# Mass of chair on weighing scale and wall

• dmouthfan2028

#### dmouthfan2028

For what it's worth, I came up with this problem, so perhaps it cannot be solved, or there could be a way to solve it without using all of the information given.

Homework Statement
A chair rests on a weighing scale and a wall. The relevant surfaces of the scale and the wall are perpendicular to each other. When upright, the scale reports 42.62 kg as its weight, but when flipped upside-down, the scale reports 26.82 kg. The chair makes contact with the scale at 0.4 m from the wall at an angle of 64 degrees. Frictional coefficient between the chair and the wall is 1.02, and between the chair and the scale is 1.16. What is the mass of the chair?

dmouthfan2028 said:
When upright, the scale reports 42.62 kg as its weight...

A correction:
When upright, the scale reports 42.62 kg as its mass...

Have I figured it out? Is this correct?

$F_{gOnScale} = 42.62*9.81$
$F_{gOnWall} = 26.82*9.81$
$F_{T} = F_{gOnScale} + F_{gOnWall} = 42.62*9.81 + 26.82*9.81$
$F_{T}/a_{g} = \frac{42.62*9.81 + 26.82*9.81}{9.81} = 69.44\text{ kg}$