In order to make an adjustment a group of engineering studen

In order to make an adjustment, a group of engineering students remove leg D from a laboratory worktable. To ensure that the table remains stable, they place a 8.0-kg stack of statues textbooks cantered at point E of the table top as shown. Determine the normal reaction force at each leg A, B, and C. The uniform table top has a mass of 37.4 kg, and each leg has a mass of 6.0 kg.

Solution

balancing moment about leg A:

(1.4 x Nb ) - (1.4 x 6g) - (sqrt(1^2 + 0.7^2) x 8g) - (sqrt((1.4/2)^2 + (2.7/2)^2) x 37.4g) - (sqrt(1.4^2 + 2.7^2) x 6g) + (sqrt(1.4^2 + 2.7^2) x Nc) = 0

1.4Nb - 82.32 - 95.7 - 557.36 - 178.83 +3.04 Nc = 0

1.4Nb + 3.04Nc = 914.21 .........(i)

about leg C:

(2.7 x Nb ) - (2.7 x 6g) - (sqrt(0.4^2 + 2.7^2) x 8g) - (sqrt((1.4/2)^2 + (2.7/2)^2) x 37.4g) - (sqrt(1.4^2 + 2.7^2) x 6g) + (sqrt(1.4^2 + 2.7^2) x Na) = 0

2.7Nb - 158.76 - 214 - 557.36 - 178.83 + 3.04Na = 0

3.04 NA + 2.7 Nb = 1008.95 ........(ii)

balancing forces in vertical,

Na + Nb + Nc - (8 + 37.4 + 6 + 6 +6)g = 0

Na + Nb + Nc = 621.32 ..........(iii)

Solving i, ii and iii,

Na = 303.11 N

Nb = 32.40 N

Nc = 285.80 N