A mass is attached to two strings, derive a formulas for sum of forces

In summary, the problem involves a 300 g sphere revolving in a horizontal circle at a constant speed of 6.50 m/s, with two wires tied to it. The task is to find the tension in the upper and lower wires, as well as write an equation for the sum of forces along the y-axis and prove that T2 is bigger than T1 using the equation sin(theta)T2-sin(theta)T1=mg. By using the fact that all values in the equation are positive, it can be concluded that T2 is greater than T1. In the x-axis, the centripetal force equation (T2+T1)*cos(theta)=mv^2/R can be used along with the
  • #1
Kat11111
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Homework Statement


Two wires are tied to the 300 g sphere shown in figure. The sphere revolves in a horizontal circle at a constant speed of 6.50 m/s. What is the tension in the upper wire?What is the tension in the lower wire? Write an equation for the sum of the forces along y. Use it to show that T2 is bigger than T1. Then, write sum of the forces along x.



Homework Equations


ac=v^2\r
sin(theta)t2-sin(theta)t1=mg


The Attempt at a Solution



I didn't know where to start for the first two questions and for the last one, I came up with the sin(theta)T2-sin(theta)t1=mg but I didn't know how to prove that T2 is bigger than T1. Could you please help me?
 
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  • #2
What does the figure look like-- do you have a picture?
 
  • #4
We know that if A = B1 + B2 + B3 +... and A, Bn are positive, we can conclude that A > Bn

You have T2*sin(theta) = T1*sin(theta) + mg. Because all values in this eq are positive. Therefore, T2*sin(theta) > T1*sin(theta) => T2 > T1

In X-axis, you should use centripetal force: (T2 + T1)*cos(theta) = mv^2/R and use above eq that you use to show that T2 > T1 to find values of these forces.
 

Related to A mass is attached to two strings, derive a formulas for sum of forces

What is the equation for the sum of forces on a mass attached to two strings?

The equation for the sum of forces on a mass attached to two strings is F = T1 + T2 + mg, where T1 and T2 are the tensions in the strings, m is the mass, and g is the acceleration due to gravity.

How do you derive this formula?

This formula can be derived by analyzing the forces acting on the mass. The two strings exert tension forces, while the force of gravity acts in the opposite direction. By using Newton's second law (F = ma) and considering the forces in the x and y directions, we can arrive at the equation F = T1 + T2 + mg.

What assumptions are made in this formula?

This formula assumes that the strings are ideal, meaning they have no mass and do not stretch or break. It also assumes that the mass is in equilibrium, meaning it is not accelerating in any direction.

Can this formula be used for any arrangement of strings?

Yes, this formula can be used for any arrangement of strings as long as they are attached to the mass and exert tension forces.

How is this formula useful for scientists?

This formula is useful for scientists in many fields, such as physics and engineering, as it allows them to calculate the total force acting on a mass attached to two strings. This can be applied to various real-world situations, such as analyzing the forces on a hanging object or designing a pulley system.

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