Drawing a free body diagram on the mass

In summary, the question involves a 2.00 kg mass attached to a string of unknown radius r, traveling in a vertical circle with a speed of 2.31m/s and a tension of 31.6N when the string makes an angle of 52 degrees with the horizontal. Using a free body diagram and the equation F = mv^2/r, the radius of the string can be calculated by equating the vertical components of the tension and centripetal forces. The resulting answer is approximately 0.34m.
  • #1
ubiquinone
43
0
Hi, I need some help with a question involving forces. I will appreciate greatly if someone can please have a look at this. Thanks.

Question: A 2.00 kg mass, which is attached to a string of radius [tex]r[/tex], travels in a vertical circle. When the string makes an angle of [tex]\theta=52^o[/tex] with the horizontal, the speed of the mass is [tex]2.31m/s[/tex] and the tension in the string is [tex]31.6N[/tex]. Calculate the radius of the string, [tex]r[/tex].

Diagram
Code:
          Center
 ------------+--------------
              \  52 degrees
               \
                \
                 \ string
                  \
                   \
                    \
                     O mass
I tried by drawing a free body diagram on the mass, labelling two forces acting on it, the force of gravity and the tensile force.
I'm really not sure on how to solve it, but I'm guessing the vertical component of the force of tension - the weight = the vertical component of the centripetal force. Am I close? If not, may someone please give me a hand. Thank You.
 
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  • #2
I'm not sure if this is right, but I'll give it a shot.

If you do assume that the vertical components of tensile and centripal forces are the same, then you can calculate the magnitude of the centripetal force, which ends up being the same as the tension. Then use F = mv^2/r and solve for r.

I have no idea if this is right or not. I get an answer of about 0.34m.
 
Last edited:
  • #3
i did not calculate but it is just like this,

Tsin(theta)=mv^2/r,

then find r
 
  • #4
Note that T - mg cos(90-52) = mv^2 / r.
 
  • #5
Wow thank you so much radou, your method worked!

So the free diagram should look something like this:
Code:
Center
  +
   \ F_T|
    \   |
     \  |
      \ | F_Tsin52
       \|
        O
        |\ 
        | \ F_gcos(90-52)
  F_g   |  \
        |   \
        |  / 
        |/

The two components which supply the centripetal force are
F_T - F_gcos(90-52) = F_c
 

Related to Drawing a free body diagram on the mass

What is a free body diagram?

A free body diagram is a visual representation of all the forces acting on an object in a given system. It is a simplified illustration that shows the direction and magnitude of forces, as well as the object's shape and orientation.

Why is it important to draw a free body diagram on the mass?

Drawing a free body diagram on the mass is important because it helps to identify and analyze all the forces acting on the object. This is crucial in understanding the motion and equilibrium of the object, and can also aid in solving problems related to forces and motion.

What are the steps to draw a free body diagram on the mass?

The steps to draw a free body diagram on the mass are as follows:

  1. Identify the object and the forces acting on it.
  2. Draw a dot to represent the object, labeling it with the object's name.
  3. Draw arrows to represent the forces acting on the object, with the arrow pointing in the direction of the force.
  4. Label the arrows with the name and magnitude of the force.
  5. Choose a coordinate system and indicate it on the diagram.
  6. Ensure that the forces are accurately represented in relation to the coordinate system.

What are some common mistakes to avoid when drawing a free body diagram on the mass?

Some common mistakes to avoid when drawing a free body diagram on the mass are:

  • Forgetting to label the forces or labeling them incorrectly.
  • Not considering all the forces acting on the object.
  • Not drawing the forces accurately in relation to the coordinate system.
  • Not including the object's shape and orientation in the diagram.

Can a free body diagram on the mass be used for objects in motion?

Yes, a free body diagram on the mass can be used for objects in motion. In this case, the forces acting on the object may change due to acceleration, but the principles of drawing the diagram remain the same.

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