Figure 4. How to correctly measure the siba.. weight hanger carries the required added masses. M₁² (8) = 16,55 Msw (8) Table # 1: Determination of the spring constant K g= 9.80 m/s² xo (cm) = 50 100 150 200 250 MT = Mh + Msw MT (8) MT (kg) F=W=Mrg F (N) 0 xf (cm) 0.6517 1.1417 6.6.5, 0.066.5 1/6:52 0.11 6.5 166.5 0.78 6.5 1.63/7 216.2 0.2165 21217 266,55 02. 266.5 2.6117 Average force constant Kavg Force constant Ktren from the slope of the trendline in the graph % relative difference between Kavg and Ktren Mh: Mass of the weight hanger Msw: Mass of added slotted weights MT: Total Mass W: Weight of hanger plus slotted weights 1₁7 3.3 X = Xf- Xo 4.9 6.9 8 x (cm) X (m) 0 K= the F(N) x(m) K (N/m) 0.2 0.1 6/5/168 2.5ch 0.025 45.068 4on 0.09 40,7925 55 0.055 38.576 36 36 4 7.2 0.072 36.9936|||| Xo: Position of the spring's bottom (unstretched) xf Position of the spring's bottom (stretched) x: Elongation of the spring K: Force constant of the spring

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How to find the average force constant kavg and will this apply to the others on the bottom 

### Determination of the Spring Constant K

**Average force constant $K_{avg}$:**  
$K_{avg} = 1.85$

#### Table #1: Determination of the Spring Constant K

\[ g = 9.80 \, \text{m/s}^2 \]

**Explanation of Variables and Columns:**  
**$M_{sh}$:** Mass of the slotted hanger  
**$M_{th}$:** Mass of the total hanger  
**$M_{sw}$:** Mass of the added slotted weights  
**$Mt (kg)$:** Total Mass (Mt = M_{th} + M_{sw})  
**F (N):** Force (F = W = Mt \cdot g)  
**$x_0 (cm) $:** Position of the spring's bottom (unstretched)  
**$x (cn):$** Position of the spring's bottom (stretched)  
**$X_f:$** Elongation of the spring ($X_f = x - x_0$)  
**K (N/m):** Force constant of the spring (K = F/X_f)

| $ M_{sw} $ (g) | $ M_{sw} $ (kg) | $ M_{t} $ (Kg) | F (N) | $x_0$ (cm) | x (cm) | $ X_f $ (m) | K (N/m) |
|----------------|----------------|---------------|-------|------------|--------|-------------|---------|
| 0              | 0              | 0.0655        | 0.64  | 50         | 50     | 0           | -       |
| 50             | 0.05           | 0.1155        | 1.13  | 50         | 55     | 0.050       | 22.6    |
| 100            | 0.1            | 0.1655        | 1.62  | 50         | 65     | 0.060       | 26.7    |
| 150            | 0.15           | 0.2155        | 2.11  | 50         | 70     | 0.070       | 29.7    |
| 200            | 0.2            | 0
Transcribed Image Text:### Determination of the Spring Constant K **Average force constant $K_{avg}$:** $K_{avg} = 1.85$ #### Table #1: Determination of the Spring Constant K \[ g = 9.80 \, \text{m/s}^2 \] **Explanation of Variables and Columns:** **$M_{sh}$:** Mass of the slotted hanger **$M_{th}$:** Mass of the total hanger **$M_{sw}$:** Mass of the added slotted weights **$Mt (kg)$:** Total Mass (Mt = M_{th} + M_{sw}) **F (N):** Force (F = W = Mt \cdot g) **$x_0 (cm) $:** Position of the spring's bottom (unstretched) **$x (cn):$** Position of the spring's bottom (stretched) **$X_f:$** Elongation of the spring ($X_f = x - x_0$) **K (N/m):** Force constant of the spring (K = F/X_f) | $ M_{sw} $ (g) | $ M_{sw} $ (kg) | $ M_{t} $ (Kg) | F (N) | $x_0$ (cm) | x (cm) | $ X_f $ (m) | K (N/m) | |----------------|----------------|---------------|-------|------------|--------|-------------|---------| | 0 | 0 | 0.0655 | 0.64 | 50 | 50 | 0 | - | | 50 | 0.05 | 0.1155 | 1.13 | 50 | 55 | 0.050 | 22.6 | | 100 | 0.1 | 0.1655 | 1.62 | 50 | 65 | 0.060 | 26.7 | | 150 | 0.15 | 0.2155 | 2.11 | 50 | 70 | 0.070 | 29.7 | | 200 | 0.2 | 0
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