Answer to Question #90027 in Mechanics | Relativity for Hm

Question

An object of mass 3kg rests on a plane. The coefficient of static fraction and that of static fraction given by mass 0.3 and Mr =0.2. The plane inclined at an angle theta at the horizontal. (a) Find the maximum value of the theta for which the object remains at rest. (b) find the acceleration of the object of it started sliding from rest down the plane at the angle theta maximum to horizontal. (c) How long does it take the object to move from rest, a distance of 1m under the condition of B?

Answer 1

a)

$$\tan{\theta}=\mu_s$$

$$\theta=\arctan{\mu_s}=\arctan{0.3}=16.7\degree$$

b)

$$a=g(\sin{\theta}-\mu_k \cos{\theta})$$

$$a=9.8(\sin{16.7}-0.2 \cos{16.7})=0.94 \frac{m}{s^2}$$

c)

$$t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2(1)}{0.94}}=1.5\ s$$