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8. A heavy pump casing with a mass m is to be lifted off the ground using a crane. For simplicity, the motion is assumed to be two-dimensional, and the pump casing is represented by a rectangle having side dimensions ab (see figure). A cable of length L1 is attached to the crane (at point P) and the pump casing (at point O). The crane pulls up vertically on the cable with a constant velocity Vp. The center of mass G of the pump casing is assumed to lie in the center of the rectangle. It is located at a distance L2 from point O. The right side of the pump casing is located at a horizontal distance c from the vertical line passing though point P. Find the maximum cable tension during the lift, for the part of the lift before the pump casing loses contact with the ground (lift off). Evaluate for a specific case where: a = 0.4 m b = 0.6 m c = 0.2 m L1 = 3 m m = 200 kg Assume: • The friction between the pump casing and ground is high enough so that the pump casing does not slide along the ground (towards the right), before lift off occurs. • Before lift off occurs, dynamic effects are negligible and this can be treated as a statics problem. • The mass of the cable can be neglected

8. A heavy pump casing with a mass m is to be lifted off the ground using a crane. For simplicity, the motion is assumed to be two-dimensional, and the pump casing is represented by a rectangle having side dimensions ab (see figure). A cable of length L1 is attached to the crane (at point P) and the pump casing (at point O). The crane pulls up vertically on the cable with a constant velocity Vp.

The center of mass G of the pump casing is assumed to lie in the center of the rectangle. It is located at a distance L2 from point O. The right side of the pump casing is located at a horizontal distance c from the vertical line passing though point P.

Find the maximum cable tension during the lift, for the part of the lift before the pump casing loses contact with the ground (lift off).

Evaluate for a specific case where:

a = 0.4 m

b = 0.6 m

c = 0.2 m

L1 = 3 m

m = 200 kg


Assume:

• The friction between the pump casing and ground is high enough so that the pump casing does not slide along the ground (towards the right), before lift off occurs.

• Before lift off occurs, dynamic effects are negligible and this can be treated as a statics problem.

• The mass of the cable can be neglected

Grade:12

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