What is the Torque on a Crane Bar in a Fatal Accident Investigation?

In summary: Drop a vertical from P to D on AC. From D, draw a line parallel to BC to meet PC at E.In summary, a medical forensics team is investigating a fatal accident at a freight yard involving a new crane that broke while lifting a package. The crane consists of a 45.0 kg aluminum bar supported by a hinge and a support cable. The hinge is rated to support three times the weight of the package being lifted, but the accident occurred when the bar was at a 45° angle to the ground and the support cable was at a 30° angle. The team is having difficulty visualizing the situation and is seeking help in setting up a diagram to solve for forces and torque.
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Homework Statement



You are a member of a medical forensics team
investigating a fatal accident at a freight
yard. A new crane for lifting cargo broke
while lifting a package and the police suspect
sabotage. The crane consists of 45.0 kg, 15 ft
lightweight aluminum bar supported at its
base by a hinge that allows the bar to pivot
vertically. A support cable runs from the
other end of the bar to the ground. When the
hinge failed, the bar was at an angle of 45° to
the ground and the support cable was at an
angle of 30° to the ground. The yard owner
says it is impossible for this to be an accident
since the hinge is rated to support a force of
three times the weight of the 225 kg package
that was being lifted. The package was lifted
straight up from the end of the bar at a
constant speed.


Homework Equations



Torque = Force x Length

Weight = Mass x Gravity

ƩFx = 0

ƩFy = 0

ƩT = 0

T = Torque


The Attempt at a Solution



I'm having trouble setting up the picture for this problem. I understand how to solve for forces and am still getting comfortable with torque but I'm having a difficult time drawing out the picture for this problem as I felt like the information given was a bit vague. Any help is appreciated!
 
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  • #2
Draw a 45 degree right angled triangle, with the horizontal base, AB and the vertical, AC, being the two equal sides. The hypotenuse, BC, represents the bar, and the vertical is the load cable.
Extend the base AB out beyond B to a point P s.t. angle APC is 30 degrees. PC is the support cable.
 

1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

2. How is torque related to a bar on a crane?

The torque of a bar on a crane is the force that is applied to the bar as it rotates around its axis. This torque is what allows the crane to lift and move heavy objects.

3. What factors affect the torque of a bar on a crane?

The torque of a bar on a crane is affected by the force applied to the bar, the distance from the axis of rotation to the point of application of the force, and the length of the bar itself.

4. How is the torque of a bar on a crane calculated?

The torque of a bar on a crane is calculated by multiplying the force applied to the bar by the distance from the axis of rotation to the point of application of the force. This can be represented by the equation: Torque = Force x Distance.

5. Why is the torque of a bar on a crane important?

The torque of a bar on a crane is important because it determines the maximum weight that the crane can lift and move. It also affects the stability and safety of the crane, as a higher torque may require additional support or reinforcement.

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