Question

Two boxes are held together by a strong wire and attached to the ceiling of an elevator by a second wire. The mass of the top box is 14.2 kg; the mass of the bottom box is 10.4kg. The elevator accelerates upwards at 2.84 m/s2. Find the tension in both wires.

Answer 1

Tension 1, T₁ = 311.19 N

Tension 2, T₂ = 131.56 N

Step-by-step explanation:

Thinking process:

Newton's 2nd Law can be applied for m₂ as follows :

∑Fy = m×a (↑)

T₂ - W₂ = m₂×a ⇒ T₂ - m₂×g = m₂×a ⇒ T₂ = m₂×(a+g)

⇒ T₂ = (10.4 Kg)*(2.84 m/s²+9.81 m/s²) = 131.56 N

Now, we apply Newton's 2nd Law for m₁

∑Fy = m×a (↑)

T₁ - T₂ - W₁ = m₁×a ⇒ T₁ = m₁×a + W₁ + T₂ = m₁×a + m₁×g + T₂

⇒ T₁ = m₁×(a+g) + T₂ ⇒ T₁ = (14.2 Kg)×(2.84 m/s²+9.81 m/s²) + 131.56N

⇒ T₁ = 311.19 N

Answer 2

T₁ = 311.19 N

T₂ = 131.56 N

Step-by-step explanation:

We can apply Newton's 2nd Law for m₂ as follows

∑Fy = m*a (↑)

T₂ - W₂ = m₂*a ⇒ T₂ - m₂*g = m₂*a ⇒ T₂ = m₂*(a+g)

⇒ T₂ = (10.4 Kg)*(2.84 m/s²+9.81 m/s²) = 131.56 N

Now, we apply Newton's 2nd Law for m₁

∑Fy = m*a (↑)

T₁ - T₂ - W₁ = m₁*a ⇒ T₁ = m₁*a + W₁ + T₂ = m₁*a + m₁*g + T₂

⇒ T₁ = m₁*(a+g) + T₂ ⇒ T₁ = (14.2 Kg)*(2.84 m/s²+9.81 m/s²) + 131.56 N

⇒ T₁ = 311.19 N