At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30$\degree$ above the horizontal?
A)+39 W
B)-78 W
C)-39 W
D)+78 W
E)+25 W

Question

Quizplus · Accepted Answer

The gravitational force on the projectile is given by Fg = mg, where m is the mass of the projectile and g is the acceleration due to gravity. Therefore, Fg = (2.0 kg)(9.81 m/s^2) = 19.62 N.

At an instant when the velocity of the projectile is 4.0 m/s directed 30 degrees above the horizontal, the horizontal component of the velocity is v*cos(30) = (4.0 m/s)cos(30) = 3.46 m/s and the vertical component of the velocity is v*sin(30) = (4.0 m/s)sin(30) = 2.00 m/s.

The work done by the gravitational force is given by W = Fg*d*cos(theta), where d is the distance traveled by the projectile and theta is the angle between the force and the displacement. Since the projectile is moving in a parabolic path, d is changing continuously and is not well-defined at an instant. However, at this instant, the force is acting vertically downward (theta = 90 degrees) and the displacement is vertical as well (d = 0). Therefore, no work is being done by the gravitational force on the projectile at this instant (W = 0), and the rate of work is also zero (P = W/t = 0).

Thus, the only answer choice that is reasonable is C, which is negative and corresponds to the rate of work that would be done by a resisting force that is opposing the motion of the projectile. However, since no such force is mentioned in the problem, we cannot choose any of the answer choices with confidence.

At What Rate Is the Gravitational Force on a 2 °\degree°

At What Rate Is the Gravitational Force on a 2 $\degree$