Solve Elevator Problem with Weight & Acceleration on Moon

[seizureboi]

Homework Statement

The effect of gravity is approximately 1/6 of what it is on Earth. If one were to build an elevator on the moon, (a) what would be the apparent weight of a 65kg astronaut when the elevator accelerates upward at 5 m/s²? (b) What is the acceleration of the elevator if the apparent weight of the astronaut is 500N?

Homework Equations

F = ma
m = mass
m = 65 kg
w = weight
w = mg
a = acceleration
a = 5 m/s²
g_M = 1.63 m/s²

The Attempt at a Solution

The equation I set up for (a) was: ma - mg = w
OR (65)(5) - (65)(1.63) = w
OR 325 - 106 = w
Finally, w = 219N

For (b) I had the same exact formula: ma - mg = w
OR (65)a - (65)(1.63) = 500
OR 65a - 105.95 = 500
OR 65a = 605.95
Finally, a = 9.32 m/s²

Just wondering, again, if this is right or not. =)

 

[PhanthomJay]

Homework Statement

The effect of gravity is approximately 1/6 of what it is on Earth. If one were to build an elevator on the moon, (a) what would be the apparent weight of a 65kg astronaut when the elevator accelerates upward at 5 m/s²? (b) What is the acceleration of the elevator if the apparent weight of the astronaut is 500N?

Homework Equations

F = ma
m = mass
m = 65 kg
w = weight
w = mg
a = acceleration
a = 5 m/s²
g_M = 1.63 m/s²

The Attempt at a Solution

The equation I set up for (a) was: ma - mg = w
OR (65)(5) - (65)(1.63) = w
OR 325 - 106 = w
Finally, w = 219N

For (b) I had the same exact formula: ma - mg = w
OR (65)a - (65)(1.63) = 500
OR 65a - 105.95 = 500
OR 65a = 605.95
Finally, a = 9.32 m/s²

Just wondering, again, if this is right or not. =)

Ouch, you let the plus and minus sign bite you. The acceleration is always in the direction of the net force. The apparent weight (the normal force) and the true weight must act in opposite directions.