The figure shows two packages that start sliding down a 20° ramp from rest a distance d = 6.6 m along the ramp from the bottom. Package A has a mass of 5.0 kg and a coefficient of kinetic friction 0.20 between it and the ramp. Package B has a mass of 10 kg and a coefficient of kinetic friction 0.15 between it and the ramp. How long does it take package A to reach the bottom?
A) 2.7 s
B) 3.0 s
C) 3.2 s
D) 3.5 s

Question

The figure shows two packages that start sliding down a 20° ramp from rest a distance d = 6.6 m along the ramp from the bottom. Package A has a mass of 5.0 kg and a coefficient of kinetic friction 0.20 between it and the ramp. Package B has a mass of 10 kg and a coefficient of kinetic friction 0.15 between it and the ramp. How long does it take package A to reach the bottom? 
A) 2.7 s 
B) 3.0 s 
C) 3.2 s 
D) 3.5 s

Quizplus · Accepted Answer

First, we can use the equation for the acceleration of an object sliding down a ramp:

a = g(sinθ - μcosθ)

where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), θ is the angle of the ramp (20°), and μ is the coefficient of kinetic friction.

For Package A:
a = 9.8(sin20° - 0.20cos20°) = 1.59 m/s^2

Using the kinematic equation:

d = 0.5at^2

where d is the distance traveled, a is the acceleration, and t is the time it takes to travel that distance.

Rearranging for t, we get:

t = sqrt(2d/a)

Plugging in values for Package A:
t = sqrt(2(6.6 m)/(1.59 m/s^2)) = 2.7 s

Therefore, the answer is A) 2.7 s.

The Figure Shows Two Packages That Start Sliding Down a 20°