Torque-Sign hanging from a cable

[sam2k2002]

Torque--Sign hanging from a cable

Homework Statement

A 120cm-wide sign hangs from a 5.4 kg, 200cm-long pole. A cable of negligible mass supports the end of the rod as shown in the figure

What is the maximum mass of the sign if the maximum tension in the cable without breaking is 330N?


http://session.masteringphysics.com/problemAsset/1070549/3/12.P66.jpg"

Homework Equations

T = r*F*sin(phi) = F * d (d = moment arm length)

The Attempt at a Solution

I set the Torque provided by the tension in the cable equal to the torque provided by the weight of the sign because the cable will break when the mass is just above the mass at this point.

(330N)(2m)(sin 51) = (1.2m)(9.81)(max_mass)

with this I get the max_mass to = 43.6kg, a wrong answer. Can anyone help me out here? Thanks.

 

[PhanthomJay]

What happened to the weight of the pole? What point are you summing torques about?

 

[Moetasim]

I would like to start by clarifying that torque is the measure of the force that can cause an object to rotate about an axis. In the context of this problem, the torque provided by the tension in the cable is balancing the torque provided by the weight of the sign. This means that the sign is in static equilibrium, meaning it is not moving or rotating.

To solve this problem, we can use the equation T = rFsin(θ), where T is the torque, r is the moment arm length, F is the force, and θ is the angle between the force and the moment arm. In this case, the moment arm length is the length of the pole (2m) and the angle between the force of tension and the moment arm is 51 degrees.

So, the equation becomes T = (2m)(330N)sin(51) = 1078.8 Nm. This is the maximum torque that the cable can withstand without breaking.

To find the maximum mass of the sign, we can use the equation T = rmg, where m is the mass, g is the acceleration due to gravity (9.81 m/s^2), and r is the moment arm length (1.2m). So, the maximum mass can be calculated as m = T/(rg) = 1078.8 Nm/(1.2m)(9.81 m/s^2) = 90.8 kg.

Therefore, the maximum mass of the sign that the cable can support without breaking is 90.8 kg.