A man moves the 10-g object shown in a vertical plane at a constant speed from position X to position Y along a circular track of radius 20 m.The process takes 0.75 min.The work done by the man is about:

Question

Quizplus · Accepted Answer

The work done by the man is given by the formula:

Work = Force * Distance * cos(theta)

Since the object is moved at a constant speed, we know that the net force acting on it is zero. Therefore, the work done by the man must be equal and opposite to the work done by gravity:

Work = - mgh

where m is the mass of the object, h is the vertical height through which it is lifted, and g is the acceleration due to gravity.

In this case, the object is being moved in a circular path, so the distance it moves is equal to the circumference of the circle:

Distance = 2*pi*r = 2*pi*20 = 125.6 m

The vertical height through which the object is lifted can be calculated using the Pythagorean theorem:

h^2 = r^2 - d^2/4

where d is the distance between positions X and Y.

d = v*t = (125.6 m/0.75 min) * (1 min/60 s) = 2.093 m

h^2 = 20^2 - (2.093)^2/4 = 395.53

h = 19.89 m

Finally, we can calculate the work done by the man:

Work = - mgh = -(10 kg)(9.8 m/s^2)(19.89 m) = -1960.2 J

Note that the work done by the man is negative because he is doing work against the force of gravity, which is acting in the opposite direction. Therefore, the correct answer is:

Choice C) 4 J (rounded to one significant figure)

A Man Moves the 10-G Object Shown in a Vertical