Question

the speed in case a is three times that of case b. the circles radius in case a is twice that of case b. the object mass is the same in each case. how does the net force in case a compare to the net force in case b?

case a

3 - v, m

2 - r

case b

v, m

r

the net force in case a is...

tap to select answer.

... the net force of case b.

Explanation:

Step1: Recall the formula for centripetal force

The centripetal force formula is \( F=\frac{mv^{2}}{r} \).

Step2: Calculate the centripetal force for Case A

For Case A, \( v = 3v\), \(r=2R\), and \(m = m\). Substitute into the formula: \( F_{A}=\frac{m(3v)^{2}}{2R}=\frac{9mv^{2}}{2R} \).

Step3: Calculate the centripetal force for Case B

For Case B, \( v = v\), \(r = R\), and \(m = m\). Substitute into the formula: \( F_{B}=\frac{mv^{2}}{R} \).

Step4: Find the ratio of \(F_{A}\) to \(F_{B}\)

\(\frac{F_{A}}{F_{B}}=\frac{\frac{9mv^{2}}{2R}}{\frac{mv^{2}}{R}}=\frac{9}{2} = 4.5\)

Answer:

The net force in Case A is \(4.5\) times the net force in Case B.