Now, three masses m 1 = 4.2 kg, m 2 = 12.6 kg and m 3 = 8.4 kg hang from three i

Question

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.

Computed value:

246.9

3)

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

cm

Your submissions:

0.26

4)

Now the elevator is moving downward with a velocity of v = -2.9 m/s but accelerating upward with an acceleration of a = 4.3 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?

N

5)

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

cm

6)

Finally, the elevator is moving downward with a velocity of v = -2.6 m/s and also accelerating downward at an acceleration of a = -1.9 m/s2.

The elevator is:

speeding up

slowing down

moving at a constant speed

7)

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

x1 = x2 = x3

x1 > x2 > x3

x1 < x2 < x3

Explanation / Answer

Solution:

3) The strtch of the spring when m1 alone is hanging = x1 = m1g/k = (4.2)(9.8)/(246.9 = 0.167 m

For the lower spring , the gravity force= m3g = (8.4)(9.8) =82.32N

x3 = 82.32/246.9 = 0.33 m

The total extention of the lower spring = 0.167 + 0.33 3= 0.50m = 50 cm

4) The force exerted by the bottom spring on the bottom mass = m3 (g+a) (8.4)(9.8+4.3) = 118.4 N

5) The total extension of the upper spring = x1 = (m1g+m2g+m3g)/k

=(4.2+12.6+8.4) (9.8)/(246.9) = 1 m = 100cm

6) The elecvator is speeding up since the velocity and acceleration ar ein the same direction.

7) The ranking is x1<x2<x3 ( top < middle < bottom)

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