Understanding the Dynamics of a Simple Pendulum

In summary, the conversation discusses the properties of a simple pendulum consisting of a mass M suspended by a thin string. The tension, T, in the string is largest at the bottom (theta=0) and smallest when theta=+,- theta0. The vertical component of tension is constant and T depends on theta. It is incorrect to assume that T=Mg at 0, as the mass is always moving at that point and the direction of acceleration is not zero.
  • #1
vroman
9
0
A simple pendulum consists of a mas M suspended by a thin string. The magnitude of the tension is T. The mass swings back and forth between +,- theta0.
I need help identifying which of the following statements are correct. These are my answers, but I'm getting something wrong.

A)T=Mg at some angle between zero and theta0 not correct
B)T is largest at the bottom (theta=0)
Correct
C)The vertical component of tension is constant Correct
D)T is smallest when theta=+,- theta0
Correct
E)T depends on theta Correct
F)T equals Mg when theta=theta0
Not correct
G)T is greater than Mg for theta =theta0 Not correct

I would really appreciate some help with this problem, Thanks!
 
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  • #2
Discuss "A".Why do you think it is incorrect...?

Daniel.
 
  • #3
Because I thought T=mg at 0.
 
  • #4
vroman said:
Because I thought T=mg at 0.

Only if the mass is not accelerating at 0, and the only time that happens is if the mass is at rest at zero. Your mass is always moving at 0. What is the direction of acceleration at that point?
 

1. What is a simple pendulum?

A simple pendulum is a weight suspended from a pivot point that is free to swing back and forth. The weight is referred to as the pendulum bob and the distance from the pivot point to the center of the bob is called the length of the pendulum.

2. What factors affect the motion of a simple pendulum?

The motion of a simple pendulum is affected by the length of the pendulum, the mass of the pendulum bob, and the force of gravity.

3. How is the period of a simple pendulum calculated?

The period of a simple pendulum is calculated using the equation T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

4. How does the amplitude affect the motion of a simple pendulum?

The amplitude, or the maximum angle of swing, does not affect the period of a simple pendulum. However, a greater amplitude will result in a larger arc length and a longer period of oscillation.

5. How does air resistance affect the motion of a simple pendulum?

Air resistance can affect the motion of a simple pendulum by slowing down the pendulum's swing and reducing its amplitude. However, for small oscillations, the effects of air resistance are negligible.

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