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## Homework Statement

You are standing 2.7 m from the centre of a spinning merry-go-round holding one end of a string tied to a 120g mass. The merry-go-round has a period of 3.9 s.

- Draw a system diagram of the situation.
- Draw an FBD of the mass in Earth's frame of reference.
- Draw an FBD of the mass in the merry-go-round's rotating frame of reference.
- What angle does the string make with the vertical?
**Determine the magnitude of the tension in the string.**

**My issue arises with the final question only (which is at the end of this admittedly long post)**, however, I would appreciate it if you folks could look over my FBDs as well, the rest is only ancillary.

## Homework Equations

- Fac = (mv^2)/r
- V = d/t
- circumference = pi * diameter
- Fg = mg

3. The Attempt at a Solution

3. The Attempt at a Solution

__A.__

I drew a person on the outside of the merry-go-round, and the string he holds follows a path some amount below the horizontal where it connects to the 120g mass. Like this:

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__B.__

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__C.__

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D: (My solution matches the textbook's)

D: (My solution matches the textbook's)

__FNET_Y__- Fnet_Y = Fg - Ft sin x = 0
- Ft sin x = Fg
- Ft = mg / sin x

__FNET_X__- mv^2/r = Ft cos x
- mv^2/r = (mg/sin x) * cos x
- V^2 = g/sin x * cosx
- rearrange for x
- rg/v^2 = tan x

__SOLVE FOR VELOCITY__- v = d/t
- v = circumference / 3.9s
- v = 2 * pi * r / 3.9s
- v = ~4.34m/s

__SOLVE FOR THETA__- tan-1(rg/v^2)
- tanx-1[(2.7*9.8)/4.34m/s^2]
- x = 54 degrees
- since they're asking for the angle from the vertical, it would be the complementary to this one
- 90- ~54 = 36degrees

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E:E:

- Using one of my previous equations to solve for Ft
- Ft = mg/sinx
*Ft = 9.8*0.12/sin(54)**Ft = 1.45N*

Where did I go wrong in my solution?

**EDIT:**The textbook's solution is wrong. I found the solution manual and they did the following operations

- cos x = Fg / Ft (x being the angle from the vertical)
- Ft = cosx * Fg

Ah well, good learning experience

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