Final answer:
To calculate the work done by nonconservative forces, we need to find the change in potential energy of the object as it moves around the circular path. This can be done by calculating the height of the object above the center of the circle at two different locations, using the equations of motion.
Step-by-step explanation:
To calculate the work done by nonconservative forces as the object moves around the circular path, we need to find the change in mechanical energy. The mechanical energy of the object consists of its kinetic energy and potential energy. Since the object is moving at a constant speed around the circle, there is no change in kinetic energy. Therefore, the work done by nonconservative forces is equal to the change in potential energy.
The potential energy of the object is given by the equation U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point. In this case, we can use the height above the center of the circle as the reference point.
At the first location, the speed of the object is 4.00 m/s. We can find the height of the object above the center of the circle using the equation v^2 = u^2 + 2gh, where u is the initial speed of the object and v is the final speed of the object. Solving for h, we get h = (v^2 - u^2) / (2g).
At the second location, the speed of the object is 3.00 m/s. Using the same equation, we can find the height of the object above the center of the circle at this location.
Finally, the work done by nonconservative forces is equal to the change in potential energy, which is given by the equation ∆U = mg∆h. Substituting the values of mass, acceleration due to gravity, and ∆h, we can calculate the work.