A)What is the minimum weight we must place on the end of 2.0 m long uniform beam

Question

A)What is the minimum weight we must place on the end of 2.0 m long uniform beam supported at its center on a knife edge, to balance a 530 N load located 0.5 m from the other end of the beam?

B)You are given a four-wheeled cart of mass 16 kg, where the distance between a wheel and its nearest neighbors is 1.6 m. Suppose we load this cart with a crate of mass 108 kg, where the crate's center of mass is located in the back-middle of the cart, 0.400 m from its center. (a) Find the weight on the nearer wheels of the cart under this load. (b) Find the weight on the farther wheels of the cart under this load.

Explanation / Answer

A)

To balance the beam, the net torque about the edge must be zero.

Hence F1R1 = F2R2

mg*1 = 530*0.5 = 265

m = 27.01kg.

B)

suppose the Weight on the front is F1 each and for the back its F2 each.

Then 2F_1 + 2F_2 = 16g+108g = 1216.44 N

F_1+F_2 = 608.22 N ------------(i)

writing torque equation about the center.

2*F_1*0.8*sqrt(2) - 2*F_2*0.8*sqrt(2) - 108*9.81*0.400 = 0

F_1 - F_2 = 239.73 N -----------(ii)

hence F_1 = 423.976N and F_2 = 184.246N

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