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

Answer:

T₁ = 311.19 N

T₂ = 131.56 N

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

Answer 2

Answer:

Tension 1, T₁ = 311.19 N

Tension 2,  T₂ = 131.56 N

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