Tension
Variant i Dynamics first Other Variants Interactive tutorial lecture
Developed by Peter Shaffer (creator), Mark Somers (co-creator), and Greg Francis (co-creator)
The tutorial covers the concepts of tension in a rope, Newton’s second and third laws, limits, and massless strings.
Topics Mechanics / Newton's Laws: systems, vectors, forces, and free-body diagrams
Materials
Materials by the UW team
- Equipment List
- Instructor’s Guide
- Sample Pre-test
- Sample Exam Questions
Tutorial details
Students begin by considering a system of two blocks connected by a massive rope. One block is pushed to the right by a hand. Students are first asked to compare the accelerations of the blocks. They then determine the approximate directions of the forces on each block and on the rope and to compare the relative magnitudes of the horizontal components of all the forces. By applying Newton’s second and third laws they recognize that the rope exerts forces of different magnitude on the blocks connected to either end. Students then consider the case that the rope is replaced by a light string. They recognize that forces exerted by the ends of the string are more nearly equal to each other in the case of the light string than in the case of the rope. They are now in a position to understand the idealization that a massless string exerts forces of the same magnitude to the objects connected to either end.
In the second section of the tutorial, students apply the ideas developed in the first section to an Atwood’s machine. They are presented with numerical values for the weights of the objects attached to either end and are asked to compare the forces exerted by the strings and the objects. Many students fail to apply the ideas developed in the first part of the tutorial and treat the string as transmitting the weight of one object directly to the other. (i.e., They treat the upward tension on each block as being equal to the weight of the other block.) As they compare the net forces and the accelerations, students are led to confront and resolve their incorrect ideas.
For instruction tips, login or register as a verified educator to see the Instructor Guide.
Prerequisites
Prerequisite tutorials
The Forces and Newton's second and third laws tutorials are prerequisites to Tension.
Other prerequisites
Newton’s second and third laws should have previously been covered in class. It is suggested that students have already worked through the tutorials Forces and Newton’s second and third laws.
Research
- L. McDermott, P. Shaffer, and M. Somers, Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood's machine, Am. J. Phys. 62 (1), 46 (1994).
Coming Soon! We hope to release the discussion section on each tutorial by the end of July 2024.
