Example Problem with Complete Solution

1B-1 : Mass, Weight and Gravitational Acceleration 4 pts
A curious astronaut took her bathroom scale (a spring scale) and a beam scale (compares masses) to the moon. On Earth, she determined that her mass was 124 lbm. The gravitational acceleration on the moon is a = 5.3 ft/s2.
When she reaches the moon
a.) What will she weigh on the spring scale?
b.) What will the beam scale indicate for her mass?
 
Read: The key here is that a spring scale actually measures weight (which is a force) and not mass.
Use gc in Newton's 1st Law of Motion to answer this question.
Given: m 124 lbm a 5.3 ft/s2
Find: a.) Fwt ??? lbf b.) mbeam ??? lbm
Assumptions:
Equations / Data / Solve:
Part a.) The key equation here is Newton's 1st Law of Motion :
Eqn 1
Because a spring scale measures weight, which is the force exerted by the astronaut on the scale, we need to solve Eqn 1 for Fwt.
Eqn 2
Now, we can plug values into Eqn 2 : gC 32.174 lbm-ft/lbf-s2
Fwt 20.43 lbf
Part b.) A beam balance is the kind of scale used in most medical and sports facilities.
Known masses are moved along the length of the beam until the net torque around the fulcrum is zero. That is the astronaut's weight multiplied by a fixed distance along the beam to fulcrum is equal to the weight of the masses hanging from the beam multiplied by their distance from the fulcrum.
Weight is still involved in a beam balance,but the key is that the local gravitational acceleration applies to BOTH the astronaut AND the masses on the beam balance. This scale will read the same on the moon as it would in the astronaut's bathroom ! Therefore, it is actually measuring the astronaut's MASS (which is the same on the moon as in her or his bathroom.
mbeam 124 lbm
Answers: a.) Fwt 20.4 lbf
b.) mbeam 124 lbm