Question

the speed in case a is three times that of case b. the radius is the same in each case. how does the acceleration in case a compare to the acceleration in case b?

the acceleration in case a is ...

Explanation:

Step1: Write the formula for centripetal acceleration

The formula for centripetal acceleration is \(a=\frac{v^{2}}{r}\).

Step2: Calculate acceleration for Case A and Case B

For Case B: \(a_{B}=\frac{v^{2}}{r}\).
For Case A: \(v_{A} = 3v\), \(r_{A}=r\), so \(a_{A}=\frac{(3v)^{2}}{r}=\frac{9v^{2}}{r}\).

Step3: Find the ratio of \(a_{A}\) to \(a_{B}\)

\(\frac{a_{A}}{a_{B}}=\frac{\frac{9v^{2}}{r}}{\frac{v^{2}}{r}} = 9\).

Answer:

The acceleration in Case A is 9 times that in Case B.