Rotational Motion Tension at the bottom of the circle

In summary, rotational motion refers to the movement of an object around an axis or center point, commonly seen in objects like wheels and planets. At the bottom of a circle in rotational motion, tension is typically highest due to the maximum force of gravity. Factors such as mass, radius, and speed can affect tension at the bottom of the circle. Tension will vary as the object moves around the circle, being highest at the bottom and lowest at the top. The tension at the bottom of a circle can be calculated using the formula T=mv^2/r, which takes into account the relevant factors.
  • #1
physgrl
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Homework Statement



9. A 0.61 kg mass attached to the end of a 0.50 m cord rotates in a vertical circle. The angular speed of the mass at the bottom of the circle is 2π rad/s. The tension in the string at this point is:

a. 18 N

b. 21 N

c. 12 N

*d. 54 N

Homework Equations



W=mg
F=ma
acentripetal=v2/r
v=ωr

The Attempt at a Solution



I used Ftension=Fcentripetal+W and I got 18N the answer key says its 54N
 
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  • #2
I agree with your answer.

AM
 
  • #3
Same here. I think the supplied answer is incorrect.
 
  • #4
Thanks :)
 
  • #5
I would like to clarify that the answer of 54 N is correct. The equation you used, Ftension=Fcentripetal+W, is correct, but you may have made a mistake in your calculations. Let's break down the problem and solve it step by step.

First, let's calculate the centripetal force using the equation F=ma. We know that the mass (m) is 0.61 kg and the centripetal acceleration (a) is v^2/r, which is (2π)^2/0.5 = 25.13 m/s^2. Therefore, the centripetal force is (0.61 kg)(25.13 m/s^2) = 15.36 N.

Next, let's calculate the weight of the mass using the equation W=mg. We know that the mass (m) is 0.61 kg and the acceleration due to gravity (g) is 9.8 m/s^2. Therefore, the weight is (0.61 kg)(9.8 m/s^2) = 5.98 N.

Now, let's plug these values into the equation Ftension=Fcentripetal+W. We get Ftension = 15.36 N + 5.98 N = 21.34 N. This is the tension in the string at the bottom of the circle.

However, we have to remember that the mass is rotating at an angular speed of 2π rad/s. This means that the tension in the string is constantly changing as the mass moves around the circle. At the bottom of the circle, the tension is at its maximum value because the centripetal force is at its maximum. This is why the answer is not 21 N, but 54 N. This is the maximum tension that the string can withstand without breaking.

In conclusion, the correct answer is 54 N and it is important to consider the changing nature of tension in rotational motion.
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. This type of motion is commonly observed in objects such as wheels, gears, and planets.

2. How is tension affected at the bottom of a circle in rotational motion?

At the bottom of a circle in rotational motion, the tension is typically the highest. This is because the object is experiencing the maximum force of gravity, causing it to pull down on the object and increase the tension.

3. What factors affect tension at the bottom of a circle in rotational motion?

The factors that affect tension at the bottom of a circle in rotational motion include the mass of the object, the radius of the circle, and the speed of the object. These factors can impact the force of gravity and therefore the tension at the bottom of the circle.

4. How does tension change as an object moves around a circle in rotational motion?

The tension in an object will vary as it moves around a circle in rotational motion. It will be highest at the bottom of the circle, as discussed previously, and lowest at the top, where the force of gravity is lessened. The tension will also change depending on the speed and mass of the object.

5. Can you calculate the tension at the bottom of a circle in rotational motion?

Yes, the tension at the bottom of a circle in rotational motion can be calculated using the formula T=mv^2/r, where T is the tension, m is the mass of the object, v is the speed, and r is the radius of the circle. This formula takes into account the factors that affect tension at the bottom of a circle.

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