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d1i1m1o1n [39]
3 years ago
5

A spring 1.50 m long with force constant 448 N/m is hung from the ceiling of an elevator, and a block of mass 10.9 kg is attache

d to the bottom of the spring.
(a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (Enter the magnitude only.) m
(b) If the elevator subsequently accelerates upward at 1.89 m/s², what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction. (Indicate the direction with the sign of your answer.) m
(c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?
Physics
1 answer:
GuDViN [60]3 years ago
3 0

Answer:

Explanation:

Let the extension in the spring be x .

restoring force = weight of block

kx = mg

x = \frac{10.9\times9.8}{448}

= 23.84 cm

b )

When the elevator is going upwards

Restoring force = mg + ma

k x₁ = 10.9 ( 9.8 + 1.89 )

x₁ = 28.44 cm

( y coordinate will  be - ( 28.44 - 23.84 ) = - 4.6 cm )

c ) When the cable snaps , both elevator and block undergo free fall . In this case apparent g = 0

Since the spring is stretched by 28.44 cm , a restoring force continues to act on the block which is equal to

.2844 x 448

= 127.41 N

So a net acceleration a will act on the block

a = 127.41 / 10.9

= 11.68 m / s²

The block will undergo SHM with amplitude equal to 28.44 cm .

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