A single mass m 1 = 4.2 kg hangs from a spring in a motionless elevator. The spr

Question

A single mass m1 = 4.2 kg hangs from a spring in a motionless elevator. The spring is extended x = 13 cm from its unstretched length.

1) What is the spring constant of the spring?

2) Now, three masses m1 = 4.2 kg, m2 = 12.6 kg and m3 = 8.4 kg hang from three identical springs in a motionless elevator. The springs all have the same spring constant that you just calculated above.

What is the force the top spring exerts on the top mass?

3) What is the distance the lower spring is stretched from its equilibrium length?

4) Now the elevator is moving downward with a velocity of v = -3.1 m/s but accelerating upward with an acceleration of a = 4.6 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)

What is the force the bottom spring exerts on the bottom mass?

5) What is the distance the upper spring is extended from its unstretched length?

6)Finally, the elevator is moving downward with a velocity of v = -2.9 m/s and also accelerating downward at an acceleration of a = -2.3 m/s2.

The elevator is: a) speeding up. b) slowing down. c) moving at a constant speed

7) Rank the distances the springs are extended from their unstretched lengths:

a) x1 = x2 = x3 b) x1 > x2 > x3 c) x1 < x2 < x3

8)What is the distance the MIDDLE spring is extended from its unstretched length?

Explanation / Answer

ANSWER

Keep in mind that because of terms and conditions of chegg.com we, the tutors, can not answer questions with more than four (4) sub-questions. This problem has eight (8) sub-questions, I will answer only four sub-questions but I recommend to you that upload other question to the system with the other parts, and another tutor will answer it.

Part 1)

From Hooke's Law we get,

k * x = 4.2 * 9.8

k * 0.13 = 9.8 * 4.2

k = 316.615

Part 2)

Since the top spring is supporting all three masses, so the force that it is exerting will be equal to the gravitational pull of all three masses.

Ftop = (m1 + m2 + m3) g = (4.2 + 12.6 + 8.4) x 9.81 = 247.212 N

Hence, Ftop = 247.212 N

Part 3)

x3 = m3*g / k3

x3 = 8.4*9.81 / 316.615

x3 = 0.26 m = 26 cm

Part 4)

F = m3*(g + a)

F = 8.4*(9.81 + 4.6)

F = 121.044 N

Regards!!!

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