Physical Principles: Statics equilibrium

Student Prerequisites: For this demonstration, students need to be familiar with the following concepts - a.) one-dimensional vector addition, b.) mass and weight, and c.) conditions for static equilibrium.

Introduction: In this demo, we will try to understand the mechanical advantage of various pulley applications from the perspective of statics. Students will apply their knowledge of the first condition for equilibrium to make quantitative preditions about the readings of spring scale attached to the movable end of the string, and thereby to compare with the weight of masses.

The primary objective of this interactive demonstration is to help students to develop conceptual ideas about the efficacy of simple machines, and to justify their uses in daily life.

Description of the Demo: The first condition of equilibrium tells us that if the vector sum of all external forces (net force) acting on the body is zero, then the body at rest has no tendency to start moving as a whole.

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Given a setup in the stationary state, students should carefully choose some reasonable object from the whole system to analyse the forces on it. In our cases, this can be done within only one dimension as a good approximation. The optional Question 6 concerns about this approximation, which exceptionally may require students to think in two dimension.

The situation could become terribly intractable if no approximation or idealization was made to the considered systems. In all following, we always assume that strings we use are massless or negligibly light, and that pulleys are frictionless at their axles. Students may be asked to consider why these are necessary and whether there should be additional assumptions (e.g. consider the elasticity of string and the friction between pulley and string, and etc.). Advisably, it makes good sense for students to realize the difference between the idealization and the actual cases.

Instructions: When doing the demo, the spring scale should be fastened to the base of the frame to acquire desired stationary states. PLEASE click links in the question section to get the close picture and arrangement of each setup.

Note to the Instructor: Pulleys are delicate and easy to fall off if not hung tightly. Dedicated setup time may be required for a desired configuration.

Possible CPS Questions:

1. When the whole setup is kept still, does the tension along the string vary... [Question] [Answer]

2. Estimate what the spring scale attached to the free end will read for Setup 1 and 2... [Question] [Answer]

3. Estimate what the spring scale attached to the free end will read for Setup 3... [Question] [Answer]

4. Estimate what the spring scale attached to the free end will read for Setup 4... [Question] [Answer]

5. Estimate what the spring scale attached to the free end will read for Setup 5... [Question] [Answer]

6. (For extraordinary students) Do the suspension sections of string have to be perfectly vertical... [Question] [Answer]