Answer:
m₂ = 18 kg
Explanation:
Conceptual analysis
We apply Newton's second law on masses m₁ and m₂
∑F = m × a Formula (1)
∑F: algebraic sum of forces in Newton (N)
m: mass in kg
a: acceleration in m/s²
T: cord tension in Newton (N)
Known data
m₁ = 12 kg
F = 66 N
a₁ = a₂ = 2.2 m/s²
Problem development
We can see in the attached figure the free body diagram of the masses and we replace the data in formula (1), considering that positive forces are the ones that go in the same direction of acceleration::
Mass 1 (m₁) free body diagram:
∑Fₓ = m₁ × a₁
66 - T = 12 × 2.2
66 - T = 26.4
66 - 26.4 = T
T = 39.6 N
Mass 2 (m₂) free body diagram:
∑Fₓ = m₂ × a₂
T = m₂ × 2.2
39.6 = m₂ × 2.2
m₂ = 39.6 ÷ 2.2
m₂ = 18 kg
