Two boxes m1 and m2 are connected by a lightweight cord and sitting on a frictionless surface. A horizontal force of 66 N pulls
on box m1 and then m2 is pulled along. If the acceleration of both boxes is 2.2 m/s2 and the mass of m1 is 12 kg, find the mass of m2
1 answer:
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
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