**Problem Statement:**1. Calculate the work done from $ x = 0 $ to $ x = 7 \, \text{m} $ by the one-dimensional force depicted in the following graph. Suppose that $ F_0 = 68 \, \text{N} $. Calculate the total work by the force over 7 m.**Diagram Explanation:**- The graph is a line graph plotting force ($ F $) against distance ($ x $).- The vertical axis represents force in Newtons (N), ranging from $ F_0 $ to $-F_0$.- The horizontal axis represents distance in meters (m), from $ x = 0 $ to $ x = 7 $.- The graph consists of triangular and trapezoidal sections. Specifically: - From $ x = 0 $ to $ x = 1 $, force increases linearly to $ F_0 $. - From $ x = 1 $ to $ x = 2 $, force decreases linearly back to zero. - From $ x = 2 $ to $ x = 4 $, force decreases linearly to $-F_0$. - From $ x = 4 $ to $ x = 5 $, force increases linearly back to zero. - From $ x = 5 $ to $ x = 6 $, force increases linearly to $ F_0 $. - From $ x = 6 $ to $ x = 7 $, force decreases linearly back to zero.**Calculation:**- Calculate the work done in each section by finding the area under the curve and summing them.- For triangles, use the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.- For trapezoids, use the formula: $\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$.**Total Work $ W $** is computed by summing these areas (considering positive and negative areas where force is above and below the x-axis respectively).Note: Input the calculated total into the provided text field and express your answer in Joules (J

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1. Calculate the work done from x = 0 to x = 7 m by the one-dimensional force depicted in the following graph. Suppose that F = 68 N, calculate the total work by the force over 7 m. Fo HA+A= 3 12 4 6 5 7 -Fo W= √ x (m)

1. Calculate the work done from x = 0 to x = 7 m by the one-dimensional force depicted in the following graph. Suppose that F = 68 N, calculate the total work by the force over 7 m. Fo HA+A= 3 12 4 6 5 7 -Fo W= √ x (m)

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Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Problem Statement:**

1. Calculate the work done from $ x = 0 $ to $ x = 7 \, \text{m} $ by the one-dimensional force depicted in the following graph.

Suppose that $ F_0 = 68 \, \text{N} $. Calculate the total work by the force over 7 m.

**Diagram Explanation:**

- The graph is a line graph plotting force ($ F $) against distance ($ x $).
- The vertical axis represents force in Newtons (N), ranging from $ F_0 $ to $-F_0$.
- The horizontal axis represents distance in meters (m), from $ x = 0 $ to $ x = 7 $.
- The graph consists of triangular and trapezoidal sections.

Specifically:
- From $ x = 0 $ to $ x = 1 $, force increases linearly to $ F_0 $.
- From $ x = 1 $ to $ x = 2 $, force decreases linearly back to zero.
- From $ x = 2 $ to $ x = 4 $, force decreases linearly to $-F_0$.
- From $ x = 4 $ to $ x = 5 $, force increases linearly back to zero.
- From $ x = 5 $ to $ x = 6 $, force increases linearly to $ F_0 $.
- From $ x = 6 $ to $ x = 7 $, force decreases linearly back to zero.

**Calculation:**

- Calculate the work done in each section by finding the area under the curve and summing them.
- For triangles, use the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
- For trapezoids, use the formula: $\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$.

**Total Work $ W $** is computed by summing these areas (considering positive and negative areas where force is above and below the x-axis respectively).

Note: Input the calculated total into the provided text field and express your answer in Joules (J

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