Calculating Theta for Suspended Mass in Circle

[Punchlinegirl]

A mass m= 9.3 kg is suspended from a sting of length L=1.57 m. It revolves in horizontal circle. The tangential speed of the mass is 3.14 m/s. What is the angle theta between the string and the vertical in degrees?

I started off by using the equations Lsin theta= mv^2/ r and Lcos theta=mg
Solving the second one for L and plugging into the first gave me mgsin theta/ cos theta= mv^2/r. I then plugged in my numbers to get 91.14 sin theta/ cos theta = 116.8. Since sin/cos= tan, I simplified to get 91.14 tan theta= 116.8, using inverse tan to get an answer of 52 deg. This wasn't right... can someone help me?

Thanks

 

[jamesrc]

First, I think you mean T (as in the tension of the string) when you wrote L.

Second, it looks like you decided that r=L/2; what made you decide that? r is the distance between the mass and the axis it rotates about. Look at the geometry again to find r as a function of θ.

 

[quicknote]

for sharing your calculations. It seems like you have the right approach, but there may be a mistake in your calculations. Let's review the steps together:

1. First, we need to draw a diagram to visualize the problem. The mass is suspended from a string of length L and is moving in a horizontal circle with a tangential speed of 3.14 m/s.

2. Next, we can use the equation Lsin theta= mv^2/r to find the value of L. Plugging in the given values, we get Lsin theta= (9.3 kg)(3.14 m/s)^2 / r. We also know that L= 1.57 m, so we can rearrange the equation to solve for r: r= (9.3 kg)(3.14 m/s)^2 / (1.57 m)sin theta.

3. Now, we can use the equation Lcos theta= mg to find the value of theta. Plugging in the given values, we get (1.57 m)cos theta= (9.3 kg)(9.8 m/s^2). Solving for cos theta, we get cos theta= (9.3 kg)(9.8 m/s^2) / (1.57 m) = 58.89.

4. Finally, we can use the inverse cosine function to find the value of theta in degrees. Using a calculator, we get theta = cos^-1 (58.89) = 52.33 degrees.

So, the angle theta between the string and the vertical is approximately 52.33 degrees. It's possible that your mistake was in solving for cos theta, as the value you got (116.8) is much larger than the value of L (1.57 m). I hope this helps clarify the solution. Keep up the good work!