# F=ma with two accelerations

## Homework Statement

An astronaut who is weighing himself inside of a rocket blasting off from the moon with an upward acceleration of 1.26m/s^2 records a scale reading of 188N . The acceleration due to gravity on the moon is 1.67m/s^2 .
Find the mass of the astronaut

F=ma

## The Attempt at a Solution

I subtracted the accelerations to m=188N/(1.67-1.26) and it wasn't the answer, I also tried them individually and still can figure it out. m= 188N/1.67 and m=188N/1.26

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cepheid
Staff Emeritus
Gold Member
Draw a free body diagram for the astronaut. The astronaut has two vertical forces acting on him, the normal force FN upward (from the scale, which is also what the scale measures), and his weight Fg, downwards, which is the force with which the moon's gravity pulls on him.

Since the astronaut has a non-zero upward acceleration a = 1.26 m/s2, Newton's 2nd law says that there is a NET upward force acting on him. In other words, the sum of all vertical forces must be an upward force ma.

Fnet = ma

ƩF = ma

FN + Fg = ma

The gravitational force Fg is equal to -mg, with the negative sign because the force acts downwards. On the moon, g = 1.67 m/s2.

FN - mg = ma

Can you take it from here?

oooooo now i get it, thanks