Ice floats on water.
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Answer:
See below ↓
Explanation:
<u>Step 1 : Diagram</u>
- In attachment
<u>Step 2</u>
- We choose the system to be the spring, the block, and the Earth and it is isolated
- We put all the data in the figure we have created and create a zero level (initial height) of the block to be yₓ = 0 and the final position, when it stops and moves upwards again, to be yₙ = -A
- No external forces are exerted on the system and no energy comes in or out of the system
- Hence,
⇒ ΔE = 0
⇒ Eₙ - Eₓ = 0
⇒ Eₙ = Eₓ
⇒ Kₙ + Uₙ + Pₙ = Kₓ + Uₓ + Pₓ
- Final kinetic energy is 0 at the lowest point
⇒ Uₙ + Pₙ = Uₓ + Pₓ
<u>Step 3</u>
- Initial potential energy is 0 [zero level = initial height]
⇒ Uₙ + Pₙ = Uₓ
- And we know that spring was originally at normal length, so initial spring energy is also 0
⇒ Uₙ + Pₙ = 0
⇒ 1/2kxₙ² + mgyₙ = 0
⇒ 1/2kxₙ² = -mgyₙ
- We know xₙ = A and yₙ = -A from the diagram
⇒ 1/2kA² = -mg(-A)
⇒ 1/2kA² = mgA
⇒ [1/2kA = mg]
<u>Step 4</u>
- Spring force is given by : F = -kx
- Note : x = A
⇒ F = kA
⇒ k = F/A
⇒ Plug 'k' into the equation found at the end of Step 3
⇒ 1/2(F/A)(A) = mg
⇒ 2F = mg
⇒ F = 2mg (a)
<u>Step 5</u>
- We know the spring will stop oscillating and be at rest at the new equilibrium position of the system
⇒ F - mg = 0
⇒ F = mg
- We know that :
⇒ F = -kx
- In the case x = yₙ
⇒ kyₙ = mg
⇒ yₙ = mg/k
⇒ yₙ = 0.25 x 9.8 / -10
⇒ yₙ = -0.245 m
⇒ yₙ = A
⇒ yₙ = 0.245 m (b)
<u>Step 6</u>
- v(max) = Aω
- v(max) = A√k/m
- v(max) = 0.245 x √(10/0.25)
- v(max) = 1.55 m/s (c)
