A single mass m1 = 3.2 kg hangs from a spring in a motionless elevator. The spring is extended x = 13 cm from its un stretched length.

Question

A single mass m₁ = 3.2 kg hangs from a spring in a motionless elevator. The spring is extended x = 13 cm from its un stretched length.

1)

What is the spring constant of the spring?

 

2)

Now, three masses m₁ = 3.2 kg, m₂ = 9.6 kg and m₃ = 6.4 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?

3)

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

 

4)

Now the elevator is moving downward with a velocity of v = -3.9 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?

5)

What is the distance the upper spring is extended from its un stretched length?

6)

Finally, the elevator is moving downward with a velocity of v = -3.6 m/s and also accelerating downward at an acceleration of a = -1.9 m/s².The elevator is: (choose one)

speeding up

slowing down

moving at a constant speed

7)

Rank the distances the springs are extended from their un stretched lengths:(choose one)

x₁ = x₂ = x₃

x₁ > x₂ > x₃

x₁ < x₂ < x₃

8)

What is the distance the MIDDLE spring is extended from its un stretched length?

Answer 1

1) m₁g = kx, so k = m₁g/x = 3.2kg·9.81 m/s²/013 m = 241.48 N/m

3) T₁ - T₂ - m₁g = 0; T₂ - T₃ - m₂g = 0; T₃ - m₃g = 0

If we add these equations we get: T₁ = (m₁ + m₂ + m₃)g = (3.2 kg + 9.6 kg + 6.4 kg)·9.81 m/s² = 188.35 N

4) m₃g - T₃ = m₃a; T₃ = m₃(g - a) = 6.4 kg(9.8 + 4.4) m/s² = 90.88 N

5) T₁ = kx₁, x₁ = T₁/k = 188,35/241.48 = .78 m if elevator in rest.

6) slowing down

7) x₁ > x₂ > x₃ because T₁ > T₂ > T₃