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Collar $A$ can slide freely on the semicircular rod shown. Knowing that the constant of the spring is $k$ and that the unstretched length of the spring is equal to the radius $r,$ determine the value of $u$ corresponding to equilibrium when $W=50$ Ib, $r=$ 9 in., and $k=15$ lb/in.

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Physics 101 Mechanics

Chapter 10

Method of Virtual Work

Work

Potential Energy

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

Lectures

02:08

In physics, work is the transfer of energy by a force acting through a distance. The "work" of a force F on an object that it pushes is defined as the product of the force and the distance through which it moves the object. For example, if a force of 10 newtons (N) acts through a distance of 2 meters (m), then doing 10 joules (J) of work on that object requires exerting a force of 10 N for 2 m. Work is a scalar quantity, meaning that it can be described by a single number-for example, if a force of 3 newtons acts through a distance of 2 meters, then the work done is 6 joules. Work is due to a force acting on a point that is stationary-that is, a point where the force is applied does not move. By Newton's third law, the force of the reaction is equal and opposite to the force of the action, so the point where the force is applied does work on the person applying the force. In the example above, the force of the person pushing the block is 3 N. The force of the block on the person is also 3 N. The difference between the two forces is the work done on the block by the person, which can be calculated as the force of the block times the distance through which it moves, or 3 N × 2 m = 6 J.

03:23

In physics, mechanical energy is the sum of the kinetic and potential energies of a system.

03:28

Collar $A$ can slide freel…

05:57

A collar $B$ with a weight…

04:57

The uniform semicircular b…

03:38

A 4 -kg collar can slide o…

question the free body diagram of the given situation can be shown as along this. Okay, so this is the diagram for the given situation. Okay, so, no. First we need to express distance in terms of data, so we can write. That is, this distance equals two are signed to. Okay, this is angle to to to and this is angle to initial angle. And this is final angle after stretching. So now we will calculate the language in of the spring using method of section 10 point to see. So now, potential energy in the system so we can write as not initially, is equal to our and s will be equals. Two to our course, Tita. Okay, this is stretched position, and this is a stress position. So as minus has not can be bitterness to our course. Tita minus is smaller. That will be equal to R to cost two to minus one. Okay, so now we can right. Repeat equals 21 by two k s minus s not fools. Minus w y mhm. Okay, so, substituting the values we get, we p equals 21 by two k s minus is not equal to this so far, Who goes to minus one Holy square minus W Y A. And the blue Y is equal to our scientific data sign boutique. Okay, No. Okay. To determine the equilibrium of the system, Uh, the first derivative will be equals to zero. So solving it, we get minus K are square to cause Cheetah minus one, multiplied by two scientists to minus two. The blue part the blue part cause to Tita. Okay. And this will be equal to zero for the equilibrium position. So from here, we get minus care to cost two to minus one. Who sent it to minus two? W course to Tita equals to zero. So from here, after rearranging weekend, right, Who caused cheetah minus one scientific, The whereby cause to Tita equals two minus w by care. Okay, now substituting the values of the bouquet. And are we get to cost two to minus one, Manipulated by scientists to develop a course to this is a duty to mhm. Okay, equals two minus of 50 divided by 15 multiplied by nine. And that will be equals two minus zero point 370 Okay, so using the graphic calculators, we can determine the value of Twitter as 0.957 radiant, and that will be quest to 54.83 degree. Okay, so the answer for this question for the

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