What Are the True Statements About Tension in a Simple Pendulum?

[lmlgrey]

Simple pendulum question.. help needed!

http://capa.mcgill.ca/res/mcgill/dcmcgill/oldproblems/msuphysislib/Graphics/Gtype26/prob34a_pendSHM1.gif1.[/URL] The diagram shows a simple pendulum consisting of a mass M suspended by a thin string. The magnitude of the tension is T. The mass swings back and forth between ±q0 Choose True or False

True False T is greater than Mg for q = q0.
True False T equals Mg when q = q0.
True False T=Mg at some angle between zero and q0.
True False The vertical component of tension is constant.









2. is it true that T = mg*cos(theta) always?



The vertical component of tension is constant ... true, since the vertical component=force of gravity
T is greater than mg when q=q0. ... false, since q0 is the apex, and T is the smallest when the ampliude is the greatest

I don't know about the other two...especially: T=Mg at some angle between zero and q0
my guess at that question is that since T= Mgcos(theta), therefore, T will only equal to mg when theta=0 or 180? so it would be false?

 

[tiny-tim]

The diagram shows a simple pendulum consisting of a mass M suspended by a thin string. The magnitude of the tension is T. The mass swings back and forth between ±q0

Hi lmlgrey!

Don't guess!

Physics is equations, so always find the right equation, and follow it through.

In this case, the right equation is Newton's second law, F = ma.

Most of your answer is wrong, because you've ignored the ma part.

Try again!

 

[thomate1]

I cannot provide a definite answer without more information or context. However, here are some thoughts that may help with understanding the problem:

1. T is greater than Mg for q = q0: This statement is false. The tension in the string is always equal to the centripetal force, which is given by T = Mgcos(theta). At the apex (q = q0), cos(theta) = 0, so T = 0. This means that at the apex, the tension is the smallest and not greater than Mg.

2. T equals Mg when q = q0: This statement is also false for the same reason as above.

3. T = Mg at some angle between zero and q0: This statement is true. As mentioned before, T = Mgcos(theta), so when theta is between 0 and q0, the tension will equal Mg.

4. The vertical component of tension is constant: This statement is true. The vertical component of tension is the force of gravity, which is constant. So, as the pendulum swings back and forth, the vertical component of tension will remain constant.

5. Is it true that T = mg*cos(theta) always? This statement is true. This is the equation for the centripetal force, which is always equal to the tension in the string. So, T will always be equal to mgcos(theta).

I hope this helps with understanding the problem. It is always important to carefully consider the given information and equations to arrive at the correct answer. If you still have doubts, it may be helpful to consult with your teacher or a fellow classmate.