# Pendulum-Work Question

1. Jan 29, 2017

### Arman777

1. The problem statement, all variables and given/known data
A pendulum of lenght $L=1.25m$.Its bob (which effectively has all the mass) has speed $v_0$ when the cord makes an angle $θ_0=40.0^°$ with the vertical.$(a)$ What is the speed of the bob when it is in its low (est position If $v_0=8.00m/s$ ? What is the least value that $v_0$ can have If the pendulum is to swing down and then up $(b)$ to a horizontal position,and $(c)$ to a vertical position with the chord remaining straight ? $(d)$ Do the answers to parts $(b)$ and $(c)$ increase,decrease,or remain the same if $θ_0$ is increased by a few degrees ?

2. Relevant equations
$-ΔU=W$
$W=Δ(KE)$
3. The attempt at a solution

I found the answer of (a) using -
$-ΔU=W$
$W=Δ(KE)$
it came $v=8.35\frac m s$

I didnt understand (b) and part (c).so I stucked there...

Thanks

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2. Jan 29, 2017

### haruspex

Do the same calculation as you did for part a) to get an expression for the speed v at any given angle, θ, in terms of v0, θ0, L, g and θ.

3. Jan 30, 2017

### Arman777

$\sqrt {(v_0)^2+2gL(cosθ-cosθ_0)}=v$

4. Jan 30, 2017

### haruspex

Ok. So what is θ in b)?

5. Jan 30, 2017

### Arman777

90 degree

6. Jan 30, 2017

### haruspex

So plug that in. What is the smallest value v0 can have?

7. Jan 30, 2017

### Arman777

Ok I found but for c what would be the angle ?

8. Jan 30, 2017

### haruspex

θ0? Same as before.

9. Jan 30, 2017

### Arman777

θ ?

10. Jan 30, 2017

### haruspex

You told me in post #5.
I have the feeling that there is something you are not understanding about the question, and I can't figure out what it is.

11. Jan 30, 2017

### Arman777

I found the answer of (b),plotting θ=90
For (c) what is θ=?

12. Jan 30, 2017

### haruspex

I'm very sorry, my eyes kept jumping to the wrong line, so I was reading b instead of c.
For c there is a complication. For b, the speed at the horizontal position could be 0. Could the speed be zero at the top of the loop?

13. Jan 30, 2017

### Arman777

It cant

14. Jan 30, 2017

### haruspex

Right. So what is the minimum speed at the top.

15. Jan 30, 2017

### Arman777

$v=2\sqrt {gL}$

16. Jan 30, 2017

### haruspex

No. Consider this condition
What forces act on the bob at the top? What must the net force be?

17. Jan 30, 2017

### Arman777

Yeah I made a mistake I know I noticed now

18. Jan 30, 2017

### Arman777

v=6.72

19. Jan 30, 2017

### haruspex

That's not right for the speed atthe top. How did you get that? Or is that your answer for v0?

20. Jan 30, 2017

### Arman777

At the bottom total energy is 1/2mv^2 which here v is as we found ot 8.35 and at the top energy is 1/2mv^2+mg2L so I thought the should be equal