Question

Miguel learned about the difference between mass and weight. He wanted to investigate what he would weigh at different locations in our solar system. He used this table to organize data he found out about Earth, the moon, Neptune, and Mercury. He needs to fill out the rest of the table.
Use the information in the table to calculate Miguel’s weight, in pounds, on the moon, Neptune, and Mercury. Explain the way you did your work.

Answer 1

The weight of an object is given by:

$W=mg$

where m is the mass and g is the gravitational acceleration.

Miguel's mass is the same on every planet (m=60 kg), the only element changing in the formula is g, the value of the gravitational acceleration, which is different for every planet. So by knowing the ratio $\frac{g_x}{g}$, where g is the gravitational acceleration on Earth and $g_x$ is the value of the gravitational acceleration on the planet we are studying, we can calculate the ratio $\frac{W_x}{W}$, where W is Miguel's weight on Earth (which we know, it is W=132 lbs), and Wx is the weight on the planet we are studying:

$\frac{W_x}{W}=\frac{mg_x}{mg}=\frac{g_x}{g}$

- For the Moon, we have $\frac{W_x}{W}= \frac{g_x}{g}=0.17$

so the weight on the Moon is

$W_x =0.17 W=(0.17)(132 lbs)=22.4 lbs$

- For Neptune, we have $\frac{W_x}{W}= \frac{g_x}{g}=1.1$

so the weight on Neptune is

$W_x =1.1 W=(1.1)(132 lbs)=145.2 lbs$

- For Mercury, we have $\frac{W_x}{W}= \frac{g_x}{g}=0.38$

so the weight on Mercury is

$W_x =0.38 W=(0.38)(132 lbs)=50.2 lbs$