Answer to Question #104305 in Classical Mechanics for sarah

Question

1. Your doctor has told you to watch your weight. Of course, your weight comprises two factors, so you assume that she wants you to watch both your mass and the local value of g. Which explains why you are carrying a small mass m on an elastic band wherever you go. Most of the time, the elastic band is stretched by a distance of 2.1 cm. However, when you have finished lunch, you go into a very tall building and take the high speed lift. Soon after the doors close, you notice that the band is stretched by a total distance of 3.5 cm.

a) At what rate is the lift accelerating?
b) Your doctor will want to know the factor by which your weight has increased after that lunch. Suppose that you stand on scales in the lift while it is accelerating as described above. According to the scales, your weight has increased by a factor of _____ .

Answer 1

a) According to Newton's second law, at 2.1 cm the band is stretched by the force of gravity:

$$0.021k=mg.$$

When you're moving upward, not only force of gravity acts on the mass m:

$$0.035k=m(g+a),\\ \space\\ a=\frac{0.035k}{m}-g.$$

Also, from the first equation we see that

$$\frac{k}{m}=\frac{g}{0.021}.$$

After substitution to the third equation:

$$a=0.035\cdot\frac{g}{0.021}-g=0.67g=6.57\text{ m/s}^2.$$

The weight on a resting plane:

$$P=mg.$$

The weight on an elevating surface:

$$P_e=m(g+a)=1.67mg.$$

Divide:

$$\xi=\frac{P_e}{P}=1.67.$$

Your weight has increased by a factor of 1.67