A net external force is applied to a 13 kg object that is initially at rest. The graph to the left shows net force component along the displacement of the object as it varies with displacement.
1) What is the work done between 0 m and 4 m?
2. What is the work done between 0 m and 13 m?
Work =
3. What is the speed of the object at 13 m?
vf =
To find the answers to these questions, we need to use the work-energy theorem and the concept of net force.
1) To find the work done between 0 m and 4 m, we need to calculate the area under the graph between these two points. The area under a force vs. displacement graph represents the work done. In this case, since the graph is not provided, we cannot directly calculate the area. However, if you have a numerical representation or equation of the graph, you can integrate that equation between the limits of 0 m and 4 m to find the work done.
2) Similarly, to find the work done between 0 m and 13 m, you would calculate the area under the graph between these two points. Again, this would require the graph or a numerical representation of the force vs. displacement relationship.
Work = Area under the force vs. displacement graph.
3) To find the speed of the object at 13 m, we can use the work-energy theorem. According to the work-energy theorem, the work done on the object is equal to its change in kinetic energy.
Mathematically, the work done (W) can be expressed as the product of force (F) and displacement (d) along with the cosine of the angle between the force and the displacement vectors.
W = F * d * cos(theta)
Since the object is initially at rest, the initial kinetic energy (Ki) is zero. Therefore, the work done (W) between 0 m and 13 m is equal to the final kinetic energy (Kf).
So, we need to calculate the work done on the object between 0 m and 13 m and equate it to the final kinetic energy to find the speed (vf).
Work = Change in kinetic energy
Please provide the values of the net force at different points or the equation of the force vs. displacement graph to proceed with the calculations.