Question

A 12-kg turtle rests on the bed of a zookeeper's truck, which is traveling down a country road at 62.0 mi/h. The zookeeper spots a deer in the road, and slows to a stop in 11 s. Assuming constant acceleration, what is the minimum coefficient of static friction between the turtle and the truck bed surface needed to prevent the turtle from sliding?

Answer 1

0.25683

Step-by-step explanation:

t = Time taken by the truck to stop = 11 seconds

u = Initial velocity of the truck = 62 mi/h

v = Final velocity of the truck = 0

a = Acceleration of the truck

g = Acceleration due to gravity = 9.81 m/s²

Equation of motion

`v=u+at\\\Rightarrow a=(v-u)/(t)\\\Rightarrow a=(0-(62)/(2.237))/(11)\\\Rightarrow a=-2.5196\ m/s^2`

`\mu mg=ma\\\Rightarrow \mu=(ma)/(mg)\\\Rightarrow \mu=(a)/(g)\\\Rightarrow \mu=(2.5196)/(9.81)\\\Rightarrow \mu=0.25683`

The minimum coefficient of static friction between the turtle and the truck bed surface needed to prevent the turtle from sliding is 0.25683