Pendulum Suspended from Spring Scale: Testing Experiment

Aim

The purpose of the activity is to help student feel confidence in Newton's laws applied to circular motion by being able to predict the outcome of the experiment based on the knowledge of Newton's laws and circular motion.

Prior Knowledge

• Newton's Laws (all three).
• Circular motion.
• Free body diagrams.
• Vectors and vector method for determining the direction of acceleration for curvilinear motion.
• Kinetic and gravitational potential energy for advanced questions.

Description of the Experiment

A bob is hung by a string, attached to a spring scale which is suspended from a stand. First note the reading on the spring scale when the bob is not moving. The bob and string will then be pulled back so that the string makes an angle theta with the vertical. The bob will then be released and allowed to swing. Predict what will happen to the reading on the spring scale at the bottom of the swing (more, less or same as when the object is at rest). Explain your reasoning using motion diagrams, free-body diagrams, Newton's laws and your knowledge of circular motion.

Youtube movies can be stepped frame by frame using the , and . keys on your keyboard. If you want to download the movie to your computer, right-click or control-click HERE.

Youtube movies can be stepped frame by frame using the , and . keys on your keyboard. If you want to download the movie to your computer, right-click or control-click HERE.

Questions

Now that you have watched the video, did your prediction agree with the outcome of the experiment? If not, what do you need to revise? Assess how good your explanation was by working through the following questions:

1. No Swing

   • Draw a free-body diagram of forces exerted on the bob by other objects at the bottom. How are the forces related? Use Newton's second law to answer this question.
   
   
   
   • How is the reading on the spring scale related to any of these forces? Use Newton's third law to answer this question.
   
   
   
   • How would the reading change if the bob is accelerating up? Down?

2. Bottom of the swing

   • Draw a motion diagram for the bob at the bottom of the swing. For this draw the velocity arrow for the point right before the bottom and then for right after the bottom. Make sure that the points you choose are at the same distance from the bottom. What is the direction of the velocity change vector at the bottom of the swing?
   
   
   
   • Draw a free-body diagram of forces exerted on the bob by other objects at the bottom of the pendulum's swing.
   
   
   
   • Are the motion diagram and the free-body diagram consistent with each other?
   
   
   
   • If yes, indicate the direction of the acceleration on both.
   
   
   
   • If you are struggling with this, think about circular motion. Can you consider the pendulum bob to be travelling in some sort of circle or part of a circle?
   
   
   
   • Based on your answers above, is the force that the string exerts on the bob greater than, equal to or less than the force Earth exerts on the bob? Explain
   
   
   
   • Does this account for the reading on the spring scale?

3. Top of the swing

   • Draw a free-body diagram for the bob at the top of the swing.
   
   
   
   • As before, decide whether the system is accelerating and indicate the direction of the acceleration. Again, it will help to think about circular motion.
   
   
   
   • Based on your answers above, is the force that the string exerts on the bob greater than, equal to or less than the force Earth exerts on the bob? Explain. (Hint: Resolve forces into components in the radial and angular directions.)
   
   
   
   • Can you now explain the reading on the spring scale?

4. Advanced prediction

   Using only the readings on the spring scale and laws of mechanics, derive a theoretical prediction for the initial angle of release (theta). Having done this, use a protractor to make a rough measurement of the release angle on the video. Do your prediction and measurement agree? Can you account for any discrepancy?