Simple Machine Test Exchange Division B - #23 Wedge to Ramp

[j12y]

23. Suppose, for some reason, that you placed the axe blade on the ground and used it as a ramp. What is the IMA of this ramp?

The value listed in the answer key is 8.02, but I was wondering if somebody could help clarify how that value was calculated.

It's easy to be tricked into thinking 8, but the length of the wedge is not the length of the ramp but just the distance of the base.

Is the answer to calculate the hypotenuse of the triangle, and then IMA = length of ramp / height of ramp.

Is there a second trick?

Thanks, all of the other questions were good practice.

[smayya337]

I don't know the blade's dimensions, but here is what I can figure out:

The other wedge face should be at an incline if you use the first as the base, so the length of the wedge should be the length of the ramp. The IMA of a wedge is 1/sin(x), where x is the angle between the base and the incline. In this case, x is just the angle of the wedge. While one of the wedge's faces is the base, the distance of the base that actually matters for this problem is (length of incline) cos(x). (The rest of it is the base for a different incline, which is irrelevant.)

I'm a really bad explainer, so hopefully I didn't confuse you, but if I did, feel free to reach out and ask!

[j12y]

Thanks, I was referring to this test: https://scioly.org/tests/files/simplema ... me_key.pdf
The height was given to be 5cm and the length along the ground of 40cm.