Vertical component of moving weight at a 45 degree angle

Question

Here's an easier one. I use the leg press machine at the gym so I don't have to worrying about hurting myself while lifting heavier weight.

The weight glides on a track that looks to be 45 degrees.

What's the equation to figure out how much weight I would be able to squat normally. IE the vertical component of moving 400lbs at a 45 degree angle.

Answer 1

You can understand Mike's answer by looking at this diagram:

The forces involved are the weight (W) you are lifting, the contact force (Fc) with the inclined plane (the rail of the bench press) and the force with your legs (F). The weight can be decomposed into a force parallel to the plane (Wx) and another perpendicular to it (Wy).

If you can lift the weight, it means that $F>W_x$. Using trigonometry, $W_x = W\,\sin(\alpha)$, so you are doing that much force with your legs.