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
To determine what happens to centripetal force when speed decreases in the special case that the object continues moving in a circle of the same radius, we can examine the formula for centripetal force. Centripetal force is given by the equation:
Fc = (mv^2) / r
where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circle.
In this scenario, we are given that the radius remains the same. So, let's consider the factors that affect centripetal force:
1. Mass (m): If the mass of the object remains unchanged, it will not affect the centripetal force.
2. Velocity (v): In the given scenario, the speed (magnitude of velocity) is decreasing. As v decreases, the square of the velocity (v^2) will also decrease.
3. Radius (r): We are told that the radius remains the same, so it does not affect the centripetal force.
From the equation Fc = (mv^2) / r, we can conclude that if the speed (v) decreases, the centripetal force (Fc) will also decrease. Therefore, the correct answer is option B) The force also decreases.