MadSci Network: Physics

Re: How can one calculate the force needed to lift a weight off the ground?

Date: Wed Jul 19 16:19:32 2000
Posted By: Gareth Evans, Senior Research Associate
Area of science: Physics
ID: 963869875.Ph

As usual, it depends ! If you bend down and start to lift you could apply a force vertically upwards equal and opposite to the weight of the barbell i.e. 600 lbs.wt. The floor which previously provided this force which kept the barbell at rest now feels no weight. A small additional upward force on the barbell would start to accelerate the barbell vertically so one answer to your question could be "just over 600 lbs. wt". Let's say the extra or net vertical force was 1 lb. wt. How fast would the acceleration be? We know that the acceleration due to gravity is 32 ft per second per second. That is, if there was no other force on the barbell it would fall with that acceleration under the influence of the force of gravity on it of 600 lbs. wt. Because we define force as mass times acceleration, we can work out that the acceleration due to the net 1 lb. wt upwards force is 32 x 1/600 or 0.05333 feet/second/second. This, as you would expect, is very slow and if you only used this 601 lbs. wt. you will have spent tens of seconds moving it a few inches so your back would be ruined your muscles will have been exhausted and you'd crumple to a defeated heap!

You need to accelerate the bar at a reasonable rate so that you can lift it in one or two seconds. Lets first make an approximation by making a very simple model of the lift which makes the arithmetic easy. Let's say the acceleration is about 1foot/second/second and that we approximate the motion to a foot in the first second and two feet in the next second. Our approximate net force has produced 1/32 of the acceleration of gravity and corresponds to a force on the barbell of the 600 lbs. wt needed to counteract gravity plus an extra 600 x 1/32 or about 19 lbs. wt. The momentum will take the barbell a little higher than the 3 feet over which we have exerted the lifting force. As a rough guide then you would need a force about 619 lbs. wt.

To get a bit more accurate, we can use a formula which calculates the acceleration, "A", needed in a time "t" to move the barbell a distance "d". The expression we use is A=2d/t2. Now we need to chose the height we need to raise the barbell, say 3 feet and the time it will take, say 2 seconds. A then becomes 2 x 3 / 2 x 2 or 1.5 feet per second per second, a little more than we were assuming before. This makes the force needed 628 lbs. wt. This doesn't sound much, about 4.7% of the weight of the barbell, but then, the acceleration produced is still quite slow. Imagine if the barbell were stuck to the ceiling and it suddenly came unstuck, it would travelling pretty fast by the time it hit the floor having been accelerated by the 600 lbs. wt exerted by gravity.

To work things out accurately you would need to work out how high the final position is and how fast you want to lift taking into account the over-run due to the momentum of the weights. Also, in practice, the force on the barbell exerted by your muscles changes with time as the geometry of your body changes and allows you to exert different vertical forces as you straighten up. We would need all this information to work out what the maximum force you would be applying in practice. The slower the lift, the less force is needed and the longer you can apply a steady force the better also. It is probably the case that you need to accelerate the weight faster so that the majority of the speed needed to achieve the height required is produced early, while the legs are bent an in a better position to provide the upwards force. In that case our estimate of 628 lbs. wt based on a constant force would be on the low side.

To get a better idea of a real lift, I thought you might like to try an experiment. When you lift the bar it bends. You could support the bar in the middle in the same way that you would hold it in a lift and measure the amount of bending at with different weights on the end. The force exerted by the bar trying to straighten itself out equals the weight of the weights at each end. You could then video a real lift using your 600 lbs. set of weights. ( I'd rather you than me ! ) As you accelerate the weights upwards the bar will bend more than it did when the weights were not moving but were off the floor. The extent of the extra bending is a measure of the extra force you are exerting to produce the acceleration upwards. This will only work in the early part of the lift as the bar accelerates. After that the situation becomes complicated by the momentum of the weights.

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