- #1

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Says the answer is 25.6 Degrees, but I'm unsure even the right ways to start this problem.

It's not a homework question, just curious if anyone can show me the steps they would use to solve this? Dying to find out.

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- Thread starter Stingarov
- Start date

- #1

- 22

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Says the answer is 25.6 Degrees, but I'm unsure even the right ways to start this problem.

It's not a homework question, just curious if anyone can show me the steps they would use to solve this? Dying to find out.

- #2

radou

Homework Helper

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- #3

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F friction (Uk * Fn) and Applied Force, correct?

- #4

radou

Homework Helper

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F friction (Uk * Fn) and Applied Force, correct?

Correct. Now, what is your next step?

- #5

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W = F * d,

457.2 = F * 9.49

48.18 = F ? but I'm uncertain where to go from here with it.

457.2 = F * 9.49

48.18 = F ? but I'm uncertain where to go from here with it.

- #6

radou

Homework Helper

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W = F * d,

457.2 = F * 9.49

48.18 = F ? but I'm uncertain where to go from here with it.

Right, now, since F is the

- #7

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Probably a newbie question but what's the best way to solve for theta, from here?

- #8

radou

Homework Helper

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Probably a newbie question but what's the best way to solve for theta, from here?

Total work = (F*cos(theta) - Ffr) * displacement.

F is the pushing force, and Ffr is the force of kinetic friction, which equals Ffr = uk * N. The normal force N equals the weight of the chair. Now plug in and solve for theta.

- #9

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457.2 = x * 9.49 -> 457.2 /9.49

48.18 = Fnet

48.18 = F cos theta - 30.87?

Wow if I'm really messing this up let me know, things were clicking until this one and it seems like it should be easy. I understand where I used sin wrong, mistake.

- #10

radou

Homework Helper

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457.2 = x * 9.49 -> 457.2 /9.49

48.18 = Fnet

48.18 = F cos theta - 30.87?

Wow if I'm really messing this up let me know, things were clicking until this one and it seems like it should be easy. I understand where I used sin wrong, mistake.

There's something more to it, which I forgot to mention in my previous post (excuse me, please). The normal force equals the sum of the chair's weight and the vertical component of the pushing force F, so N = mg + Fsin(theta).

- #11

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48.18 = F cos theta - {(4.2)(9.8) + F sin theta}? Or am I misinterpreting you.

I'm not taking physics this semester but rather next semester, but would like to get as far ahead as possible. Forgive my simple questions eheh.

- #12

radou

Homework Helper

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48.18 = F cos theta - {(4.2)(9.8) + F sin theta}? Or am I misinterpreting you.

I'm not taking physics this semester but rather next semester, but would like to get as far ahead as possible. Forgive my simple questions eheh.

OK, let's slow down then.

Since the chair has constant velocity, the sum of all forces must equal zero, hence the sum of all horizontal components must equal zero. So, we have:

[tex]F\cos\theta - F_{fr}=0[/tex]. (1)

Further on, since the sum of all vertical components must equal zero, you have:

[tex]N = mg + F\sin\theta[/tex].

You know that the force of friction is [tex]F_{fr}= \mu_{k}N =[/tex]

[tex]=\mu_{k}(mg + F\sin\theta)[/tex].

After plugging that equation into equation (1), you have:

[tex]F\cos\theta = \mu_{k}(mg + F\sin\theta)[/tex]. (2)

Now, since you know the work of the applied force, [tex]W=F\cos\theta d[/tex], you have [tex]F =\frac{W}{d \cos\theta}[/tex]. Plug F into

equation (2), and you'll get an equation which you'll be able to solve for [tex]\theta[/tex]. I hope this helps.

- #13

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48.18 = .75 (mg + FsinTheta)

---->F = W/cosTheta*d

48.18 = 30.87 + .75 * 48.18tanTheta?

---->F = W/cosTheta*d

48.18 = 30.87 + .75 * 48.18tanTheta?

- #14

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- #15

cristo

Staff Emeritus

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You have the equation [tex]F =\frac{W}{d \cos\theta}[/tex] . Plugging this into ragou's eqn (2) gives [tex] \frac{W}{d}= \mu_k (mg+\frac{W}{d}\tan\theta) [/tex] which I think you hav. Solving for theta gives [tex] \tan\theta = \frac{1}{\mu_k}-\frac{mgd}{W} [/tex] Plugging your values in gives the solution.

It's a lot easier to work in algebraic terms, and then plug in the values when you have a final equation. It's a good idea to get used to algebra, as this will assist you later on in your studies.

edit: incidentally, your equation above gives the correct answer.

It's a lot easier to work in algebraic terms, and then plug in the values when you have a final equation. It's a good idea to get used to algebra, as this will assist you later on in your studies.

edit: incidentally, your equation above gives the correct answer.

Last edited:

- #16

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I see where I went wrong now. Yeah it is easier completely in algebraic terms, interesting.

- #17

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Thanks guys, much appreciated.

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