As Newton showed, gravity is a force that acts along the line separating two bodies and causes the two bodies to be attracted to each other (i.e. it is a central force). In this problem, assume that the planetary orbits about the Sun are circular.
a. Does the force of gravity from the Sun do work on a planet in orbit about the Sun? Why or why not?
b. What does your answer to the previous part of this problem mean for the speed of the planet as it moves about the Sun? What about its velocity?
I will be happy to critique your work , when shown any.
a horizontal force of 8.0 N is used to pull a 20-N wooden box moving toward the right along a horizontal,wood surface,as shown.The diagram below shows the vector force acting representing the normal force acting on the box
a. To determine if the force of gravity from the Sun does work on a planet in orbit, we need to consider the definition of work. Work is defined as the product of the force applied on an object and the displacement of that object in the direction of the force. In this case, the force of gravity between the Sun and the planet is always directed towards the center of the circular orbit.
In circular motion, the displacement of an object is always perpendicular to the direction of the force acting on it. For instance, if you tie a weight to a string and swing it around in a circle, the weight moves in a circle while the force exerted by the string is directed towards the center of the circle.
Since the displacement is perpendicular to the force, the angle between them is 90 degrees. According to the definition of work, the work done by a force is zero when the angle between the force and displacement is 90 degrees. Therefore, in the case of a planet in circular orbit around the Sun, the force of gravity from the Sun does not do work on the planet.
b. Since the force of gravity from the Sun does no work on the planet, this means that the planet's total mechanical energy remains constant throughout its orbit. In other words, the planet's total energy, which is the sum of its kinetic energy and gravitational potential energy, remains the same.
The speed of the planet as it moves around the Sun remains constant because the gravitational force does not change its kinetic energy. This means that the planet's speed is constant at every point in its circular orbit.
However, the velocity of the planet is not constant. Velocity is a vector quantity that includes both speed and direction. While the planet's speed remains constant, its direction continuously changes as it moves in a circular path. Therefore, the planet's velocity is changing at every instant in its orbit.