A single mass (m 1 = 3.3 kg) hangs from a spring in a motionless elevator. The s

Question

A single mass (m1 = 3.3 kg) hangs from a spring in a motionless elevator. The spring constant is k = 257 N/m.

1)What is the distance the spring is stretched from its unstretched length? ___________________cm

2)

Now, three masses (m1 = 3.3 kg, m2 = 9.9 kg and m3 = 6.6) hang from three identical springs in a motionless elevator. The springs all have the same spring constant given above.

What is the magnitude of the force the bottom spring exerts on the lower mass? _______________N

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

4)Now the elevator is moving downward with a velocity of v = -3.5 m/s but accelerating upward at an acceleration of a = 4.4 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)

What is the magnitude of the force the upper spring exerts on the upper mass? _______________N

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

6)Finally, the elevator is moving downward with a velocity of v = -2.2 m/s but accelerating downward at an acceleration of a = -3 m/s2.

Compare the magnitude of the NET force on each mass:

A) F1 = F2 = F3

B) F1 > F2 > F3

C) F2 > F3 > F1

7)What is the magnitude of the net force on the middle mass? N

Explanation / Answer

As per the chegg rules one question should post at once or one question with maximum of four sub-qurries related to that same question.

The spring supporting mi is Si. Since there is a top spring, middle and bottom, then it must be that:

s1 is attached to the ceiling (elevator) and m1 hangs from it;
s2 is attached to m1; m2 hangs from s2;
s3 is attached to m2; m3 hangs from s3.

IOW, they're attached in series.

Since we're not given the masses of the springs, I'm assuming that their masses are negligible.

OK, now for the individual questions:

1.What is the spring constant of the spring? [4.1kg, 12cm extension]

NOTE: Although the question says "x = 12 cm" (implying a horizontal extension using the usual coordinate system), the word "hanging" implies vertical, or the y-direction.

1) as per the hook’s law
F = kx

Fg = m g

mg= k x
x = m1 g /k

= 3.3 x 9.81 / 257

x= 0.125m.

4)
Since the top spring s1 is supporting all 3 masses, it is exerting a force equal to gravity's downward pull but in the opposite direction

Fg = (m1 + m2 + m3) g

= 19.8 x 9.81

Fg= 194.24N

2)

The lower spring S3 is supporting only m3; applying Hooke's law:

x = Fg / k = m g / k
x1 = 0.126
Notice, however that m3 = 2 xm1, therefore:

x3 = 2 x1

= 2 x 0.126 =0.252m

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

F3net = m3 (g + a)

= 6.6 (9.8 + 4.4)

= 93.79N

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