Work in Uniform Circular Motion

[dasrheingold]

Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket ship) traveling in a straight line in space with a constant speed, the only way I can get it to move in a uniform circle would be to have some sort of thruster acting perpendicular to the direction of movement. I am imagining a spaceship and thrusters being continually applied perpendicular to direction of motion. Energy would be depleted as the rocket fuel is used. If I stop using energy, by turning off the motor the ship stops its uniform circular motion and continues in a straight line. It seems energy must be continually expended to maintain uniform circular motion. However, this seems to contradict the accepted answer that no work is done on an object by the force that causes the uniform circular motion. What am I missing?

 

[Dale]

Turning using rockets is 100% inefficient. It uses energy for no change in energy. That is why real space missions use gravity to turn whenever possible.

 

[Andrew Mason]

Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket ship) traveling in a straight line in space with a constant speed, the only way I can get it to move in a uniform circle would be to have some sort of thruster acting perpendicular to the direction of movement. I am imagining a spaceship and thrusters being continually applied perpendicular to direction of motion. Energy would be depleted as the rocket fuel is used. If I stop using energy, by turning off the motor the ship stops its uniform circular motion and continues in a straight line. It seems energy must be continually expended to maintain uniform circular motion. However, this seems to contradict the accepted answer that no work is done on an object by the force that causes the uniform circular motion. What am I missing?

Welcome to PF dasrheingold!

You are forgetting about the mass that you have to eject outward at great speed in order to make the rocket prescribe a circle. Ejecting mass at great speed requires energy. But one does not need to continually eject mass from the system in order to create a force.

If the centripetal force is supplied by another body such that the two bodies prescribe a circle about the centre of mass of the two-body system, no mass leaves the system, no energy is expended and no work is done by either body.

AM

 

[A.T.]

It seems energy must be continually expended to maintain uniform circular motion. However, this seems to contradict the accepted answer that no work is done on an object by the force that causes the uniform circular motion.

A hovering helicopter must continually expend energy to remain a constant altitude. Does this imply that staying at constant altitude, like a book on a table does, requires energy?

 

[PJC01]

Your understanding is correct. In uniform circular motion, the object is moving at a constant speed but changing direction constantly, which requires a force to act perpendicular to the velocity. This force does not do any work on the object because the displacement of the object is always perpendicular to the force, and therefore there is no component of the force parallel to the displacement to do work.

However, in order to maintain this uniform circular motion, a continuous supply of energy is required to keep the thrusters running and applying the necessary force. This energy is being depleted as the rocket fuel is used, but it is not being used to do work on the object. Instead, it is being used to continuously change the direction of the object's motion.

In contrast, in the case of a rocket ship traveling in a straight line at a constant speed, there is no force acting perpendicular to its velocity, so no work is being done on the ship. However, if you were to suddenly apply a perpendicular force to change its direction and make it move in a uniform circular motion, energy would need to be expended to do this work and maintain the motion.

In summary, the concept of work being done by a force only applies when there is a parallel component of the force acting on the displacement of the object. In uniform circular motion, this is not the case, but energy is still required to maintain the motion. This does not contradict the accepted answer, it simply means that the concept of work does not apply in this specific scenario.