No, that is not correct. The correct answer is F_t(y) = [m(gL - gy)]/L.

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In summary, the conversation discussed the calculation of the tension in a uniform rope of length L and mass m when hung vertically. The final answer given was F_t(y)= [m(L-y)*g] which was questioned due to the difference in units on both sides of the equation. The correct answer was then stated as force of tension a distance y from the bottom = m [(L-y)/L]*g, taking into account the mass per unit length and gravity.
  • #1
ahhgidaa
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a uniform rope of length L and mass m is hung vertically. what is the tension a distance y from the bottom?

my final anwer that i got was F_t(y)= [m(L-y)*g]

is this correct?
 
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  • #2
No.

For one thing, the units are different on the left side of the equation vs. the right side.

How did you get your answer?

What does the answer you posted say in the case that y = L ?
 
  • #3
force of tension a distance y from the bottom = m [(L-y)/L]*g
tension = mgh

mass per unit length times gravity
 
  • #4
ahhgidaa said:
force of tension a distance y from the bottom = m [(L-y)/L]*g
tension = mgh

mass per unit length times gravity

yup! :smile:
 
  • #5


No, that is not correct. The correct answer is F_t(y) = [m(gL - gy)]/L. The equation you provided does not take into account the length of the rope and does not properly account for the varying tension along the rope. The correct equation takes into account the weight of the rope and the distance from the bottom, as well as the length of the rope.
 

Related to No, that is not correct. The correct answer is F_t(y) = [m(gL - gy)]/L.

1. What is the formula for calculating the tension in a hanging object?

The correct formula for calculating the tension in a hanging object is F_t(y) = [m(gL - gy)]/L, where m is the mass of the object, g is the acceleration due to gravity, L is the length of the hanging object, and y is the distance from the hanging point.

2. How is this formula different from the commonly known formula for tension?

This formula is different from the commonly known formula for tension (F = mg) because it takes into account the vertical distance of the hanging object from the hanging point, while the commonly known formula only considers the mass and acceleration due to gravity.

3. Can this formula be applied to any hanging object?

Yes, this formula can be applied to any hanging object as long as the hanging point and the hanging object are in a vertical position and the mass and length are known.

4. Why is this formula important in scientific research?

This formula is important in scientific research because it allows for more accurate calculations of tension in hanging objects, which can be useful in various fields such as engineering, physics, and mechanics.

5. Are there any limitations to this formula?

One limitation of this formula is that it assumes a perfectly vertical hanging object, so it may not be as accurate for objects that are not perfectly aligned. Additionally, it does not take into account factors such as air resistance or other external forces.

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