Question

Jasmine is cycling at 12 m s−1 when her bag falls off the back of her bicycle.The bag slides a distance of 9 m before coming to rest. Calculate the coefficient of friction between the bag and the road.

Answer 1

The work-energy theorem states that the work done on an object by the net force is equal to the change in its kinetic energy:

$$\dfrac{mv_2^2}{2}-\dfrac{mv_1^2}{2}=-F_{fr}\cdot s$$ $$F_{fr}=\mu m g$$

$$\dfrac{mv_2^2}{2}-\dfrac{mv_1^2}{2}=-\mu mg\cdot s$$

$$\mu=\dfrac{v_1^2-v_2^2}{2gs}$$

Given $v_1=12\ m/s, v_2=0\ m/s, s=9m, g=9.81\ m/s^2.$

$$\mu=\dfrac{(12\ m/s)^2-(0\ m/s)^2}{2(9.81\ m/s^2)(9\ m)}=0.8155$$

The coefficient of friction between the bag and the road is 0.8155.