# Reaction force exerted by pulley's support

Consider an in-extensible string passing over an ideal pulley connected to a block of mass $$m$$ as shown:

The ends are pulled with a force $$F$$

Am I correct in saying that the block will experience a reaction force $$\sqrt{2}F$$? The forces acting are perpendicular to each other and the support of the pulley is inclined at an angle of $$45^\circ$$ with horizontal.

In other words can the forces acting on the string be vectorially added to find the resultant reaction force exerted by pulley?

• I encountered this specific scenario while solving an entirely different question. That is the reason I havent given any context. Im not sure about why this is tagged as a homework question. This is a purely conceptual doubt – newbie105 Jan 2 at 16:27