Work and energy with normal force

[Maiia]

Homework Statement

Starting from rest, a 5.85 kg block slides 2.07m down a rough 26.4degree incline. The coefficient of kinetic friction between the block and the incline is 0.427. The acceleration of gravity is 9.8m/s^2. Find the work done by the normal force. Answer in units of Joules.

Here's my FBD.

I know the formula for work is Fcos(theta)d. But I don't know how to find the angle for the normal force...
If someone could help out, I would really appreciate it.

 

[mgb_phys]

The normal force acts at right angles to the slope.
You 26.4 is in the wrong place - a slope angle of 26.4 means the angle between the slope and horizontal.

 

[Maiia]

yes, but if you draw some parallel lines, the 26.4 degrees of the slope angle is also equivalent to that angle up there. oh but i see what you said about the normal being perpendicular...wouldnt that mean work is zero then?

 

[LowlyPion]

yes, but if you draw some parallel lines, the 26.4 degrees of the slope angle is also equivalent to that angle up there. oh but i see what you said about the normal being perpendicular...wouldnt that mean work is zero then?

Yes you are right that forces in the direction of motion are the ones that do work, but in the case of the Normal force there is a resulting force along the direction of motion as determined by the Normal force * the Coefficient of Friction.