# Vertical component of moving weight at a 45 degree angle

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.

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400 * sin(45) = 283 – Mike Dunlavey Nov 22 '11 at 21:06

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.

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Keep in mind there are several important differences between squatting and using this type of leg press machine:

In addition to the weight plates on the leg press you are lifting the carriage holding them and in addition to the barbell during the squat you are lifting most of your bodyweight.

Most leg press machines load you through the pelvis rather than the spine - the barbell squat requires a significant amount of back strength while most leg press machines require none.

Depending on your foot positioning and range of motion the average levers the hip and knee extensors work against will vary to some degree between the two.

On older or poorly maintained leg press machines friction is also a factor.

Leg presses with the same track angle but different seat angles can vary in difficulty due to the starting angle of the hips - the more reclined the seat the easier the exercise, all else being equal.

Due to the additional risks involved in squatting if you are not sure how much you can squat safely you should not guess based on other exercises. Start with a light weight, test for a few reps, add weight and repeat if necessary. Once you have started to squat down with a barbell on your back is not the time to find out you overestimated.

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sin x


So roughly multiply with 0.707 for a 45 degree angle. Thats the only sin/cos value that I know by hard. But a very convenient one.

sin 45° = sin (pi/4) = about 0.707

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downvoter, please leave comments ? - I thought the other answers were just too long and boring for such a simple question. – bvdb Mar 23 at 10:48