Answer:
α = 13.7 rad / s²
Explanation:
Let's use Newton's second law for rotational motion
∑ τ = I α
we will assume that the counterclockwise turns are positive
F₁ 0 + F₂ R₂ - F₃ R₃ = I α
give us the cylinder moment of inertia
I = ½ M R₂²
α = (F₂ R₂ - F₃ R₃) 
let's calculate
α = (24 0.22 - 13 0.10)
2/12 0.22²
α = 13.7 rad / s²
A) We balance the masses: 4(1.00728) vs 4.0015 + 2(0.00055)4.02912 vs. 4.0026This shows a "reduced mass" of 4.02912 - 4.0026 = 0.02652 amu. This is also equivalent to 0.02652/6.02E23 = 4.41E-26 g = 4.41E-29 kg.
b) Using E = mc^2, where c is the speed of light, multiplying 4.41E-29 kg by (3E8 m/s)^2 gives 3.96E-12 J of energy.
c) Since in the original equation, there is only 1 helium atom, we multiply the energy result in b) by 9.21E19 to get 3.65E8 J of energy, or 365 MJ of energy.
Label A: sublimation
Label B: condensation
Label C: melting
Answer: 0.798 m
Explanation:
Given
Mass of the spring oscillator, m = 1.48 kg
Force constant of the spring, k = 35.4 N/m
Speed of oscillation, v = 3.9 m/s
Kinetic Energy = 1/2 mv²
Kinetic Energy = 1/2 * 1.48 * 3.9²
KE = 0.5 * 22.5108
KE = 11.26 J
Using the law of conservation of Energy. The Potential Energy of the system is equal to Kinetic Energy of the system
KE = PE
PE = 1/2kx²
11.26 = 1/2 * 35.4 * x²
11.26 = 17.7x²
x² = 11.26 / 17.7
x² = 0.6362
x = √0.6362
x = 0.798 m