Question

You’ve set up a frictionless car racetrack, with a loop of radius 0.5 m. Your toy car of mass 2 kg starts at rest at the top of a ramp and is released so that it slides down and approaches the loop. What condition must be present so that the car just completes the loop? How high must you make the ramp in order to complete the loop?

Answer 1

Answer

h = 1.12 m

Explanation:

given,

mass of the car = 2 kg

radius = 0.5 m

let h be the height of the ramp

when the car reaches at the top point

gravity = centripetal force  

$mg =\dfrac{mv^2}{r}$

$g =\dfrac{v^2}{r}$

$v = \sqrt{gr}$

using conservation of energy

$\PE_i = PE_f + KE_f$

$m g h = m g (2r)+\dfrac{1}{2}mv^2$

$g h =g (2r)+\dfrac{1}{2}(\sqrt{gr})^2$

$g h =2 gr +\dfrac{gr}{2}$

$h =\dfrac{5r}{2}$

$h =\dfrac{5\times 0.5}{2}$

h = 1.12 m

hence, height of the ramp should be greater than  1.12 m so that it can complete the loop.