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A small block $B$ fits inside a slot cut in arm $…

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Problem 60 Easy Difficulty

A semicircular slot of 10 -in. radius is cut in a flat plate which rotates about the vertical $A D$ at a constant rate of $14 \mathrm{rad} / \mathrm{s}$. A small, $0.8-\mathrm{lb}$ block $E$ is designed to slide in the slot as the plate rotates. Knowing that the coefficients of friction are $m_{x}=0.35$ and $m_{k}=0.25,$ determine whether the block will slide in the slot if it is released in the position corresponding to $(a) \mathrm{u}=80^{\circ},(b) \mathrm{u}=40^{\circ} .$ Also determine the magnitude and the direction of the friction force exerted on the block immediately after it is released.

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Video Transcript

Yes. Question. We have this set up. Hey, there's a block. Small block V Sweeter inside. Uh, this, uh, slot thing. Okay. And then we are told that the speed he is 1.4 m close. Second for data, uh, is in between potato between zero degrees, 250 degrees. Okay. And then we know that the block we are given that lock flights when data, it goes 250 degrees. Okay. And then the rotation is in constant read. Mm. So this means there's no tangential acceleration. Okay, so the question wants us to find a coefficient of static friction between the block and the slot. Okay. Okay. So, uh, using the given information, KB. So we will only look at the situation when data, it goes 250 degrees. Okay. And we look at the free body diagram of the block. Oh, okay. So at 100 GPS, it will look something like this. This is, uh, and large region of the block. And then, uh, so you draw this, um, political lying. Okay, so this is 30 degrees on the block. You have the weight mg. Okay. You have the normal force, but in this direction. Okay, then you have friction pointing in this direction. Yeah. Okay. So, um, as mentioned just now, there's no tangential acceleration. 80 0. I'm going also going to, uh, indicator acceleration. The acceleration. There is a normal component. Yeah, because the whole thing is in secular motion. Okay, but just at the speed is constant. So there's no tangential acceleration that you have, uh, acceleration along the normal components, which is the centripetal acceleration. Okay, so, uh, the e n s. We square overrode A B is 1.4 and then roll is your country. Okay, so this is Oh, something that we need to use later. You calculate needs to be 6.533 You know this post second square, Okay. And then from the free body diagram, Okay. I'm going to use a coordinate system that looks like this accent. Why, then, using you then second law, it forces along the X direction will give us an a N k. So I will write mg. Of course. I 30 degrees okay. Minus f equals two and the square. We're okay. O m a n key. Yeah. So how do I know that it is co sign. So the angle 30 degrees is with the vertical. It is also this angle here. The new single here is 30 degrees. Uh huh. And then, uh, forces along the y is zero. Okay, because 1/10 century zero. Okay, so if you look at the diagram again, then we have ah mg sine 30 degrees. It was too. Uh okay, then, Uh uh, fiction. It's going to be equal to u S n. Okay, so, uh, problem. Oh, from equation one. Okay. And combined to he This is what we are going to have mg co sign 30 degrees minus us. And because two and we square over All right. And then n is mg side 30 degrees so you can cancel the M. Yeah. And then you make, uh, us Julie. Sorry. 30 degrees and the left hand side. And you get G cause I d. Degrees, right? Yes. We square overall. T So your ass with Jesse to cause i d degrees finance lease where we roll with it. Bye bye. Do you say the D degrees? Okay. Very kind. Who in the numbers the company is You get 0.400 So this is that coefficient of static friction. And that's all for this question.

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Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

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A small block $B$ fits inside a slot cut in arm $…

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Video Transcript

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Liev Birman

Farnaz Mohseni

Jared Enns

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Liev Birman

Farnaz Mohseni

Jared Enns

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Liev Birman

Farnaz Mohseni

Jared Enns

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek

Vector Mechanics for Engineers: Statics and Dynamics