be eliminated. So we can say that philosophy final would be two times nine points, eight meters per second squared and then this this would be multiplied by delta Y of 2.0 meters. Also the 1/2 power. And so we can say that velocity final would be equal to 6.26 meters per second and the suffice to Bill and Karen. So let's draw the free body diagram for these two climbers. My apologies going straight up would, of course, be force tension, and then going straight down would be the force of gravity. So we can say that due to angular other two d cinematics, uh, the acceleration is gonna be equal to negative. The initial squared divided by two Delta y and so this is going to be equal to negative 6.26 meters per second. Quantity squared, divided by two times 1.0 meters and this is giving us negative 19 0.494 need ersfirst second squared. So essentially, we can say that in order to find the road, the tension in the rope we can say that the sum of forces in the UAE direction would equal and a and in this case, the sequel's mg minus the force of the rope. We know that the force of the rope would be equal to mg minus m a and so the force of the rope was taken. Rather, force of the rope divided by M G would be equal to one minus a over G on the force of the rope over mg which would this would give us essentially forced tension in terms of their own body weight. So by using this equation, we can find the ah essentially the force of the rope, but relative to their own body weight. So when we solve, it will be one, uh minus and negative. So it'll be one plus 19.594 meters per second squared divided by 9.8 meters per second squared and this is giving us approximately 3.0 out. Therefore, the rope pools on Karen with an average force of three times her body weight. And now we have to assign the weather go about the same exact process for Bill. So for Bill again, velocity final equals 6.2 six meters per second. However, we need to find a new acceleration because here this is an equal negative 6.26 meters per second quantity squared. But then it will be divided by two times 20.30 meters and we find that this is gonna be equal to negative 65.313 meters per second squared. And so when we want to find the force of the rope divided by M. G. Ah, this is an equal one minus a over G. So this legal one plus 65.313 uh, the vital 99 28 and this is giving us 7.66 So essentially Ah, in this case, the rope toes on bill with an average of 7.66 times his weight. That is the end of the solution. Thank you for watching

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