A single mass m 1 = 3.5 kg hangs from a spring in a motionless elevator. The spr

Question

A single mass m1 = 3.5 kg hangs from a spring in a motionless elevator. The spring is extended x = 15 cm from its unstretched length.

1)What is the spring constant of the spring?

Now, three masses m1 = 3.5 kg, m2 = 10.5 kg and m3 = 7 kg hang from three identical springs in a motionless elevator. The springs all have the same spring constant that you just calculated above.

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

Now the elevator is moving downward with a velocity of v = -2.9 m/s but accelerating upward with an acceleration of a = 3.7 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)

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

Finally, the elevator is moving downward with a velocity of v = -3.3 m/s and also accelerating downward at an acceleration of a = -1.9 m/s2.

4) is the elevator speeding up or slowind down?

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

Explanation / Answer

1) A weight of 3.5 kg hangs from a spring. Let the spring constant be k. The equation is m1g = kx, where m1 is is the mass hanging, g is acceleration due to gravity, k is the spring constant and x is the legth by which the spring elongates.

Then 3.5 x 9.8 = k x 0.15 . This gives k = 3.5 x 9.8 / 0.15 = 228.67 N/m......................Ans

2) Now three springs hang one below the other, supporting masses 3.5,10.5 and 7 kg respectively.

The top spring counteracts the total downward pull of all the three masses, so it must be exerting an upward force of (3.5+10.5+7) x g = 21 x 9.8 = 205.8 N...................................Ans

3) As the lift is slowing down at the rate of 3.7 m/s2, there must be a force acting in the opposite direction of gravity because of this deceleration, that means in the same direction as the spring force acting on the third mass. So these two forces are additive. The third mass is 7 kg and the value of acceleration due to gravity is 9.8 m/s2

So the force exerted by the bottom spring on the on the bottom mass = 7(3.7 +9.8) = 94.5 N...........Ans

4) Finally as the elevator is moving downward and also accelerates downward, the reaction due to gravitational acceleration works upwards and reaction due to deceleration is in the opposite direction. So the elevator is speeding up.................Ans

5) Force, F acting on the middle spring in this condition counteracts the gravitational pull on second and third mass and also counteracts the force of deceleration = (10.5 + 7) x (9.8 +1.9) = 204.75 N

The spring will stretch to an extent of F/k = 204.75/228.67 = 0.895 m = 89.5 cm.................................Ans

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