Amount of force in pounds it takes to get a person that weighs 120lb 3ft off the ground?

Answer 1

Let us examine the mechanics of a jumping person. First the person imparts some force on the ground over a small amount of time, this is known as an impulse. This impulse gives the person an upward speed which is reduced, by gravity, to zero at the apex of the jump. Gravity still acting on the person accelerates them back to the earth hitting with the same speed they jumped up with. Because of the symmetry of the problem it will take the same amount of time for the person to go from 0 to 3 feet as it will from 3 feet back to the ground (0 feet).

Using the equations of motion we can calculate for how long it would take to free fall from 3 feet at initial velocity of 0.

gravity = 32.2 [ft/s^2]

Time = (2*3 [feet] / gravity)^0.5 = 0.432 [seconds]

Next, using the equations of motion still, we calculate the speed we would hit the ground with falling from 3 feet.

Speed = gravity * Time = 9.48 [mph]

Knowing our speed and mass we can calculate the amount of momentum we have right as we jump.

momentum = mass * speed = 51.81 [lbs*sec]

Now here is the interesting part, the amount of force required to achieve that momentum depends on how fast your muscles "twitch". Impulse is force times time.

51.81 [lbs*sec]

Force = -------------------

time [sec]

This says that if you could apply approx 52 pounds of force for 1 second you would have enough velocity to reach 3 feet above ground. This answer of course is not reasonable as the total time to jump 3 feet and land again is less than one second. A more reasonable time needs to be considered. Think about how a person jumps, first the bend their legs and then very quickly push against the ground. Lets say that this happens in a range of between 0.05 and 0.15 seconds.

For a time of 0.05 seconds the calculation is:

Force = 51.81/0.05 = 1036 pounds

This too may seem unreasonable let us examine the case for 0.15 seconds

Force = 51.81/0.15 = 345.4 pounds

It seems that the answer may lie somewhere in between those two values. The value for the amount of time could be determined for an individual experimentally. Have a stop watch running and the person of interest performing a jump. Make sure both are in the frame of the camera. Rewind and watch frame by frame to get an estimate of how long the muscles are working. This of course will give you an average value but is probably within the scope of what you are looking for.