the graph of a force function (in newtons) is given. how much work is done by the force in moving an object…
the graph of a force function (in newtons) is given. how much work is done by the force in moving an object 10 m? the amount of work done by the force in moving an object 10 m is j. (type a whole number.)
Answer
Explanation:
Step1: Recall work - force formula
Work (W=\int_{a}^{b}F(x)dx). Geometrically, it is the area under the force - displacement graph.
Step2: Divide the graph into shapes
The graph from (x = 0) to (x=2) is a triangle and from (x = 2) to (x = 10) is a trapezoid. For the triangle from (x=0) to (x = 2): The base (b_1=2) and height (h_1 = 12). The area of the triangle (A_1=\frac{1}{2}\times b_1\times h_1=\frac{1}{2}\times2\times12 = 12). For the trapezoid from (x = 2) to (x=10): The lengths of the parallel sides are (a = 12) and (b=8), and the height (h_2=8). The area of a trapezoid (A_2=\frac{(a + b)h_2}{2}=\frac{(12 + 8)\times8}{2}=80).
Step3: Calculate total work
The total work (W=A_1+A_2). (W=12 + 80=92).
Answer:
92