What is the minimum weight we must place on the end of 1.6 m long uniform beam s

Question

What is the minimum weight we must place on the end of 1.6 m long uniform beam supported at its center on a knife edge, to balance a 427 N load located 0.4 m from the other end of the beam?

Consider two masses that hang from an overhead beam. The first mass of 55.3 kg is attached to the beam using an ideal rope. The second mass of 31.2 kg is attached to the first mass with an ideal rope and hangs directly under the first mass.

Find the tension in the lower rope.

Find the tension in the upper rope.

You are given a four-wheeled cart of mass 15 kg, where the distance between a wheel and its nearest neighbors is 1.4 m. Suppose we load this cart with a crate of mass 110 kg, where the crate's center of mass is located in the back-middle of the cart, 0.350 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

1) net torque should be zero.


let w is the weight

(0.8-0.4)*427 = 0.8*W

==> w = 0.4*427/0.8 = 213.5 N

2)

T_lower= 31.2*9.8 = 305.76 N

T_upper = (31.2+55.3)*9.8 = 847.7 N

3)


W1 + w2 = (110+15)*9.8 = 1225 N --(1)

W1*(0.7 - 0.35) = (0.7+0.35)*w2

w1*0.35 = 1.05*w2

w1 = 3*w2

from equation 1

4*w2 = 1225

==> w2 = 306.25 N (farher wheels)

==> w1 = 3*w2 = 306.25 (nearer wheels)

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