Grantham PHY220 Week 2 Assignment Problem 6

If the acceleration due to gravity on the Moon is 1/6 that what is on the Earth, what would a 100 kg man weight on the Moon? If a person tried to simulate this gravity in an elevator, how fast would it have to accelerate and in which direction?

SOLUTION:

The acceleration due to gravity on the moon is $g_m=\frac{1}{6}\left(9.80\:m/s^2\right)=1.63\:m/s^2$

The weight of a 100-kg man on the moon is $W_m=mg_m=\left(100\:kg\right)\left(1.63\:m/s^2\right)=163.3\:N$

If the elevator is accelerating upward then the acceleration would be greater. The person would be pushed toward the ﬂoor of the elevator making the weight increase. Therefore, the elevator must be going down to decrease the acceleration.

For a 100 kg man to experience a 163.3 N in an elevator, $F=ma$ $163.3\:N=100\:kg\:\left(9.80\:m/s^2-a_e\right)$ $9.80-a_e=\frac{163.3}{100}$ $a_e=9.80-\frac{163.3}{100}$ $a_e=8.167\:m/s^2$

Therefore, the elevator should be accelerated at 8.167 m/s2 downward for a 100-kg man to simulate his weight just like his weight in the moon which has 1/6 of the Earth’s gravity acceleration.