K, so we are doing this lab in physics where a ball on a string is put through a glass tube and then different washers (masses) are added to the string. A radius is measured out, and then the string is spun in a horizontal direction...so with different radii and different masses, at different points of the lab. Anyways, I have all of my data, which is mass, rotation, and time..then this question asks us to calcualte the gravitational force, and it says that the centripetal fore will be the same as the gravitationla force...this leads to a problem...we are also asked to calculate frequeny and frequency squared, but this after the first calculation, but I did it first...then used the f^2 to find centripetal force..and I then found graviatationl force using f=mg....the values don't match....so why are the two calculations the same, and how do u calculate the gravitational force with the information I have (before the frequency) and why is it the same as the centripetal force?
Thanks, sorry this is long! I like to understand what I am doing!
The lab involved two masses: one on the end of the rotating end of string (Me) and one (Mg)on the end hanging through the glass. What holds it in equilibrium?
Well centripetal force is the force on the rotating part of the string, and what is supplying it is gravity, so
me v^2/r = mg*g
NOTE: the masses are not usually the same.
now a note on procedure: You measured period T and radius r.
v= 2Pi*r/T or 2PI*r*frequency
v^2= (2PI)^2*(r/T)%2 or(2pi)^2 *(f*r)2
me v^2/r= me (2pi*f)^2 * r
you might check that, and then set it equal to mg*g and the results normally are pretty good for this lab (that is averaging several trials).
I completely faill to understand where you are getting these equations from, and how & why you are using them. Firstly, the mass at the end of the string that hold the washers on it, it was never measured, none of the groups measured it, I didn't even think to measure it until last night, and it never said to measure it....also why are you finding v and then v^2? Please explain...and also why mgg? where does that come from? We never learned that before....Thanks, and sorry Im not understanding...Im trying!
None of the groups measured it? Ask your teacher about it...I sense there is a great lack of prelab understanding of this classical lab.
The idea is to let centripetal force be balanced by a weight, thence to use that concept.
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular%20Motion/labs/cf_and_speed.htm
No problem, I'm here to help! Let's break down your question one step at a time.
Firstly, in your lab, you are studying the motion of a ball on a string being spun in a horizontal direction. To analyze this motion, you are considering the effect of different masses and radii on the ball's rotation.
Now, let's talk about the concept of centripetal force. When an object moves in a circular path, it experiences an inward force known as centripetal force, which acts perpendicular to the object's velocity. This force keeps the object moving in a curved path rather than moving in a straight line. In the case of your experiment, the centripetal force is provided by the tension in the string.
The key idea is that the centripetal force acting on the ball is equal to the gravitational force acting on the ball. This is because, in the absence of any other forces, the ball moves in a circular path due to the gravitational force acting as the centripetal force.
Now, let's move on to calculating the gravitational force.
To calculate the gravitational force acting on the ball, you can use the formula F = mg, where F is the gravitational force, m is the mass of the ball, and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth). In this case, the mass you need to consider is the mass of the ball alone, excluding any additional masses you added to the string. So, make sure you are using the correct mass value when calculating the gravitational force.
Regarding the frequency and frequency squared, it's important to note that the frequency of an object in circular motion is defined as the number of complete rotations (or revolutions) it makes in a given time period. The frequency squared (f^2) is not directly related to the gravitational force or centripetal force calculation. However, it might be used in subsequent calculations to find the centripetal force.
To summarize:
1. Make sure you are using the correct mass value when calculating the gravitational force. Only include the mass of the ball without any additional masses on the string.
2. The gravitational force acting on the ball is equal to the centripetal force because the centripetal force is necessary to keep the ball moving in its circular path against the force of gravity.
I hope this explanation helps clarify the concept and calculations for you. If you have any further questions, feel free to ask!