Circular motion with a string with weight

In summary, the tension in the cord as a function of radial position is given by T(r) = m_1*2*pi*L + T(0).
  • #1

Homework Statement


A block of mass m2 is attached to a cord of mass m1 and length L, which is fixed at one end. (Note, not a massless cord!) The block moves in a horizontal circle on a frictionless table. If the period of the circular motion is P, find the tension in the cord as a functions of radial position along the cord, 0 <_ r <_ L. (<_ meaning greater than or equal to)


Homework Equations


a = v^2/r, F = ma


The Attempt at a Solution


So I could immediately tell that this problem involves setting up an integral equation of some sort. I've learned in class how to solve for integral equations when a block is hanging on a ceiling or things as simple as that, but none of these.
So if L is the distance from the center of the circle to some arbitrary point on the cord, I think the tension at the very end of the cord connected to the mass will just be the centripetal acceleration of the mass multiplied by m1, so there's one of the limits of the integral equation. The other limits should be 0 and L for the radius. The last one will be the unknown for which I have to solve for.
But when I set up my equation and solved for it, I somehow got T(L) = m_1*2*pi*L + T(0), which doesn't make sense.
 

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  • #2
giggidygigg said:
So if L is the distance from the center of the circle to some arbitrary point on the cord, I think the tension at the very end of the cord connected to the mass will just be the centripetal acceleration of the mass multiplied by m1

Why? Does the mass of the block dissappear? For any point on the string at a distance x, if you assume the linear mass density to be [tex]\lambda =\frac{m_1}{L}[/tex] then the string at that point is [tex]\lambda xdx+ m_2[/tex]. Figure out the variation of x and then integrate.
 
Last edited:
  • #3
oops i meant m2. but anyway i'll try to carry it out with your advice
 

What is circular motion with a string with weight?

Circular motion with a string with weight is a type of motion in which an object is attached to a string and moves in a circular path due to the tension and force of the string. The weight of the object creates a centripetal force that keeps it moving in a circle.

How is centripetal force related to circular motion with a string with weight?

Centripetal force is the force that keeps an object moving in a circular path. In circular motion with a string with weight, the tension in the string creates a centripetal force that pulls the object towards the center of the circle, keeping it in motion.

What factors affect the speed of circular motion with a string with weight?

The speed of circular motion with a string with weight is affected by the length of the string, the weight of the object, and the tension in the string. A longer string, heavier object, and higher tension will result in a faster speed.

What is the difference between uniform circular motion and non-uniform circular motion with a string with weight?

In uniform circular motion, the speed of the object remains constant, while in non-uniform circular motion, the speed changes at different points along the circular path. In circular motion with a string with weight, the speed can be either uniform or non-uniform, depending on the factors mentioned above.

How is circular motion with a string with weight related to real-world applications?

Circular motion with a string with weight has many real-world applications, such as amusement park rides, pendulum clocks, and centrifuges in laboratories. It is also used in sports, such as swinging a bat or throwing a discus, and in engineering for designing machinery and structures that require circular motion.

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