Question

A car in an amusement park ride rolls without friction around a track (Fig. P7.42). The hB car starts from rest at point A at a CR height h above the bottom of the loop. Treat the car as a particle. (a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)

Answer 1

Answer:

$h>\dfrac{5}{2}R$

Explanation:

Given that

Height = h

Radius = R

From energy conservation

$KE_A+U_A=KE_B+U_B$

At point B

The minimum speed to complete the   the circle

$V_B=\sqrt{gR}\ m/s$

So the kinetic energy at point B

$KE_B=\dfrac{1}{2}mV^2$

$KE_B=\dfrac{1}{2}mgR$

$KE_A+U_A=KE_B+U_B$

$0+mgh=\dfrac{1}{2}mgR+2mgR$

Without falling off at the top (point B)

$0+mgh>\dfrac{1}{2}mgR+2mgR$

$mg(h-2R)>\dfrac{1}{2}mgR$

$g(h-2R)>\dfrac{1}{2}gR$

$h>\dfrac{5}{2}R$