2000000000 2. An object of mass 1.50 kg and density 3500 kg/m is completely submerged under oil and in a static equilibrium hanging from a spring (k 150 N/m) that is fixed from the top as shown in the figure. (The density of oil is 920 kg/m®). a) Draw a free body diagram for the suspended object. P. b) Derive the algebraic expression for the stretched distance in the spring. c) Calculate the stretched distance in the spring.

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## Problem Statement

An object of mass 150 kg and density 3600 kg/m³ is completely submerged under oil and in static equilibrium, hanging from a spring (k = 150 N/m) that is fixed from the top as shown in the figure. The density of oil is 920 kg/m³.

### Tasks:

a) Draw a free body diagram for the suspended object.

b) Derive the algebraic expression for the stretched distance in the spring.

c) Calculate the stretched distance in the spring.

---

### Diagram Description:

The diagram shows a container partially filled with oil. Inside the container, a spring is suspended from the top. The spring is attached to a spherical object submerged in the oil. Arrows indicate forces acting on the object. The force of gravity (mg) is acting downward, and a buoyant force (\(F_b\)) is acting upward.

### Given Calculation:

- \(F_b\) (Buoyant force) and \(mg\) (Gravitational force) need to be considered in equilibrium.
- The spring constant, \(k\), is 150 N/m.
- A calculation using the formula \( k = \frac {2(0.5)(9.8)(6.945) - (6.145)}{0.002} \) is provided. The derived equilibrium constant \(k\) comes out to be approximately 0.002.

Additional calculations and derivations are handwritten beside the problem.
Transcribed Image Text:## Problem Statement An object of mass 150 kg and density 3600 kg/m³ is completely submerged under oil and in static equilibrium, hanging from a spring (k = 150 N/m) that is fixed from the top as shown in the figure. The density of oil is 920 kg/m³. ### Tasks: a) Draw a free body diagram for the suspended object. b) Derive the algebraic expression for the stretched distance in the spring. c) Calculate the stretched distance in the spring. --- ### Diagram Description: The diagram shows a container partially filled with oil. Inside the container, a spring is suspended from the top. The spring is attached to a spherical object submerged in the oil. Arrows indicate forces acting on the object. The force of gravity (mg) is acting downward, and a buoyant force (\(F_b\)) is acting upward. ### Given Calculation: - \(F_b\) (Buoyant force) and \(mg\) (Gravitational force) need to be considered in equilibrium. - The spring constant, \(k\), is 150 N/m. - A calculation using the formula \( k = \frac {2(0.5)(9.8)(6.945) - (6.145)}{0.002} \) is provided. The derived equilibrium constant \(k\) comes out to be approximately 0.002. Additional calculations and derivations are handwritten beside the problem.
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