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(II) Repeat Problem 63 assuming a coefficient of friction $\mu_{\mathrm{k}}=0.10$

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$$2.45 \mathrm{m} / \mathrm{s}$$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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so here for we first need Teo. Take this sum of forces in the UAE direction. This is going to be equal to force normal minus four Supplied time, sign of fi and then minus mg co sign If I ah, this is going to equal zero because we have translational equilibrium in the wind direction. We know that the sum of forces and the ex direction will be weather. We can't say anything in some of forces of extraction because it has acceleration in the extraction. So let's leave that for now and simply say that the force normal equals the force. Applied Time's sign if I plus mg co sign if I so at this point, we can say that for part, a thie angle measure equals 32 degrees on this is between the force applied ah, and displacement. So this simply means that the work done by the Applied Force would be equal to the magnitude of the Applied force times the distance co sign of Fada And this is giving us 150 Nunes times the distance of five meters Times Co sign of 32 degrees and we have that the work done by the Applied Force is going to be equal to 636 jewels. So this Abeer answer for party and then for part B, they want us to find the work done by gravity. The measure of the angle equals 132 degrees between the force of gravity and that this spaceman. So we can say that the work done by gravity is going to be equal to the force. The force of gravity Times d Co sign of theta. And this is equal in, of course, 18 kilograms times the acceleration due to gravity 9.8 meters per second squared time's a displacement of five meters and then co sign of 132 degrees. So that work done by gravity is going to be negative. 467 jewels. So this would be our answer for part B and then for port. See, we know that forced normal is going to be perpendicular to displacement. So this means that the work done by the normal force is simply equal to zero jewels because here co sign of 90 degrees with equal zero and then lastly for Part D. We want to find the final velocity so we can say that the work done by friction is equal to the frictional force. Times the distance co sign of theta on this is going to equal the coefficient of kinetic friction times Thie Applied force A sign of Fi plus mg ko sign If I times d co sign of theta We know that this is going to equal negative one So we can say that here the a work of fiction it is going to be equal to negative 0.10 The new coefficient of connect friction ah times 150 Nunes Times sign of 32 degrees plus 18 kilograms, 9.8 meters per second squared as on times again co sign of 32 degrees close apprentices. And so this is going to equal The work of friction is going to equal negative 114.5 jewels. So essentially just keep note of this number because then in order to find the network, it will be the work applied plus the work of gravity. People were gravity, plus the work do the normal force, plus the work of friction and this will be the change in kinetic energy. We know that this is going to be equal to zero and this will equal 1/2 em times velocity final, squared minus Flossie National squared. We know that the initial velocity is going to be zero. So essentially here. Ah, the velocity final will be equal to two times the work divided by M to the 1/2 power. And this is equaling too. Times 636 minus 467.4 minus 114.5. Divided by the mass of 18 kilograms, all to the 1/2 power. And we find that the final velocity is going to be approximately 2.5 meters per second. So this would be our final answer for party. That is the end of the solution. Thank you for watching

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