Torque on crane arm and load limit

In summary, the conversation discusses a problem involving a crane with a 15.0 m long arm at a 20.0 degree angle with the horizontal. The maximum load for the crane is limited by the amount of torque it can withstand. The conversation goes on to discuss calculations for finding the maximum torque and maximum load for the crane at different angles. After some clarification on the use of cosine instead of sine, the correct answers are obtained.
  • #1
syncstarr
8
0
hello-

i had this problem: the arm of a crane is 15.0 m long and makes an angle of 20.0 degrees with the horizontal. assume that the maximum load for the crane is limited by the amount of torque the load produces around the base of the arm.
a) what is the mximum torque the crane can withstand if the maximum load is 450 N?
b) what is the maximum load for this crane at an angle of 40.0 degrees.

my answer/work: a) max=450 N t=?
t=fd
=(15)(450)
(6300)(sin 20)
2154.73 N m​

b) t=fd(sin 40)
2154.73=15d(sin40)
divide by 15d(sin 40) on both sides
92.34=d
92.34N

is this correct? are my answers and work correct? please let me know by commenting on this post. thank you:smile:
 
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  • #2
syncstarr said:
hello-

i had this problem: the arm of a crane is 15.0 m long and makes an angle of 20.0 degrees with the horizontal. assume that the maximum load for the crane is limited by the amount of torque the load produces around the base of the arm.
a) what is the mximum torque the crane can withstand if the maximum load is 450 N?
b) what is the maximum load for this crane at an angle of 40.0 degrees.

my answer/work: a) max=450 N t=?
t=fd
=(15)(450)
(6300)(sin 20)
2154.73 N m​

Firstly, note that you require cos20, not sin20 (check your diagram!)
I'm not sure how you've gone from the 2nd to the 3rd line. It should read t=fd=450*cos(20)*15

b) t=fd(sin 40)
2154.73=15d(sin40)
divide by 15d(sin 40) on both sides
92.34=d
92.34N

Once again, you have the wrong angle. However, your method is correct, apart from the bit in bold.. you should only divide by 15 sin(40)! (although, I must reiterate; this is not the correct angle)
 
  • #3
first off i want to thank you for taking the time to try to help me out.
secondly so the answer for part a should be 6342.93 N m?? why do you use cos instead of sin?
thirdly i do not understand what you are talking about in part b. what angle would i use? am i suppose to use cos instead of sin?

-confussed
 
  • #4
syncstarr said:
first off i want to thank you for taking the time to try to help me out.
You're welcome.
secondly so the answer for part a should be 6342.93 N m?? why do you use cos instead of sin?
I've not done the calculation, but if you've used the right angle then this should be correct. If you imagine the diagram, you have the angle between the crane and the horizontal. Now the load will be hanging vertically downwards, and we want the angle between this and the normal to the crane. This angle is equal to the angle the crane makes with the horizontal (try it for yourself, using simple trig). Thus, since we are resolving through this angle, we require cos(20).
thirdly i do not understand what you are talking about in part b. what angle would i use? am i suppose to use cos instead of sin?
Sorry, that wasn't very clear- it was late last night when I typed the response! We require cos(angle) for the same reasoning as above.
 
  • #5
thank you again that made a lot more sense and i was able to get an answer. thank you!
 

What is torque?

Torque is a measure of the twisting force on an object. It is calculated by multiplying the force applied to an object by the distance from the point of rotation to the point where the force is applied.

How is torque related to crane arms?

Crane arms use torque to lift and move heavy loads. The crane's motor applies a force to the arm, which then produces torque at the point where the arm connects to the crane's base. The amount of torque applied determines the maximum weight that the crane arm can lift.

What is the load limit of a crane arm?

The load limit of a crane arm is the maximum weight that the arm can safely lift. It is determined by the torque produced by the crane's motor and the structural strength of the arm itself. Going over the load limit can result in damage to the crane and potential injury to workers.

How does the length of a crane arm affect torque and load limit?

The longer the crane arm, the more torque it can produce. This means that a longer arm can lift heavier loads. However, a longer arm also increases the stress on the crane's motor and structural components, so the load limit may still be the same as a shorter arm.

What safety precautions should be taken when working with cranes?

It is important to always follow the manufacturer's guidelines and instructions when operating a crane. Before each use, the crane should be inspected for any damage or wear. The load limit must be strictly adhered to, and the crane should never be used to lift loads beyond its capacity. Additionally, the crane should be operated by a trained and licensed operator and appropriate safety measures should be in place, such as barriers or warning signs around the work area.

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