MHB Balancing Weight on an 8m Pole: Find the Solution

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To solve the problem of balancing weight on an 8m pole held by a man and a boy, the mass of 200 kg must be positioned at a specific distance from the man. The man supports four times the weight of the boy, leading to a torque equation that balances the forces. By setting the net torque to zero and simplifying the equation, it is determined that the distance d from the man can be calculated as d = (8/5) meters. This means the weight should be tied approximately 1.6 meters from the man. The solution emphasizes the importance of correctly identifying distances and forces in torque problems.
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A man and a boy hold opposite ends of 8m long pole which is horizontal. A mass of 200 kg is tied to the pole. If the man is to support four times as much weight as the boy where along the pole must the weight be tied?
Can someone please help
 
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Hint: Make a sketch.

Put the man on the left and the boy on the right. Let the mass hang a distance d from the man. Then the mass is a distance 8 - d from the boy. Call the force the boy exerts F. Then the man exerts 4F. The pole does not rotate so the net torque on it is 0 Nm. Pick an axis, say at the man and call a clockwise rotation positive. Then the net torque is
0 = d(4F) - (8 - d)F. Now pick an axis at the mass and see if you can find F.

-Dan
 
topsquark said:
Hint: Make a sketch.

Put the man on the left and the boy on the right. Let the mass hang a distance d from the man. Then the mass is a distance 8 - d from the boy. Call the force the boy exerts F. Then the man exerts 4F. The pole does not rotate so the net torque on it is 0 Nm. Pick an axis, say at the man and call a clockwise rotation positive. Then the net torque is
0 = d(4F) - (8 - d)F. Now pick an axis at the mass and see if you can find F.

-Dan
Thank you so so much!
 
You CAN'T "find F" because F cancels out of that equation.

0= d(4F)- (8- d)F. Dividing by F

0= 4d- (8- d)= 4d- 8+ d= 5d- 8

and you can easily solve for d, not F.

Don't forget that the answer must be given as a distance from a specific person and must be stated in meters.
 
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