Answer to Question #199277 in Mechanical Engineering for Ola

Question

Your go karts have a mass of 450kg and travel around a circular curve on a flat, horizontal track at a radius of 42 m.

a) Draw a diagram to show the go kart on the track and add an arrow to show the direction of the frictional force needed for the car to travel around the curve at a radius of 42 m.

b) The maximum frictional force between the tyres and the road is equal to 20% of the weight of the car and driver. Calculate the coefficient of friction when an adult of mass 70kg is driving the kart.

c) Calculate maximum angular velocity at which the car can travel round the curve at a constant radius of 42 m.

d) Calculate the maximum linear velocity.

e) You decide that this is not nearly fast enough and decide to create a banked track of 12O, what is the maximum linear velocity now?

f) Describe qualitatively how this could change if a child were driving the kart.

Answer 1

Part a

Part b.

$F_f=\mu N= \mu Mg$

$\frac{20}{100}*520= \mu*520 *9.8 \implies \mu=0.0204$

Part C

$0.5I \omega^2=\tau_{max} \triangle \theta \implies \omega ^2 =\sqrt{\frac{2 \tau_{max} \triangle \theta}{I}}$

$\omega ^2 =\sqrt{\frac{2 *520* \frac{20}{100}*9.8*42*2 \pi}{520*42^2}}=0.24 rad/s$

Part d

$v= \omega r=0.24 *42=10.27 m/s$

Part e

$F_{net}=N sin \theta- F_c =520*9.8sin 120 -\frac{20}{100}*520=4309.3 N$

$\omega ^2 =\sqrt{\frac{2 *4309.3*42*2 \pi}{520*42^2}}=1.57 rad/s$

$v= \omega r=1.57 *42=66.13 m/s$

Part f

The speed of the the kart would have been slower.