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$\bullet$$\bullet$A tetherballagainst the smooth, fric-tionless post to which it isattached. (See Figure $5.45 . )$The string is attached to the ball such that aline along the string passes through the cen-ter of the ball. If the string is 1.40 $\mathrm{m}$ long-and the ball. has a radius of 0.110 $\mathrm{m}$ withmass $0.270 \mathrm{kg},$ (a) make a free-body dia-gram of the ball. (b) What is the tension inthe rope? (c) What is the force the poleexerts on the ball?

A. see DIAGRAM B. 2.65 $\mathrm{N}$C. 1.93 $\mathrm{N}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Aeych A.

October 17, 2020

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

Lectures

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04:34

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(II) A ball on the end of …

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A child's toy has a $…

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As shown in Fig. El0.20, a…

03:59

A block of mass $M$ is pul…

01:25

A 0.72 -kg ball is swung v…

04:59

In Fig. $12-26,$ a uniform…

02:00

A 2.0 -kg ball tied to a s…

A stone with mass 0.80 kg …

04:00

A conical pendulum is hang…

all right, So today's problem has to do with a tether ball that is leaning against a pole. It's attached by a stroke. Suffers were asked to make a free body diagram of the problem, and here it is. I've already drawn it up. So first you have the weight of the ball pointing downwards. And then, since the bowl is touching the pool right over here, there's a contact force that is pushing it away principle. So that is your normal doors over here. And then this tension in the strings. He's pulling the ball upwards into the side and have decomposed it here, where you have your case of X and your case of why now? Normally, when you have such situations, you confined piece of accent. Ease of why, by knowing what the angles? Because you know that piece of X is equal to thi co sign data and you know that, he said, wise equal to t sign. But we aren't really given it. We are given, however, the lengths of the strings, um, the length of the string, which would be the high part news of the triangle and the diameter of the ball, which would end up being the X component of this force. What? Um, so I went ahead and drew out the triangle a little bit bigger. Just everyone can see. And I have the 0.11 meters, which is a radius of a bowl over here. And I have 1.4 meters, which is selected. The shrink over here and co sign data would be equal to 0.11 over 1.4 and there can be found to be equal to 4.5 degrees. And then they use this answer to go over here and write down, um, Newton's second law for the Ex direction, the wind direction missile help of soul for being C. So, since we're trying to find attention force first, we're gonna go over here for part B, and we know that the two forces in the white direction are I should know the free body diagram, the upwards component of tension, which is he supply of the downwards force of gravity, which would be w which is the weight of the ball. And this is equal toe m A y. But a Y is equal to zero since the entire structure is still the ball isn't moving. So, um, we get the key supply in minus dub. You is equal to zero and recon substitute T sub y clear t signed data and we get t send data is equal to W and we're trying to find t here. We know data and we know W because W is just mg and were given in and and we nog So we can just say that t is equal to W over signed data which is equal to M G or beside their. And if we calculate that out, this is the answer that we get. Yet T is equal to 2.65 mutants. And then after that, we are asked about the force of the boat off the pole onto the ball. And this is the normal force that's over here that we've market everybody diagram. So same thing were it turns rewrite done using the second law, and we write out the forces we have peace of X minus and physical toe M x and again A is equal to zero because of all isn't moving at all. So we get t's, affects Linus and is equal to zero. We can change that, um, into t cosign video. And we get Ticos and data is equal to We're trying to find that we already know t We already know data so we can go ahead and calculate it out, and we get N is equal to 1.93 movements and these are our answers.

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