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You have a person doing a bench press. Their hands are equidistant apart and they are centered on the bar - each hand about 1.5 feet from center of the bar. The bar weighs 45 pounds.

In example 1 there are two 45 pound weights on each side at 2.5-3 feet each from the center (lets say each weight is 3 inches wide).

In example 2 there are nine 10 pound weights on each side starting at 2.5 feet again and then ending 27 inches later.

What are the forces that cause example to to feel heavier and is there any way to calculate it.

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This isn't a homework question! I am trying to take something that is very practical and have the physics behind it interpreted so that we can figure out why we are getting outcomes. –  David Moore Aug 21 '13 at 21:11
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2 Answers

To start with, the downward force is the same in both cases, so you're right to say that might 'feel' heavier rather than actually being heavier (of course!). My guess at the reason for this illusion is that in example 2, the mass is distributed further from the centre of mass (of the bar+weights), giving a higher moment of inertia for the bar+weights. This means that if the lifter's hands are not quite placed correctly (centered) and the bar begins to tilt, the torque required (and so the force required for hands placed at a given distance) to compensate is increased. The amount of work done in lifting the mass is unchanged, but one arm may need a greater force than the other, and there may be some additional effort from the torso and legs to stabilize the lifter against (in the extreme case) rolling off the bench.

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How does spreading your arms out or narrowing them affect the lift and center of mass? –  David Moore Aug 21 '13 at 15:41
    
I am asking because I am trying to logically explain a technique I have used with lifters. In that once they hit a max, I then take the same "max" weight but distribute it further from the center of the bar. Logically the lifter feels that they should be able to lift it but often times they can't or if they do it is slower or less reps. –  David Moore Aug 21 '13 at 15:43
    
re: 1st comment: spreading or narrowing arms changes the force required to achieve a given torque on the bar (so it's harder to avoid tilting with hands close together). It can also change the muscles involved in the lift, but being a physicist and not a personal trainer, I couldn't tell you the details of that side of things. re: 2nd comment: To reduce my above answer to one sentence, "a wider weight distribution requires more effort to stabilize". –  Kyle Aug 21 '13 at 16:19
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As far as the total weight being lifted obviously it's the same. But, there are two factors I can think of. 1) is the psychological factor of lifting what appears to be more mass. But, 2) is that the distribution of mass affects the moment of inertia. This means that it's harder to make corrections to the bar once it's rotating. Also, each half of the total weight is more completely over an arm when they are separated more, so each arm has to lift that much. When the weights are closer, it's easier for one arm to support some of the other's weight if needed.

So, my guess is that if a weightlifter has any issue with keeping the bar stable, or any imbalance in the strength of their arms, then having the weights further out from the center can be more difficult.

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Is the center of mass "moved" based on not having your hands exactly centered? How does that play into it? –  David Moore Aug 21 '13 at 18:13
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The center of mass of the bar+weights stays the same, but if you put your hands unevenly on each side it will change how much each arm has to bare. The hand that's closer to the center is holding up more of the weight than the other. –  Owens Aug 21 '13 at 18:38
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