Calculating the Unbalanced Force in a Pendulum System

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In summary, the unbalanced force acting on the pendulum bob is 5.4N at an angle of 35 degrees above the horizontal.
  • #1
krypt0nite
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I don't know how to calculate the magnitude of the unbalanced force.

A pendulum bob with a mass of 1.80 kg is displaced from its equilibrium position, A, to an unstable position, B, by means of a string which is kept horizontal. The force applied to the string is, F. The length of the pendulum is 1.25 m. The angle through which the pendulum is displaced is 30.0 degrees as measured from the vertical. Determine the following.

diagram

Draw a free body diagram for the pendulum bob when it is at an angle of 12.0 degrees as measured from the equilibrium position. Ca1culate the magnitude of the unbalanced force acting upon the bob. In what direction must the unbalanced force act?

I've calculated the speed which is 1.66m/s. And from the speed I've got the centripedal force which is 3.96N. I know the unbalanced force acts toward the center.

Ok, how do show how i calculated the unbalanced force.
I was thinking T- mg(cos something)= centripedal force but unsure of how and what to do next.
 
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  • #2
krypt0nite said:
I've calculated the speed which is 1.66m/s. And from the speed I've got the centripedal force which is 3.96N. I know the unbalanced force acts toward the center.
Careful. While there must be an centripetal force (which you calculated), it is only a component of the unbalanced (net) force. (If the unbalanced force only acted towards the center, then the speed of the pendulum would not change--it would just keep going in a circle--but you know it speeds up as it falls!)

Ok, how do show how i calculated the unbalanced force.
I was thinking T- mg(cos something)= centripedal force but unsure of how and what to do next.
First find the tension in the string by applying Newton's 2nd Law in the centripetal direction: [itex]T - mg cos\theta = ma_c = m v^2/r[/itex]. (Solve for T.)

There are two forces on the pendulum bob: the weight and the tension in the string. Add them (as vectors, of course) to find the net unbalanced force.
 
  • #3
Does Fnet=5.4N 35 degrees above horizontal sound right?
 
  • #4
Sounds good to me.
 

1. How do I calculate the period of a pendulum?

The period of a pendulum can be calculated using the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.8 m/s² on Earth).

2. What affects the period of a pendulum?

The period of a pendulum is affected by the length of the pendulum, the mass of the pendulum bob, and the acceleration due to gravity. The period also depends on the angle of release and the air resistance.

3. How does the length of a pendulum affect its period?

The longer the length of the pendulum, the longer its period will be. This is because a longer pendulum has a greater distance to travel, and therefore takes longer to complete one swing.

4. Can the mass of the pendulum bob affect its period?

Yes, the mass of the pendulum bob can affect its period. A heavier pendulum bob will have a longer period because it requires more energy to swing back and forth.

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

Air resistance can affect the period of a pendulum by slowing it down and reducing its amplitude. This can make the period longer and less predictable. To minimize the effect of air resistance, pendulums are often operated in a vacuum.

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