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**Static Equilibrium KEY**

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**Unstable: Corners + sides = 8 + 12 = 20**

1. How many different positions of stable equilibrium and unstable equilibrium are there for a cube (consider each surface, edge and corner to be a different position)? Stable: flat sides = 6 Unstable: Corners + sides = = 20

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2. A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold eights 200 N and is 3.00 m long. What is the tension in each rope when the 700 N worker stands 1.00 m from one end? T1 T2 Sum torques around T1: Sum torques around T2: 200N 700N

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**Sum torques around 50cm mark:**

3. A student hangs a 25g mass from the 0.0 m mark on a meterstick and another at the 20. cm point. How large of a mass should the student hang at the 85 cm point if the student wants to perfectly balance the meterstick on her finger placed at the 50. cm mark? 0.025kg 20 50 85 m = ? Sum torques around 50cm mark:

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**4. A 245 N shop sign is hung from the end of a 1. 70 m, 155 N beam**

4. A 245 N shop sign is hung from the end of a 1.70 m, 155 N beam. The beam is placed flat against the wall m from the wall, a cable is attached, one end to the beam and the other end to the wall. What is the tension in the wire if the wire makes a 35o angle with the beam? WALL T 35o Tsin35o 155N 245N 0.85m 1.35m 1.7m Sum torques around the wall because I don’t know the frictional force provided by the wall.

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50.0kg(9.8m/s2) 45kg(9.8m/s2) 35kg(9.8m/s2) 0.45m 1.00m 0.35m T1 T2 5. A 50.0 kg porch swing is 2.00 m long and is supported by two cables vertically connecting each side of the swing to the ceiling of the porch. If a 35 kg kid is sitting 0.35 m from the right end of the swing and a 45 kg kid is sitting 0.45 m from the left end, what is the tension in each support cable?

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