Calculate Distance of Man Walking on Plank Before Tipping

  • Thread starter ramalik
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In summary, the conversation is about finding the distance a person can walk on the overhanging part of a plank before it begins to tip. The person must solve for their lever length by setting the torque of the plank equal to the torque of the person. The weight of the plank effectively acts at the center, so the difference between the center point and the overhanging piece must be calculated. The center of mass of the plank is 1.5 m from the pivot point at the right support.
  • #1
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A uniform plank of length 5.2 m and weight 213 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 445 N walk on the overhanging part of the plank before it just begins to tip?

I know you have to set the torque of the plank equal to the torque of the man and solve for his lever length. I just don't know how to get the torque of the plank.
 
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  • #2
ramalik said:
I just don't know how to get the torque of the plank.
Where does the weight of the plank effectively act?
 
  • #3
the center! so i have to find the difference between the center point and the piece hanging off the side?
 
  • #4
Yes. Hint: Choose the right support as the pivot point for calculating torques. How far from that point is the center of mass of the plank?
 
  • #5
2.6-1.1 = 1.5 m. Thanks!
 

1. How do you calculate the distance a man can walk on a plank before it tips over?

To calculate the distance, we need to consider the length of the plank and the weight of the man. Using the formula for torque, we can determine the maximum distance a man can walk on the plank before it tips. This calculation also takes into account the center of mass and the angle at which the man is walking.

2. What factors affect the distance a man can walk on a plank before it tips?

The main factors that affect the distance a man can walk on a plank before it tips are the length and weight of the plank, the weight and position of the man, and the angle at which he is walking. Other factors such as the material and thickness of the plank may also play a role.

3. Is there a maximum distance a man can walk on a plank before it tips?

Yes, there is a maximum distance that a man can walk on a plank before it tips. This distance is dependent on the factors mentioned above. However, in theory, if the plank is long enough and the man is light enough, he could potentially walk an infinite distance before the plank tips.

4. Can you calculate the distance a man can walk on a plank before it tips without knowing the weight of the man?

No, the weight of the man is a crucial factor in this calculation. Without knowing the weight, it is impossible to accurately determine the distance he can walk before the plank tips. The weight of the man affects the torque and center of mass, which are essential in this calculation.

5. How can this calculation be useful in real-life situations?

This calculation can be useful in various real-life situations, especially in construction and engineering. It can help determine the maximum load a plank can withstand before it tips, which is crucial in building structures and bridges. It can also be applied in physics experiments and demonstrations to understand the concept of torque and balance.

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