Consider the penguin on the ramp shown in the figure. The penguin has a mass of

Question

Consider the penguin on the ramp shown in the figure. The penguin has a mass of 22 kg, the coefficient of kinetic friction between the penguin and the ramp is 0.30, and the angle between the ramp and the floor is 35 degree. (a) What is the acceleration of the penguin as it slides down the ramp? (You can assume the penguin is actually sliding down the ramp!) (b) How long does it take the penguin to slide to the bottom of the ramp, if the ramp is 15.5 m long? (c) How fast is the penguin moving at the bottom of the ramp?

Explanation / Answer

m = 22 kg, uk =0.3 , theta = 35 degrees

(a) from newton seocnd net force along perpendicular to plane

N = mgcos(35)

net force along parallel to plane

mgsin(35) - Fk = ma

Friction force Fk= uk*N

mgsin(35) - uk*mgcos(35) = ma

9.8*sin(35) - 0.3*9.8*cos(35) =a

a = 3.213 m/s^2

(b) s = 15.5 m

from kinematic equation

s = ut +0.5at^2

15.5 = 0 +0.5*3.213*t^2

t = 3.1 s

(c) v = u +at

v =0+3.213*3.1

v = 9.96 m/s

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