Chapter 9, Problem 4Q

To determine

Your doctor’s scale has arms on which weights slide to counter your weight. These weights are much lighter than you are. How does this work?

Answer to Problem 4Q

Solution:

When the person stands on the scale, the doctor begins to move the small masses until the system becomes balanced, in other words: the torque applied by the person is equal to the torque made by the sliding masses.

Explanation of Solution

According to figure, this type of scales work with the equilibrium of balances.The lighter weight ( $m$ )rest on a long lever arm ( $B$ )of known length. The other system in which the person is mounted, the lever arm ( $b$ )is short compared to the upper arm. We have then: A long lever arm ( $B$ )with small masses ( $m$ )and another short lever arm ( $b$ )with a large mass $(M)$. Both arms have their fulcrum. When the person stands on the scale, the doctor begins to move the small masses until the system becomes balanced, in other words: the torque applied by the person is equal to the torque made by the sliding masses:

$M.b=m.B$                     (1)