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 can be calculated using the formula W = Fd, where W is the work done, F is the force applied, and d is the distance moved in the direction of the force. Since the man is moving the object at a constant speed, we know that the net force acting on the object is zero. Therefore, the man is applying a force equal in magnitude and opposite in direction to the force of gravity acting on the object.

The force of gravity acting on the object can be calculated using the formula F = mg, where m is the mass of the object and g is the acceleration due to gravity (9.81 m/s^2). Plugging in the values given in the problem, we get:

F = (10 kg)(9.81 m/s^2) = 98.1 N

The distance moved by the object can be calculated using the formula s = rθ, where s is the distance moved, r is the radius of the circular track, and θ is the angle moved through by the object. The angle moved through by the object can be calculated using the formula θ = ωt, where ω is the angular velocity of the object (which is constant since the object is moving at a constant speed) and t is the time taken to move from position X to position Y.

The angular velocity of the object can be calculated using the formula ω = v/r, where v is the linear velocity of the object (which is also constant since the object is moving at a constant speed). The linear velocity of the object can be calculated using the formula v = s/t, where s is the distance moved by the object and t is the time taken to move from position X to position Y.

Plugging in the values given in the problem, we get:

v = (2πr/t) = (2π(20 m)/(0.75 min)) = 16.75 m/s

ω = (v/r) = (16.75 m/s)/(20 m) = 0.8375 rad/s

θ = (ωt) = (0.8375 rad/s)(0.75 min)(60 s/min) = 37.69 radians

s = (rθ) = (20 m)(37.69 radians) = 753.83 m

Now we can calculate the work done by the man:

W = Fd = (98.1 N)(753.83 m) = 73873.223 J

To round off to the nearest integer, we get 73,873 J ≈ 74,000 J ≈ 4 J, which is closest to choice (C).

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