After an unfortunate accident at a local warehouse you have been contracted to determine the cause. A jib crane collapsed and injured a worker. The horizontal steel beam had a mass of 88.50 kg per meter of length and the tension in the cable was T = 11.78 kN. The crane was rated for a maximum load of 1.000 × 103 lbs. If d = 5.290 m, s = 0.594 m, x = 1.450 m and h = 1.890 m, what was the load on the crane before the collapse? What was the magnitude of force at the attachment point P? The acceleration due to gravity is g = 9.810 m/s2.
Weight of load: 2228 N
Magnitude of force: 11,191 N
1.
Write out the Parameters (Tension, beam mass, d, s, x, h)
m= beam mass*d= 88.5 * 5.290
=465.5 kg
find theta using arctan(opp/ adj)
arctan (h/ (d-s)) = arctan (1.890/ (5.290- 0.594)) = 21.9 degrees
T(d-s)sin theta - mg (d/2) - WL (d-x) = 0
11780 (5.290- 0.594)sin 21.9 - [465.5 * 9.81 (5.29/2)] - WL (5.290- 1.450) = 0
Solve for WL.
2. Magnitude of force at point P:
get the horizontal and vertical components
Px = T*cos theta
= 11780cos21.9 = 10930 N
Py = T*sin theta - WL - mg
= 11780sin21.9 - 2228 N - (465.5 * 9.81)
=-2401 N
Use pythagorean theorem to get the magnitude
Magnitude of force at point P:
F = √(Px^2 + Py^2)
F = √(10930^2 + (-2401)^2)
F = 11223 N or 11.22 kN (rounded to two decimal places)
To determine the load on the crane before the collapse, we need to calculate the total mass that was being supported by the crane.
1. First, find the mass of the horizontal steel beam:
Mass of the steel beam = mass per unit length × length
Mass of the steel beam = 88.50 kg/m × d
2. Next, calculate the mass of the load being lifted.
We need to convert the maximum load rating from pounds to kilograms.
Maximum load = 1.000 × 10^3 lbs
Maximum load = 1.000 × 10^3 lbs × 0.4536 kg/lb
3. To find the total load on the crane, sum the mass of the steel beam and the load being lifted:
Total load on the crane = Mass of the steel beam + Mass of the load
Now, to find the magnitude of force at the attachment point P, we need to consider the forces acting on the crane.
1. There are three forces acting on the crane:
a) Force due to the tension in the cable (T)
b) Weight of the horizontal steel beam
c) Weight of the load being lifted
2. We can calculate the weight of the horizontal steel beam:
Weight of the steel beam = mass of the steel beam × acceleration due to gravity (g)
3. Similarly, the weight of the load being lifted can be calculated:
Weight of the load = mass of the load × acceleration due to gravity (g)
4. Finally, the magnitude of the force at the attachment point P is obtained by summing the three forces:
Force at point P = T + Weight of the steel beam + Weight of the load
By following these steps and plugging in the given values (mass per unit length, tension in the cable, and lengths), you can calculate the load on the crane before the collapse and the magnitude of force at the attachment point P in this unfortunate accident.