The arm of a crane at a construction site is 15.0 m long

AI Thread Summary
The discussion focuses on calculating the maximum torque a crane can withstand given its arm length of 15.0 m and a maximum load of 779 N at an angle of 15.8 degrees with the horizontal. The formula for torque is correctly identified as torque = radius * Force * sin(θ). However, there is confusion regarding the use of sine versus cosine for the angle in the torque calculation. The correct approach involves using the sine function to account for the angle between the load and the arm's direction. Ultimately, the participants clarify that the torque should be calculated using sine due to the nature of the force's direction relative to the pivot point.
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Homework Statement


The arm of a crane at a construction site is
15.0 m long, and it makes an angle of 15.8
with the horizontal. Assume that the max-
imum load the crane can handle is limited
by the amount of torque the load produces
around the base of the arm.
What maximum torque can the crane with-
stand if the maximum load the crane can
handle is 779 N?
Answer in units of N · m

Homework Equations


torque = rFsin θ

The Attempt at a Solution


torque = radius * Force of gravity * sin θ
= 15 m * 779 N * sin 15.8
I don't get what is wrong...
 
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"torque = 15 m * 779 N * sin 15.8"

Surely it should be cosine rather than sine?
 


uhhh can i ask why it's cosine?
 


Torque is the vertical force times the horizontal distance from the pivot. The angle of the crane with horizontal is given. So 15*cos(15.8) is the horizontal component of the crane's length.
 

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