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Chapter 9: Problem 23

Is it possible to swing a mass attached to a string in a perfectly horizontal circle (with the mass and the string parallel to the ground)?

Short Answer

Expert verified
Answer: No, it is not possible to swing a mass attached to a string in a perfectly horizontal circle with both the mass and the string remaining parallel to the ground, due to the inability to maintain vertical equilibrium in this situation.

Step by step solution

01

Identify the forces acting on the mass

To analyze the feasibility of this situation, we need to identify all the forces acting on the mass. the following forces act on the mass: 1. Tension force (T) from the string, acting towards the center of the circular path. 2. Gravitational force (mg) acting vertically downward.
02

Analyze the vertical forces

Since the mass is in a horizontal circle and the string is parallel to the ground, the vertical component of the tension force (T) must be equal and opposite to the gravitational force acting on the mass which is mg. T_y = mg However, since the string is parallel to the ground and there is no vertical component in tension, this equation is impossible to satisfy.
03

Analyze horizontal forces

Assuming there was a vertical equilibrium, we can analyze the horizontal forces. The tension force should provide the centripetal force to maintain the circular motion, and thus, needs to have a horizontal component in the force. F_c = T_x
04

Conclusion

Since the vertical equilibrium is impossible to maintain due to the string being horizontal, it is not possible to swing a mass attached to a string in a perfectly horizontal circle with both the mass and the string remaining parallel to the ground.

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