Answer to Question #197183 in Physics for gibson

Question

1.A car moving at speed of 25m/s can go around a curve of 80m radius without skidding

away if the road is unbanked. Determine the coefficient of static friction between the road

and tires that would ensure the car not skid.

2. A grasshopper of mass 200g sits 20cm from the centre of a blade of a ceiling fan rotating

at 35rev/min.

(a) Determine the size of the centripetal force on a grasshopper.

(b) Calculate the value of static friction between the fly and the blade required to prevent

a grasshopper from sliding off.

Answer 1

1)

$$F_c=F_{fr},$$ $$\dfrac{mv^2}{r}=\mu mg,$$ $$\mu=\dfrac{v^2}{rg}=\dfrac{(25\ \dfrac{m}{s})^2}{80\ m\cdot9.8\ \dfrac{m}{s^2}}=0.80$$

2)

(a)

$$F_c=ma_c=\dfrac{mv^2}{r},$$ $$F_c=\dfrac{m(\omega r)^2}{r}=m\omega^2r,$$ $$F_c=0.2\ kg\cdot(35\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot\dfrac{2\pi\ rad}{1\ rev})^2\cdot0.2\ m,$$ $$F_c=0.54\ N.$$

(b)

$$\mu=\dfrac{v^2}{rg}=\dfrac{\omega^2r}{g},$$ $$\mu=\dfrac{(35\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot\dfrac{2\pi\ rad}{1\ rev})^2\cdot0.2\ m}{9.8\ \dfrac{m}{s^2}}=0.27$$