Question

13 0/2 points multiple choice find the change in energy based on the following graph force (n) 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 distance (m) 30 joules 36 joules 0 joules 6 joules

Explanation:

Step1: Analyze the graph structure

The graph of force vs. distance can be divided into three parts: a triangle (from \(x = 0\) to \(x = 6\)), a rectangle (from \(x = 6\) to \(x = 8\)), and a triangle (from \(x = 8\) to \(x = 10\)). But actually, the area under the force - distance graph gives the work done (which is equal to the change in energy, \(W=\Delta E\)). The formula for the area of a trapezoid (or we can break it into simpler shapes: triangle, rectangle, triangle).

First, for the first part (from \(x = 0\) to \(x = 6\)): it's a triangle with base \(b_1=6\ m\) and height \(h_1 = 6\ N\). The area of a triangle is \(A_1=\frac{1}{2}\times b_1\times h_1\).

Step2: Calculate the area of the first triangle

\(A_1=\frac{1}{2}\times6\times6 = 18\)

Step3: Analyze the second part (from \(x = 6\) to \(x = 8\))

It's a rectangle with length \(l = 8 - 6=2\ m\) and width \(w = 6\ N\). The area of a rectangle is \(A_2=l\times w\)

Step4: Calculate the area of the rectangle

\(A_2 = 2\times6=12\)

Step5: Analyze the third part (from \(x = 8\) to \(x = 10\))

It's a triangle with base \(b_2=10 - 8 = 2\ m\) and height \(h_2=6\ N\) (but since it's a decreasing part, the area is still calculated as a triangle, but we can also think of it as a triangle with base \(2\) and height \(6\)). The area of a triangle is \(A_3=\frac{1}{2}\times b_2\times h_2\)

Step6: Calculate the area of the third triangle

\(A_3=\frac{1}{2}\times2\times6 = 6\)

Step7: Calculate the total area (total work done, change in energy)

The total area \(A=A_1 + A_2+A_3\)
\(A=18 + 12+6=36\) Joules.

Answer:

36 Joules (the correct option is the one with "36 Joules")