Demos: 1J-05 Scale Paradox 2

The entire frame is suspended from Scale 1 which shows a total weight of 34 N. What does Scale 2 read?

Directions: Set up the equipment as shown, making sure that the Scale 2 is covered until you are ready to reveal the answer. When the cover is removed, Scale 2 is seen to read 40 N!

Suggestions for Presentation: You might want to “lead” the students a little, capitalizing on their likely belief that scale 2 will read less than Scale 1 (see discussion below). Before uncovering the scale, ask if a free-body-diagram might help answer the question.

Discussion: One is likely to get an “intuitive” answer, namely that Scale 2 must read less than Scale 1 because Scale 1 supports everything, whereas Scale 2 supports only the 2-kg mass and should read 20 N (or at least less than 34 N). The frame and everything within it has a total weight of 34 N, as seen on Scale 1. To see why Scale 2 reads 40 N, draw a Free-Body-Diagram (FBD) for the pulley (which is very light) and for the 2-kg mass:

2-kg mass:

T = 20 N

The Pulley:

T_s = 2T = 40 N

Applications: Sometimes forces can be generated within a system that are greater than the weight of the system itself.

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