Question

1. A solid cube with mass 80 kg Is put in an elevator. The length of each side is 40 cm. The elevator is moved up and down repeatedly. When It moves upward, it able to reach speed 5 m/s in 4 seconds, while when It moves downward It able to reach speed 8 m/s in 2 seconds. Find the pressure experiences by the elevator caused by the solid cube, when:
a. it moves downward
b. it moves upward
c. It moves with constant speed 1 m/s
d. What you can conclude based on the result on a, b, and c?

Answer 1

Answer on Question #58064-Physics-Mechanics

1. A solid cube with mass $80\,\mathrm{kg}$ is put in an elevator. The length of each side is $40\,\mathrm{cm}$. The elevator is moved up and down repeatedly. When it moves upward, it able to reach speed $5\,\mathrm{m/s}$ in 4 seconds, while when it moves downward it able to reach speed $8\,\mathrm{m/s}$ in 2 seconds. Find the pressure experiences by the elevator caused by the solid cube, when:

a. it moves downward

b. it moves upward

c. it moves with constant speed $1\,\mathrm{m/s}$

d. What you can conclude based on the result on a, b, and c?

Solution

a.

$$m g - N = m a \rightarrow N = m (g - a).$$ $$P = \frac {N}{A} = \frac {m (g - a)}{d ^ {2}} = \frac {8 0 \mathrm{~k g} \left(9 . 8 \frac {\mathrm{m}}{\mathrm{s} ^ {2}} - \left(\frac {8}{2}\right) \frac {\mathrm{m}}{\mathrm{s} ^ {2}}\right)}{(0 . 4 \mathrm{~m}) ^ {2}} = 2 9 0 0 \mathrm{~P a}.$$

b.

$$N - m g = m a \rightarrow N = m (g + a).$$ $$P = \frac {N}{A} = \frac {m (g + a)}{d ^ {2}} = \frac {8 0 \mathrm{~k g} \left(9 . 8 \frac {\mathrm{m}}{\mathrm{s} ^ {2}} + \left(\frac {5}{4}\right) \frac {\mathrm{m}}{\mathrm{s} ^ {2}}\right)}{(0 . 4 \mathrm{~m}) ^ {2}} = 5 5 2 5 \mathrm{~P a}.$$

c.

$$N - m g = 0 \rightarrow N = m (g).$$ $$P = \frac {N}{A} = \frac {m (g)}{d ^ {2}} = \frac {8 0 \mathrm{~k g} \left(9 . 8 \frac {\mathrm{m}}{\mathrm{s} ^ {2}}\right)}{(0 . 4 \mathrm{~m}) ^ {2}} = 4 9 0 0 \mathrm{~P a}.$$

d. I can conclude that maximal pressure experiences by the elevator caused by the solid cube, when it moves upward. The minimal pressure experiences by the elevator caused by the solid cube, when it moves downward.

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