What is the maximum mass that can be hung from the end of a boom?

[a.wright]

Homework Statement

In the figure, a boom of mass 1000kg is supporting a mass m. The base has a mass of 10,000kg. (a) What is the maximum mass m that can be hung from the end of the boom? (b) If this amount of mass is haning off the boom, where is the center of gravity of the entire system relative to C.G. (base)? (c) What is the corresponding tension in the cable assuming the cable makes an angle of 46.5 degrees relative to the horizontal? (d) What is the strain in the boom's pin (support)?

Homework Equations

Torque net=0
Force net=0
Weight=mg

The Attempt at a Solution

Weight of boom=(1000kg)(9.80m/s²)=9800N
Torque net=0
0=-W(boom)rsin(theta)-W(mass)rsin(theta)+Tensionrsin(theta)
0=(9800N)(10m)sin(theta)-m(9.80m/s²)rsin(theta)+Trsin(theta)

I don't know what values to use for my angles, but there would still be too many unknowns. so i think that I'm setting up my equation completely wrong, but can't think of anything else to do. once i find the mass then i think i know how to do the other parts of the question.

 

[tiny-tim]

Welcome to PF!

Hi a.wright! Welcome to PF!

(have a theta: θ )

In the figure, a boom of mass 1000kg is supporting a mass m. The base has a mass of 10,000kg. (a) What is the maximum mass m that can be hung from the end of the boom?
…
Weight of boom=(1000kg)(9.80m/s²)=9800N
Torque net=0
0=-W(boom)rsin(theta)-W(mass)rsin(theta)+Tensionrsin(theta)
0=(9800N)(10m)sin(theta)-m(9.80m/s²)rsin(theta)+Trsin(theta)

I don't know what values to use for my angles, but there would still be too many unknowns. so i think that I'm setting up my equation completely wrong, but can't think of anything else to do. once i find the mass then i think i know how to do the other parts of the question.

I don't understand your torque equation …

about which point are you taking torques?

and why does the tension come into it?

Perhaps you're missing the point … if the mass is too heavy, the whole system will overbalance, and your torque equation should be determining when that happens.

 

[kerimek]

I would approach this problem by considering the physical limitations and properties of the materials involved. The maximum mass that can be hung from the end of a boom will depend on the strength and stability of the boom itself, as well as the supporting cable and base. In this problem, we are given the mass of the boom (1000kg) and the base (10,000kg), but we do not have any information on the strength or material of the boom. Therefore, it is not possible to determine the maximum mass that can be hung from the end of the boom without additional information.

In order to determine the maximum mass, we would need to know the maximum weight or force that the boom and supporting cable can withstand without breaking or becoming unstable. This would depend on factors such as the material, thickness, and design of the boom and cable.

Once we have this information, we can use the equations for torque and force to calculate the maximum mass that can be hung from the end of the boom. We would also need to consider the angle and position of the cable relative to the boom and the center of gravity of the entire system.

To answer the other parts of the question, we would need to know the specific values for the angle and position of the cable, as well as the strength and properties of the boom and cable. Without this information, it is not possible to accurately determine the center of gravity of the system or the corresponding tension in the cable and strain in the boom's pin.

In conclusion, the maximum mass that can be hung from the end of a boom depends on various factors and cannot be determined without additional information. As a scientist, it is important to consider all relevant factors and variables when solving a problem and to always use accurate and specific information in our calculations.