A 1.0-kg ball on the end of a string is whirled at a constant speed of 2.0 m/s in a horizontal circle of radius 1.5 m. What is the work done by the centripetal force during one revolution?
I did:
F=m(v^2)/r
F=1(2^2)/1.5=2.7 J
The answer that was provided was 0. Can someone explain the reasoning? Thanks
The object has no displacement during that time, therefore no work is done. Plus the ball traveled at a constant speed which makes the accleration zero, the force zero, and the work zero.
There is no displacement in the direction of the force.
work=force * displacement in the direction of the force.
If you look at the final displacement after a full revolution, it will be back where it started. Since work is Force dot Displacement, since displacement is zero, so is work.
It seems to me that centripetal force is directed inward, but the direction of travel is tangent to the circle. How can a force ninety degrees to travel do any work?
Work is transferred, not made.
Well, well, well, it seems we have a little confusion here about the work done by the centripetal force. Let me shed some light on this with a little humor.
You see, the centripetal force is quite the comedian. It likes to play tricks on us when it comes to work. In this case, the centripetal force is actually a sneaky little fella, as it doesn't do any work at all! That's right, zero work, nada, zip, zilch!
You might be wondering, "Why is that, Clown Bot?" Well, the centripetal force is always perpendicular to the displacement of the object it's acting on. And as you may recall, in order for work to be done, there needs to be a component of force in the direction of the displacement.
In this scenario, the ball is moving in a circle, so its displacement is always perpendicular to the force acting on it. As a result, no work is being done by the centripetal force. It's just having a grand old time making the ball go round and round without breaking a sweat!
So, even though you calculated a value for the centripetal force, it doesn't actually represent the work done. The work done in this particular case is indeed zero. Trust me, the centripetal force is one tricky joker!
To determine the work done by the centripetal force during one revolution, we need to understand the nature of centripetal force and how it affects the work done.
Centripetal force is the force that keeps an object moving in a circular path. It always acts towards the center of the circle and is responsible for pulling the object inwards, preventing it from moving in a straight line. In this case, the centripetal force acting on the ball is provided by the tension in the string.
When an object moves in a circular path at a constant speed, the net work done on the object is zero. This is because work is defined as the dot product of force and displacement. In the case of circular motion, the force is always perpendicular to the displacement, causing the dot product to be zero.
In this scenario, as the ball goes around the circular path, the centripetal force is perpendicular to the displacement of the ball at each point. This means that the work done by the centripetal force is zero for each infinitesimal displacement during the revolution. As a result, the total work done by the centripetal force over the entire revolution is also zero.
Therefore, the correct answer is 0 J, not 2.7 J.
It's important to note that while centripetal force does not do any work on the object, it still provides the necessary force to keep the object moving in a circular path. Work is only done when the force and the displacement have components in the same direction. In the case of circular motion, the force and displacement are always orthogonal (perpendicular) to each other, resulting in no work done by the centripetal force.