Question

the speed in case a is twice 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
2·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: Write the formula for net force (centripetal force)

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

Step2: Calculate the net force for Case A

For Case A, \(v = 2v\) and \(r=2R\). Substituting into the formula: \(F_{A}=\frac{m(2v)^{2}}{2R}=\frac{4mv^{2}}{2R}=\frac{2mv^{2}}{R}\).

Step3: Calculate the net force for Case B

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

Answer:

The net force in Case A is twice the net force in Case B.