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Denoting by $\mathrm{m}_{*}$ the coefficient of static friction between the block attached to rod $A C E$ and the horizontal surface, derive expressions in terms of $P, m_{s},$ and u for the largest and smallest magnitude of the force $Q$ for which equilibrium is maintained.

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Physics 101 Mechanics

Chapter 10

Method of Virtual Work

Work

Potential Energy

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

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.

02:51

Denoting the coefficient o…

02:43

Knowing that the coefficie…

03:07

The coefficient of static …

39:31

As you can see, I already have the answer here. Um, I did all the work and recorded the video and made ever so slight of a mistake in the end by not dividing by two right here. Um, so I made a slight mistake, and now I am recording the whole thing over again. But this is the answer. And as we scroll up, we can see the work. Ah, I drew the diagram. Um, notice that there is a normal force at both a and B, and that was my mistake before, um, those counter act the force at p um, such that and trying to write it down and is p over to, um nevertheless, I can begin the virtual mo mentum analysis by getting the Y value at point F, which is here. Take the derivative of that. Then I need the X value. Appoint a take the derivative of that. It's pretty straightforward now, um, changing potential energy is zero p is in the negative direction times delta y f. And then I have Q and friction opposing each other. Um, times. Ah, Delta X A. Now I put friction and red because depending on the values of Q and P. Um, the friction might actually be pointing the opposite direction. So, um, here's where I figured out P over to. So the friction force is just gonna be Musa sp over to. So I substituted that into this equation, simplified a little bit. Keep simplifying, and I simplified to get q equals three p over two tangent data plus or minus music. S pew over to the plus goes along with the force of friction in the direction shown minus would be a force of friction in the opposite direction. OK, but that is the answer.

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