Question

When being unloaded from a moving truck, a 16.0- kilogram suitcase is placed on a flat ramp inclined at 40.0 o. When released from rest, the suitcase accelerates down the ramp at 1.36 m/s². What is the coefficient of kinetic friction between the suitcase and the ramp?

Answer 1

Answer:

0.65812

Explanation:

m = Mass of suitcase = 16 kg

$\theta$ = Incline angle = 40°

g = Acceleration due to gravity = 9.81 m/s²

a = Acceleration of the block = 1.36 m/s²

f = Frictional force

The normal force is given by

$N=mgcos\theta$

In x direction

$mgsin\theta-f=ma\\\Rightarrow f=mgsin\theta-ma\\\Rightarrow f=16\times 9.81\times sin40-16\times 1.36\\\Rightarrow f=79.13194\ N$

Frictional force is given by

$f=\mu N=\mu mgcos\theta\\\Rightarrow \mu=\dfrac{f}{mgcos\theta}\\\Rightarrow \mu=\dfrac{79.13194}{16\times 9.81\times cos40}\\\Rightarrow \mu=0.65812$

The coefficient of kinetic friction between the suitcase and the ramp is 0.65812