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A bicyclist can coast down a $5.0^{\circ}$ hill at a constant speed of6.0 $\mathrm{km} / \mathrm{h}$ . If the force of air resistance is proportional to thespeed $v$ so that $F_{\text { air }}=c v,$ calculate $(a)$ the value of the constant $c,$ and $(b)$ the average force that must be applied inorder to descend the hill at 18.0 $\mathrm{km} / \mathrm{h}$ . The mass of thecyclist plus bicycle is 80.0 $\mathrm{kg}$ .

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a. $41 \frac{\mathrm{N}}{\mathrm{m} / \mathrm{s}}$b. $140 \mathrm{N}$

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

Simon Fraser University

Hope College

University of Sheffield

McMaster 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.

04:30

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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A bicyclist of mass 75 $\m…

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A bicyclist is coasting st…

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A bicyclist is coasting s…

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ssm A bicyclist is coastin…

11:50

If a bicyclist of mass 65 …

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(III) A bicyclist of mass …

03:09

(1II) A bicyclist coasts d…

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(II) A cyclist intends to …

01:55

(III) A bicyclist coasts d…

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04:45

A person on a bicycle (com…

So let's draw the free body diagram for the bicyclist. We can say that this box represents the bicyclist. The force normal would always be perpendicular to the surface of contact. Opposite to the direction of motion would be the force of air resistance. And then going straight down would be, of course, the weight of the bike bicyclist system. Ah, here would be our angle theta. And so we can say that the sum of forces in the ex direction would be equal to M g sign of Seita minus the force of the air resistance. This is equaling zero because he's coasting downhill, which means that he wants to have a constant velocity downhill. Ah, we can then see that the force of the air resistance would be equal to the X component of the of his weight. And this is gonna equal CV now to find See, we simply take mg sign of Seita. We're going to divide this by the by V and this is gonna equal the mass of the bike bicyclist system. 80 kilograms multiplied by the acceleration due to gravity on earth, 9.80 meters per second squared multiplied by sine of the angle of incline. So five point zero degrees, this would all be divided by the velocity. So he's moving at 6.0 kilometers per hour. Let's convert one meter per second for every 3.6 kilometers per hour and we find that sea is gonna be equal to approximately 41. Aah! This would be Newtons per meter for a second back. The better way to, uh, express the units with the Newtons over meters per second. So this would be the value of C. Now for part B, we're going to, um, redraw the free body diagram because now this would be the bicyclist forced normal, perpendicular to the surface of contact. Always going straight down would be the mass. The weights of the bike bicyclist system. Going opposite to the direction of motion would be the force of air resistance. But now he has a force applied again. This would be our angle, Fada. So here we're going to, uh, be essentially the bicyclist is now applying a force in addition to the force of gravity. So we can say that the sum of forces in the ex direction ah would be equal to the force applied plus mg sign of Fada minus the force of air resistance. This is equal to zero. We can say that the force applied would then be equal to the force of air resistance minus and G sign of data. And then this is equaling CV minus mg sign of data. So here, essentially force applied would be equal to 40.998 Let's Onley converts at the very it's only round rather the very at the very end. So Newton's per meter per second and then this would be multiplied by 18.0 kilometers per hour. Most Clyde by one meter per second, divided by 3.6 kilometers per hour. Close parentheses, close parentheses minus the weight. So 80.0 kilograms times 9.80 meters per second squared times Sign of the incline. So sign of 5.0 degrees and we find that the force applied there's gonna be equal to approximately 136 0.7 Newton's. This would be our answer for part B. That is the end of the solution. Thank you for watching

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