Question

0.5 kg car rolls through a vertical loop with a radius of 0.3 m. determine the minimum speed the car must have to make it around the loop.

Explanation:

Step1: Analyze forces at top of loop

At the top of the loop, the centripetal force \(F_c=\frac{mv^{2}}{r}\) is provided by the gravitational force \(mg\) (when normal force \(N = 0\) for minimum speed). So, \(\frac{mv^{2}}{r}=mg\).

Step2: Solve for speed \(v\)

Cancel out \(m\) from both sides of the equation \(\frac{mv^{2}}{r}=mg\). We get \(v^{2}=gr\). Given \(g = 9.8\space m/s^{2}\) and \(r=0.3\space m\), then \(v=\sqrt{gr}=\sqrt{9.8\times0.3}\).

$$v=\sqrt{2.94}\approx1.71\space m/s$$

Answer:

The minimum speed of the car is approximately \(1.71\space m/s\).