Exploring Circular Motion: 3.60 kg Object in P6.11

In summary, the problem involves a 3.60 kg object attached to a vertical rod by two strings, rotating at a constant speed of 7.20 m/s in a horizontal circle. The task is to find the tension in the upper and lower strings. Attempting to solve for the radius and angle did not yield the correct answer, as the equations used only accounted for one string. A proper solution requires considering the forces acting on the object and using separate tension forces for each string in the equations.
  • #1
zcabral
30
0
***circular motion!***

Homework Statement


http://www.webassign.net/pse/p6-11.gif
A 3.60 kg object is attached to a vertical rod by two strings as in Figure P6.11. The object rotates in a horizontal circle at constant speed 7.20 m/s.


(a) Find the tension in the upper string.

(b) Find the tension in the lower string.

Homework Equations



T=mg/costheta
m(v^2/r)=Tsintheta


The Attempt at a Solution



I tried to solve for r and i got 1.32 but when i plugged it into the equation for tension it said it was wrong. i tried to solve for theta and got 41.3 in order to plug into the equation and it was wrong as well. what am i doing wrong??
 
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  • #2
I think you are forgetting there are two strings. You can't use your equation and do each string separately. You need two different tension forces in your equations. Draw a free body diagram of the ball and sum up the forces in each direction like you would do for any other force problem.
 
  • #3


Circular motion is a complex concept that involves both rotational motion and centripetal force. In order to accurately solve this problem, you will need to use the correct equations and understand the physical principles at play. It is important to note that the tension in the strings will vary at different points in the motion, as the object is constantly changing direction and velocity.

To solve for the tension in the upper string, you will need to use the equation T=mg/cosθ, where θ is the angle between the string and the vertical axis. This angle can be found by using the relationship between the velocity, radius, and angle in a circular motion, as shown in the equation m(v^2/r)=Tsinθ. By solving for θ, you can then plug in the value in the equation for tension to find the correct answer.

Similarly, to solve for the tension in the lower string, you will need to use the same equations and principles. However, in this case, the angle θ will be different from the upper string, as the lower string is attached at a different position on the object.

It is important to carefully consider the variables and equations involved in circular motion problems, as well as the physical principles at play. I recommend reviewing your calculations and equations to ensure accuracy in your solution.
 

Related to Exploring Circular Motion: 3.60 kg Object in P6.11

1. What is circular motion?

Circular motion is the movement of an object along a circular path. This means that the object is constantly changing direction and its velocity is always tangent to the circle at any given point.

2. How is circular motion different from linear motion?

Circular motion involves the object moving along a curved path, while linear motion involves the object moving along a straight path. In circular motion, the velocity and acceleration vectors are constantly changing, whereas in linear motion they remain constant.

3. What is the centripetal force in circular motion?

The centripetal force is the force that acts towards the center of the circle, keeping the object in circular motion. It is responsible for continuously changing the direction of the object's velocity and keeping it on its circular path.

4. How is centripetal force related to the object's mass and velocity?

The magnitude of centripetal force is directly proportional to the mass and the square of the velocity of the object. This means that a heavier object or an object with a higher velocity will require a greater centripetal force to maintain circular motion.

5. How can we calculate the centripetal force in this scenario?

In this scenario, the centripetal force can be calculated using the formula Fc = mv^2/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path. Simply plug in the given values to find the centripetal force acting on the 3.60 kg object.

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