A single mass m 1 = 3.7 kg hangs from a spring in a motionless elevator. The spr

Question

A single mass m1 = 3.7 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? ________________N/m

2)

Now, three masses m1 = 3.7 kg, m2 = 11.1 kg and m3 = 7.4 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?______________N

3)What is the distance the lower 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 with 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 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 = -2.2 m/s and also accelerating downward at an acceleration of a = -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?__________________cm

Explanation / Answer

1. as per formula F = Kx ( k= constant)

hence k = F/x = mg/x

k = 9.8*3.7/ 0.1 = 362.6N/m

2. the total force will be addition of all three masses.

hence force will be = (m1+m2+m3)*9.8N

= (3.7+11.1+ 7.4 )*9.8

= 217.56N

3. stretch length of last spring

as, F= Kx

here force is 7.4Kg i.e. weight of only m3

7.4*9.8 = 362.6 * x

hence x= 0.2m

4. as as system is slowing down with downward velocity with acceleration 4.4

hence w = mg-ma

m3 = 7.4

hence force = F = m(g-a)= 7.4 (9.8 - 4.4) = 39.96N

5.the distance the upper spring is extended,

As F=Kx

here F is total weight of all masses

(m1+m2+m3)(g -a) = Kx

(3.7+11.1+ 7.4 ) ( 9.8 - 4.4) = 362.6* x

x = 0.33061224m

x =

6. Ans = A

As both things speed and acceleration are in same direction, its sppeding up

7. Ans = B

as the total weight is being exerted on the upperspring it will stretch more

8. assuming the elevator is stationary

the force on middle spring is addition of lower 2 masses

As, F=Kx

(11.1+ 7.4 )* 9.8 = 362.6*x

x = 0.5m

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