A 0.800-kg ball is tied to the end of a string 1.60 m long...

Name: Problem 9, Chapter 6: University Physics with Modern Physics
Uploaded: 2021-06-07T04:52:08-08:00
Duration: 3 min 11 s
Channel: Sheh Lit Chang
Description: A 0.800-kg ball is tied to the end of a string 1.60 m long and swung in a vertical circle. (a) During one complete circle, starting anywhere, calculate the total work done on the ball by (i) the tension in the string and (ii) gravity. (b) Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path.

A 0.800-kg ball is tied to the end of a string 1.60 m long and swung in a vertical circle. (a) During one complete circle, starting anywhere, calculate the total work done on the ball by (i) the tension in the string and (ii) gravity. (b) Repeat part (a) for motion along the semicircle from the lowest to the highest point on the path.

Key Concepts

Work

Work refers to the energy transferred by a force acting over a displacement; mathematically defined as the dot product of force and displacement vectors. In circular motion, calculating the work done by forces requires considering both the magnitude and direction of the force relative to the instantaneous displacement along the path.

Tension in Circular Motion

In vertical circular motion, the tension force in the string always acts radially towards the center of the circle and is perpendicular to the tangential displacement of the moving object. This perpendicularity means that the tension does no work because the dot product of two perpendicular vectors is zero.

Potential Energy

Potential energy in the context of gravity is the energy stored due to an object’s position relative to a reference height. The difference in gravitational potential energy between two positions represents the work done by gravity during the displacement, which is central to analyzing energy changes in vertical circular motion.

Gravitational Force

Gravity is a conservative force that acts vertically downwards. The work done by gravity is directly related to the vertical displacement of the object. In problems involving vertical circles, the change in gravitational potential energy between the highest and lowest points can be used to determine the work done by gravity, exploiting the property that work done by conservative forces is path-independent.

Transcript

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