You know that you can safely stand on the hang-over end of a heavy plank that rests on a table. How far depends on your mass and the mass of the plank. Suppose you can stand on the end of a plank that overhangs the edge of the supporting table 1/4 its total length. Then how massive is the plank compared to your mass?
a. 1/2 your mass
b. same as your mass
c. 1 1/2 your mass
d. twice your mass
e. 4 times your mass
any help would be appreciated!
1 answer
The weight of the plank acts at its center, 1/4 of the length of the plank inward from the edge of the table. Your weight acts 1/4 of the length of the plank beyond the edge of the table. Since at the tipping point all upward force to balance the downward weights of you and the plank are at that edge, your weight times (1/4) L = plank weight times (1/4) L or in other words, you weigh less than or equal to the weight of the plank.
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