A circular object is pushed into a v$-$shaped slot by a force F

as shown in the figure below. The weight of the object is negligible compared to the external force $.$

The v$-$shaped slot consists of two frictionless surfaces at angles $\backslash$alpha $=40\mathrm{.}7$

and $\backslash$beta $=28\mathrm{.}5$

to the x

$-$axis as shown in the figure.

Two force sensors $($green in figure$)$ are used to measure the compressive force on the walls. The sensors at A

and B

measure a compressive force of magnitudes $864\mathrm{.}3$ N and $395$ N$,$ respectively.