A single mass m1 = 4.6 kg hangs from a spring in a motionless elevator. The spri

Question

A single mass m1 = 4.6 kg hangs from a spring in a motionless elevator. The spring is extended x = 10 cm from its unstretched length. 1) What is the spring constant of the spring? 450.8 N/m Submit 2)masseshangingfromsprings2smaller Now, three masses m1 = 4.6 kg, m2 = 13.8 kg and m3 = 9.2 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? 270.48 N Submit 3) What is the distance the lower spring is stretched from its equilibrium length? 20 cm Submit 4) Now the elevator is moving downward with a velocity of v = -2.2 m/s but accelerating upward with an acceleration of a = 4.1 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? 127.88 N Submit 5) What is the distance the upper spring is extended from its unstretched length? 85.1429 cm Submit 6) Finally, the elevator is moving downward with a velocity of v = -2.8 m/s and also accelerating downward at an acceleration of a = -2.6 m/s2. The elevator is: speeding up slowing down moving at a constant speed Submit 7) Rank the distances the springs are extended from their unstretched lengths: x1 = x2 = x3 x1 > x2 > x3 x1 < x2 < x3 Submit 8) What is the distance the MIDDLE spring is extended from its unstretched length?

all of the numbers are right I cant figure out 8

Explanation / Answer

Given,

m1 = 4.6 kg ; x = 10 cm = 0.1 m

1) let k be the soring constant.

F = mg = kx

k = mg/x = 4.6 x 9.8 / 0.1 = 450.8 N/m

Hence, k = 450.8 N/m

2)m2 = 13.8 kg ; m3 = 9.2 kg

M = m1 + m2 + m3 = 13.8 + 9.2 + 4.6 = 27.6 kg

force that top spring would be exterting is equal to that of gravity but in opposire direction to balance.

F = M g = 27.6 x 9.8 = 270.48 N

F = 270.48 N

3)Let this be x1.

lower spring is supporting only m3.

F = kx1 = m3g

x1 = m3g/k = 9.2 x 9.8 / 450.8 = 0.2 m = 20 cm

Hence, x1 = 20 cm

4)v = -2.2 m/s ; a = 4.1 m/s2

When its moving down with an upwards acc. net force will be:

F(bottom) = m3 ( g + a) = 9.2 x (9.8 + 4.1) = 127.88 N

Hence, F(bottom) = 127.88 N

5)The net force on upper spring will be;

F(net) = kx2 = M (g + a)

x2 = M (g +a ) / k = 27.6 x (9.8 + 4.1) / 450.8 = 0.851 m = 85.1 cm

Hence, x2 = 85.1 cm

6) v = -2.8 m/s ; a = -2.6 m/s2

slowing down at constant speed.

7)x1 = x2 = x3 x1 > x2 > x3 x1 < x2 < x3

8)middle string is supporting just m2 and m3

So, M = m2 + m3 = 13.8 + 9.2 = 23 kg

F = k x3 = M (g + a)

x3 = M(g +a )/ k = 23 (9.8 + 4.1) / 450.8 = 0.71 m = 71 cm

Hence, x3 = 71 cm

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