I have a lever that is 16 feat long and pivots on a fixed point 4 ft from the left/heavy end, and 12ft from the right/light end. I wanted to calculate the acceleration of the right end due to gravity. The right end ways 10 lbs. The left end weighs 1000 lbs.
I calculated the acceleration, but I am skeptical of my accuracy, and was wondering if I did it correctly. What I did was this: I calculated the force on each side(unit: lb*ft/s^2): - F = 1000*32ft/s^2 = 32000 - (force) = (mass, 1000lbs) * acceleration due to gravity) - F = 70*32ft/s^2 = 2240 - (70 because I am accounting for the weight of the beam, which overall is about 90lbs)
Because of the mechanical advantage of the right side, I multiplied the force of the left side by .3 (3.5ft/11.5ft) (the weight would really be attached approximately 6 inches from the end of the board), which gave me 9600lb*ft/s^2.
Then, since these forces are on opposite ends of the pivot point, they counter each other, so, I subtracted the answers, and got 9600-2240 = 7360lb*ft/s^2. So since I want acceleration, which is measured in ft/s^2, I divided by the mass of the light end. 7360/70 = 105.14286 ft/s^2. Did I reach the answer correctly? It's been a while since I took physics :).
Note: I am aware I did have a few inaccuracies in rounding, and not accounting for the mass of the beam on the left side, I am more concerned that in principal, I used valid math.
Also, once I have the acceleration, if I wanted to figure out how fast it would be going in say... 3 seconds, I would just do: 105*3^2 = 105*9 = 945?(Which obvoiusly doesn't acc