Vertical pendulum, mass of object

[lizzyb]

Hi. Consider an object attached to the end of the string that is whirled vertically in a circle of radius r. When it is @ degrees from the horizontal, it has the speed v and the tension in the string is T. What is the mass of the object?

The picture shows that the object is in the first quadrant traveling clockwise.

What I've done so far is:

T + cos @ mg = m v^2 / r

After plugging in the values given, I've failed to come up with the correct answer. What am I doing wrong? Thank you.

 

[lizzyb]

I had the cosine and sine messed up; it should be:

T + sin @ m g = m v^2 / r

 

[kyle8921]

Hello, thank you for your question. It seems like you are on the right track in your approach to solving this problem. However, there are a few things to consider that may be causing your difficulty in finding the correct answer.

First, it's important to clarify the direction of the tension in the string. In this scenario, the tension is acting upwards, opposite to the force of gravity. Therefore, the equation should be written as T - cos @ mg = mv^2 / r.

Secondly, it's important to note that the angle @ is measured from the vertical, not the horizontal. So, when the object is at @ degrees from the horizontal, it is actually at 90 - @ degrees from the vertical. This means that the value of cos @ should be replaced with sin (90 - @) = cos @.

Finally, make sure that all units are consistent in your calculations. The unit for mass should be in kilograms, while the unit for speed should be in meters per second. If you are using different units, you may need to convert them before plugging them into the equation.

I hope this helps you to find the correct answer. Keep in mind that solving problems in physics often requires attention to detail and careful consideration of units and directions. Good luck!