Question

A laboratory exercise on the concept of static equilibrium uses an apparatus called a force table. The force table consists of a round, level platform marked in degree increments about its circumference. In the center of the table sits a massless ring, to which three strings are tied. Each string is strung over a separate pulley clamped to the edge of the platform and then tied to a freely hanging mass, so that each string is under tension and the ring is suspended parallel to the table surface. There is a mass of m

1
​
=165 g located at θ
1
​
=22.5
∘
and a second mass of m
2
​
=227 g located at θ
2
​
=279
∘
. Calculate the mass m
3
​
and the location θ
3
​
(in degrees) that will balance the system and hold the ring stationary over the center of the platform.

Answer 1

To solve this problem, set up equilibrium equations for the forces acting on the ring and solve for the unknowns m₃ and θ₃.

Step-by-step explanation:

To solve this problem, we need to set up an equilibrium equation for the forces acting on the ring. Since the ring is stationary, the sum of the forces in both the x and y directions must be zero. In the x direction, we have T₁ * cos(θ₁) + T₂ * cos(θ₂) - T₃ * cos(θ₃) = 0. In the y direction, we have T₁ * sin(θ₁) + T₂ * sin(θ₂) + T₃ * sin(θ₃) - m*g = 0.

Using the given values for m₁, θ₁, m₂, and θ₂, we can plug them into the equilibrium equations and solve for the unknowns m₃ and θ₃. Solving these equations will give us the values of m₃ and θ₃ that will balance the system and hold the ring stationary over the center of the platform.Granola bars and trail mix are also commonly marketed as healthy snacks. However, they can be high in added sugars, unhealthy fats, and artificial ingredients. Raw almonds, on the other hand, are a healthier option as they are a good source of healthy fats, protein, and fiber.

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