Question

the speed in case a is one - half 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?
case a
case b
the acceleration in case a is...
... the acceleration of case b.

Explanation:

Step1: Write the centripetal acceleration formula

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

Step2: Calculate acceleration for Case A and Case B

For Case A: \(a_{A}=\frac{(\frac{1}{2}v)^{2}}{R}=\frac{v^{2}}{4R}\).
For Case B: \(a_{B}=\frac{v^{2}}{R}\).

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

\(\frac{a_{A}}{a_{B}}=\frac{\frac{v^{2}}{4R}}{\frac{v^{2}}{R}}=\frac{1}{4}\).

Answer:

The acceleration in Case A is \(\frac{1}{4}\) of the acceleration in Case B.