Using Vector in Determining Period of Pendulum Inside a Moving Train

In summary, the question relates to the period of a pendulum and involves calculating the tension in the string when the pendulum is at rest with respect to a train moving with an acceleration of 0.2g. A diagram is provided to explain the forces acting on the pendulum, with gravity and tension combining to create a net horizontal force labeled as F. It is clarified that the tension is not the same as the net force and that there is no force exerted by the train.
  • #1
science_world
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Hi all, i have a question relating to the period of pendulum. I got this question:
A bob of mass 0.5 kg is suspended by a string from the ceiling inside a train moving on a straight level rail (to the right). If the train has an acceleration of 0.2g, what is the tension in the string when the bob is at rest with respect to the train? (picture 1)

Someone explained to me that we must draw the tension as a vector joining the force by train to the pendulum and the pendulum's weight (picture 2). I don't understand. Isn't the pendulum supposed to be the resultant of those 2 forces (picture 3) and not the force by train who become the resultant (picture 2)?

Please do explain. Thanks a lot.
 

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  • #2
science_world said:
Isn't the pendulum supposed to be the resultant of those 2 forces (picture 3) and not the force by train who become the resultant (picture 2)?
The net force is not the tension. The forces acting on the pendulum bob are gravity and tension. They add together to give s horizontal net force that you have labeled as F in your diagram. So you add a tension that is "up" and "to the right" to the weight that is "down". The "up" part of the tension exactly cancels the "down" weight and all that's left is the "to the right" part of the tension. There is no force exerted by the train.
 

FAQ: Using Vector in Determining Period of Pendulum Inside a Moving Train

1. How does the motion of the train affect the period of the pendulum?

The motion of the train will affect the period of the pendulum due to the principle of relative motion. As the train moves, it carries the pendulum with it, creating an additional horizontal component of motion that will impact the period of the pendulum.

2. Can the vector method accurately determine the period of the pendulum inside a moving train?

Yes, the vector method is a reliable and accurate way to determine the period of a pendulum inside a moving train. It takes into account both the horizontal and vertical components of motion and can accurately calculate the period of the pendulum.

3. How does the angle of the pendulum affect the vector calculations?

The angle of the pendulum does not affect the vector calculations as long as the angle remains constant. As the pendulum swings, the angle will change, but the vector calculations take into account the average angle over the course of one period.

4. Do the speed and direction of the train affect the vector calculations?

Yes, the speed and direction of the train will impact the vector calculations. The faster the train is moving, the greater the horizontal component of motion will be, resulting in a longer period for the pendulum. The direction of the train's motion will also affect the angle of the pendulum, which will in turn affect the vector calculations.

5. How can the vector method be applied in real-world situations?

The vector method can be applied in various real-world situations, such as determining the period of a pendulum on a moving ship or car, or even calculating the motion of a pendulum during an earthquake. It can also be used to study the effects of air resistance or other external forces on the pendulum's motion.

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