A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end.The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball.As the ball swings from its lowest point to its highest point
A) the work done on it by gravity and the work done on it by the tension in the string are both equal to -118 J.
B) the work done on it by gravity is -118 J and the work done on it by the tension in the string is +118 J.
C) the work done on it by gravity is +118 J and the work done on it by the tension in the string is -118 J.
D) the work done on it by gravity is -118 J and the work done on it by the tension in the string is zero.
E) the work done on it by gravity and the work done on it by the tension in the string are both equal to zero.

Question

Quizplus · Accepted Answer

The work done by gravity can be calculated using the formula $W = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $h$ is the height change, which is $2.00 m$ in this case. Thus, $W = 3.00 \times 9.8 \times 2.00 = 58.8 \times 2 = 117.6 J$, which rounds to $-118 J$ when considering the direction (upward against gravity). The tension in the string does no work because it acts perpendicular to the displacement of the ball at all points in its path, meaning the force vector of tension and the displacement vector are orthogonal, resulting in zero work done by tension.

A 300-Kg Ball Swings Rapidly in a Complete Vertical Circle of of Radius