A seesaw has a length L and uniform mass m and is resting at an angle of 𝚹 with respect to the ground

 A seesaw has a length L and uniform mass m and is resting at an angle of 𝚹  with respect to the ground (see the following figure). 

The pivot is located at a distance R from the lowered end. 

What magnitude of force needs to be applied perpendicular to the seesaw at the raised end so as to allow the seesaw to barely start to rotate?

Hint: 

F (L-R) = mg (R- L/2) cos 𝚹

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below).

The smaller flywheel of radius R₁ has a cord that has a pulling force F₁ on it.
What pulling force F₂ needs to be applied to the cord connecting the larger flywheel of radius R₂ such that the combination does not rotate? 

Input your answer in N using 3 significant figures. 

Hint: 

Uniform Meterstick in Static Rotational Equilibrium

A uniform meter stick in static rotational equilibrium when a mass m₁ is suspended from the x₁ mark, a mass m₂ is suspended from the x₂ mark,
and the support stand is placed at the xₛ mark. What is the mass of the meterstick, mₘ?

Hint:
F₁ + F₂ + Fₘ + Fₛ = 0
𝛕₁ + 𝛕₂ + 𝛕ₘ + 𝛕ₛ = 0

m₁ g + m₂ g + mₘ g - N = 0
x₁ m₁ g + x₂ m₂ g + mₘ xₘ g - N xₛ = 0
xₘ is the position of the center of mass for the uniform meter stick.
xₘ = 50cm

Physics + Probability Theory

Express C₂ in terms of T₁, T₂, T, and C₁.

Two bodies 1 and 2 with heat capacities C₁ and C₂ and temperatures T₁ and T₂ are brought into thermal contact in a thermostat, after which the temperature T is reached in thermal equilibrium.
Express C₂ in terms of T₁, T₂, T, and C₁.

Solurtion:


Q₁ = C₁ (T-T₁)
Q₂ = C₂ (T-T₂)
Q₁ + Q₂ = 0

C₁ (T-T₁) + C₂(T-T₂)=0
C₂(T-T₂) = C₁ (T₁-T)
C₂ = C₁ (T₁-T) / (T-T₂)

Physics Problem: Two bodies 1 and 2 with heat capacities C₁ and C₂ ...

Two bodies 1 and 2 with heat capacities C₁ and C₂ and temperatures T₁ and T₂ are brought into thermal contact in a thermostat, after which the temperature T is reached in thermal equilibrium. Express T in terms of C₁, C₂, T₁, T₂. 

Problems in Physics: "Two point masses A and B ..."

Problems in Physics.

1. Two point masses A and B are located on the x-axis. When mass A occupies the X_A coordinate and mass B occupies the X_B coordinate, then their common center of gravity is at the X coordinate. Where is their common center of gravity when the first mass occupies the X_A2 coordinate and the second mass occupies the X_B2 coordinate?
2. When two bodies A and B with temperatures T_A and T_B are brought into thermal contact in a thermostat, then temperature T is reached in thermal equilibrium. What temperature will be in thermal equilibrium if the bodies are initially heated to temperatures T_A2 and T_B2?
3. There is a mark on a thin rubber cord somewhere between the ends of the cord. The locations in space of the ends A and B of the stretched cord and the marks on it are given by the vectors: R_A , R_B and R. Express the location of the mark on the cord when the ends of the stretched cord are located at the points given by the vectors R_A2 and R_B2.