6. The cable of a 2070 - kg elevator has broken, and the elevator is moving down

Question

6. The cable of a 2070 - kg elevator has broken, and the elevator is moving downward at a steady speed of 1.6 m/s. A safety braking system that works on friction prevents the downward speed from increasing. (a) At what rate is the braking system converting mechanical energy to thermal energy? (b) While the elevator is moving downward at 1.6 m/s, the braking system fails and the elevator is in free - fall for a distance of 4.9 m before hitting the top of a large safety spring with force constant of 1.50 x 10^ 4 N/m. After the elevator hits the top of the spring, find the distance d that the spring is compressed before the elevator is brought to rest. The rate of conversion of mechanical energy can be determined from the definition of power. Draw a sketch showing three states of the elevator: moving downward just as it goes into freefall, just before It strikes the relaxed spring, and momentarily at rest on the compressed spring. Let the system consist of Earth, the elevator, and the spring. Then you can apply conservation of mechanical energy to the analysis of the falling elevator and compressing spring.

Explanation / Answer

final velocity when elevator juust hits the spring

v^2 = u^2 + 2as

v^2 = 1.6 ^2 + 2*9.81*4.9

v= 9.93 m/s

now the kinetic energy of elevator will be converted into potential energy of spring

- k * d = 0.5 * m * v^2 { d is compression of spring }

- 1.5 * 10 ^4 * d = 0.5 * 2070 * 9.93^2

d = 0.68517 m

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