Question

Determine the maximum mass of the crate so

Answer 1

Answer:

293 kg

Explanation:

Let's say the tension in each cable is Tb, Tc, and Td.

First, find the length of cable AD:

r = √(2² + 2² + 1²)

r = 3

Using similar triangles:

Tdx = 2/3 Td

Tdy = 2/3 Td

Tdz = 1/3 Td

Sum of the forces in the x direction:

∑F = ma

Tb − 2/3 Td = 0

Td = 3/2 Tb

Sum of the forces in the y direction:

∑F = ma

2/3 Td − Tc = 0

Td = 3/2 Tc

Sum of the forces in the z direction:

∑F = ma

1/3 Td − mg = 0

Td = 3mg

From the first two equations, we know Td is greater than Tb or Tc.  So we need to set Td to 8.6 kN, or 8600 N.

8600 N = 3mg

m = 8600 N / (3 × 9.8 m/s²)

m ≈ 292.5 kg

Rounded to three significant figures, the maximum mass of the crate is 293 kg.