Respuesta :
A centripetal force f is applied to an answer moving at a constant speed v in a horizontal circle of radius r. if the same force is applied, but the radius is halved, Both the frequency f and velocity or speed v of the eraser will increase.
What is the centripetal force in circular motion?
The centripetal force acting on a mass in circular motion is given by equation,
Fc = mv² /r
where,
m is the mass of the object,
r is radius of the circle.
From the above equation, we see that the centripetal force is directly proportional to the square of the velocity and inversely proportional to the radius of the circular path.
However, according to the problem, the force is constant while the radius and the velocity changes. Therefore we can write the following equation,
mv₁² / r₁ = mv₂²/r₂
Also recall that m is constant so it cancels out from both sides of the above equation. Therefore from equation we can write the following;
v₂ = [tex]\sqrt{\frac{v1^{2}r1 }{r2} }[/tex]
By observing equation carefully, the ratio r2/r1 will with the square root increase v1 since r2 is lesser than r1.
Hence by implication, the value of v2 will be greater than v1.
As the radius changes from r1 to r2, the velocity also changes from v1 to v2 .
When the radius reduces, the circumference of the circular path becomes smaller which means that more number of revolutions can be made per unit time as long as the force is kept constant; this is an increase in frequency.
Learn more about the centripetal force,
https://brainly.com/question/14249440
#SPJ1
