What happens to centripetal force when speed decreases, in the special case that the object continues moving in a circle of the same radius?
A) The radius cannot stay the same.
B) The force also decreases.
C) The force increases.
D) Speed does not affect centripetal force.
E) The force sometimes stays the same and sometimes decreases.
m v^2/r
v less --> force less
To answer this question, we need to understand the concept of centripetal force and how it relates to the motion of objects in a circular path.
Centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of that circle. In other words, it is the inward force that keeps an object in circular motion. This force is always perpendicular to the velocity of the object and acts in the same plane as the circular path.
Now, let's consider the given special case – an object continues moving in a circle of the same radius, but with a decreased speed. In this scenario, we have to determine what happens to the centripetal force.
To solve this, we can use the equation for centripetal force:
F = (mv²) / r
Where:
F = Centripetal force
m = Mass of the object
v = Velocity of the object
r = Radius of the circular path
In this case, we are specifically looking at what happens to the centripetal force when the object's speed decreases while keeping the radius constant.
When the speed of the object decreases, the numerator of the centripetal force equation (mv²) becomes smaller. This means that the force is directly proportional to the square of the speed. Therefore, if the speed decreases, the force will also decrease. This leads us to option B) The force also decreases.
Hence, the correct answer choice is B) The force also decreases.