An object of mass m = 0.40 kg is at rest on a flat plank. One end of the plank i

Question

An object of mass m = 0.40 kg is at rest on a flat plank. One end of the plank is slowly lifted

to increase the incline angle (angle between the plank’s surface and the horizontal). The static

frictional cooeficient is s = 0.42, and when the object is in motion the kinetic frictional coefficient

is k = 0.20.

(a) At what incline angle will the object begin to slide down the incline?

(b) Using the angle determined in part (a), find the object’s accelleration a down the incline.

(c) After the object is in motion, the end of the plank is lowered decreasing the angle of incline

until the acceleration is zero. Find the new angle of incline f .

(d) For the scenario described in part (c), will the object reach the bottom of the plank?

Explanation / Answer

m = 0.40 kg
s = 0.42
k = 0.20

(a)
The Object will start sliding when,
Weight of the object along the incline >= Friction Force
m*g*sin() = s * m*g*cos()
Solving for
tan() = s
= tan^-1(0.42)
= 22.78o

(b)
Now, once it begins to slide, Static Friction will Change to kinetic Friction.
m*g*sin(f) - k* m*g*cos(f) = m*a
sin(22.78) - 0.2*cos(22.78) = a
a = 0.203 m/s^2
Acceleration down the incline, a = 0.203 m/s^2
(c)

Motion Equation is as below -
m*g*sin(f) - k* m*g*cos(f) = m*a
Now as Acceleration is 0.
sin(f) = k * cos(f)
tan(f) = k
f = 11.3o
New angle of incline, f = 11.3o

(d)
No, It won't reach the bottom.
Friction force would increase as angle of inclination decreases, and therefore the velocity will start decreasing.

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