An object of mass m travels halfway around a circle at a constant speed v. The magnitude of the total work done on the object by the net force acting on it (not counting starting and stopping at the beginning and end of the path) is
a. equal to mv
b. equal to 2mv
c equal to mv^2
d. equal to 0
e. equal to 1/2mv^2
If the speed doesn't change, no work is done.
The part about starting and stopping only confuses the question. They say the speed is constant, so forget about stopping and starting processes.
To find the magnitude of the total work done on the object, we need to consider the equation for work done, which is given by:
Work = Force x Distance x Cosine of the angle between the force and displacement
In this case, the object is moving halfway around a circle, which means it is traveling a distance equal to half the circumference of the circle. Given that the object is moving at a constant speed, we can say that there is a net force acting on it continuously, directed towards the center of the circle, providing the necessary centripetal force to keep the object in circular motion.
Now, let's consider the work done by the centripetal force. The angle between the centripetal force and the displacement is 90 degrees since the force is always perpendicular to the displacement. In this case, the cosine of 90 degrees is 0. Therefore, the work done by the centripetal force is zero (Work = Force x Distance x Cos 90 = 0).
Since the question asks for the magnitude of the total work done by the net force (excluding starting and stopping points), we need to consider any additional forces acting on the object besides the centripetal force. However, since we are not given any information about other forces, we assume there are no other forces present in this scenario. Consequently, the net force on the object is also zero, and therefore, the work done by the net force on the object is zero.
Thus, the correct answer is d. equal to 0.