Question

You slide a box of books at constant speed up a 23° ramp, applying a force of 180 N directed up the slope. The coefficient of sliding friction is 0.18.
(a) How much work have you done when the box has risen 1 m vertically?
_________J

(b) What is the mass of the box?
_________kg

Answer 1

I figure out that the work was 461.14J, but I am having difficulty relating it to mass.

Answer 2

\[\Sigma F_x = 0\]
\[F = \mu_kN\]
\[\Sigma F_y=0\]
\[N = mg\]

Answer 3

\[m = \frac{ F }{ \mu_kg }\]

Answer 4

Thanks @Ankh, you got me pointed in the right direction.

Since it's not accelerating, the \(\sum F_x = 0\) so \(\sum F_{-x} = \sum F_{+x}\)

\[\rightarrow \mu mg\cos\theta + mg\sin\theta = 180\]
\[\rightarrow m(\mu g\cos\theta + g\sin\theta) = 180\]
\[\rightarrow m = \frac{180}{(\mu g\cos\theta + g\sin\theta)}\]
\[\rightarrow m = \frac{180}{((.18\times 9.81\times\cos(0.401)) + (9.81\times\sin(0.401)))}\]
\[m = 32.997kg\]