A 56-kg rollerblader skates across a skating rink floor. The graph below shows the net external force component F cos è along the displacement as a function of the magnitude of the displacement d. Determine the Following:

(a) work done by the net force component F cos è acting on the rollerblader as he moves from 0 to 5.0 m


(b) work done by the net force component F cos è acting on the rollerblader from 5.0 m to 10.0 m

Unfortunately, I cannot see the graph you are referring to. However, I can still provide the formulas and general approach to solve problems like these.

The work done by a force is given by the equation:

W = F * d * cos(θ)

Here, W is the work done, F is the force, d is the displacement, and θ is the angle between the force and displacement vectors. Since the graph already provides F * cos(θ), all that is required is to find the area under the curve of this graph within the desired displacement range.

(a) To find the work done by the net force component F * cos(θ) acting on the rollerblader as he moves from 0 to 5.0 m, you need to find the area under the curve of the graph from 0 to 5.0 m. You can do this by approximating with rectangles, trapezoids, or by using calculus, depending on the shape of the curve.

(b) Similarly, to find the work done by the net force component F * cos(θ) acting on the rollerblader from 5.0 m to 10.0 m, you need to find the area under the curve of the graph from 5.0 m to 10.0 m. Again, you can do this by approximating with rectangles, trapezoids, or by using calculus, depending on the shape of the curve.

To determine the work done by the net force component F cos è, we need to calculate the area under the graph.

(a) To find the work done by the net force component F cos è as the rollerblader moves from 0 to 5.0 m, we need to find the area under the graph between these two points.

To do this, we calculate the area of the rectangle formed by the graph and the displacement axis between 0 and 5.0 m. The height of the rectangle is F cos è, and the width is 5.0 m since the rollerblader moved a distance of 5.0 m.

Work done = force × displacement = (F cos è) × (5.0 m) = 5(F cos è) Joules.

(b) To find the work done by the net force component F cos è as the rollerblader moves from 5.0 m to 10.0 m, we need to find the area under the graph between these two points.

To do this, we calculate the area of the triangle formed by the graph and the displacement axis between 5.0 m and 10.0 m. The height of the triangle is the difference in F cos è between 5.0 m and 10.0 m. The width is 5.0 m since the rollerblader moved a distance of 5.0 m.

Work done = 0.5 × base × height = 0.5 × 5.0 m × (F cos è) = 2.5(F cos è) Joules.

So, the work done by the net force component F cos è for (a) is 5(F cos è) Joules, and for (b) is 2.5(F cos è) Joules.

To determine the work done by the net force component F cos è on the rollerblader as he moves from 0 to 5.0 m and from 5.0 m to 10.0 m, you need to calculate the area under the graph for each section separately.

(a) Work done from 0 to 5.0 m:
To calculate the work done, you need to find the area under the graph from 0 to 5.0 m.
Since the graph represents the net external force component F cos è along the displacement d, the area under the graph represents the work done.
In this case, the graph seems to be a triangle. To calculate the area of a triangle, you need to multiply the base by the height and divide by 2.

To find the base:
The base is the displacement from 0 to 5.0 m, which is 5.0 m.

To find the height:
The height is the net external force component F cos è at 5.0 m.

So, multiply the base (5.0 m) by the height (F cos è at 5.0 m) and divide by 2 to calculate the work done from 0 to 5.0 m.

(b) Work done from 5.0 m to 10.0 m:
Similarly, to calculate the work done from 5.0 m to 10.0 m, you need to find the area under the graph for that interval.
The graph shows a constant net external force component F cos è during this interval, which means the graph represents a rectangle.

To calculate the area of a rectangle, you need to multiply the base by the height.
In this case, the base is the displacement from 5.0 m to 10.0 m, which is 5.0 m.
The height is the net external force component F cos è during this interval.

Multiply the base (5.0 m) by the height (net external force component F cos è during this interval) to calculate the work done from 5.0 m to 10.0 m.