Question

A solid sphere rolls down an inclined plane without slipping. If the center of mass of the sphere has a linear acceleration of 1.21 m/s^2, what is the angle of the incline to the horizontal?

Answer 1

Answer:

angle of inclination to the horizontal is 9.95°

Step-by-step explanation:

Let the angle of inclination be θ

We know acceleration , a = 1.21 m/$s^{2}$

Now using effective mass concept, we get

$a = \frac{m.g.sin\theta }{\frac{m+l}{r^{2}}}$

$a = \frac{m.g.sin\theta }{\frac{m+0.4.m.r^{2}}{r^{2}}}$

$a = \frac{m.g.sin\theta.r^{2} }{m(1+0.4r^{2})}$

$a = \frac{m.g.sin\theta }{1.4m}$

$1.21= \frac{9.81sin\theta }{1.4}$

Therefore, solving for θ, we get

θ = 9.95°

Therefore, angle of inclination to the horizontal is 9.95°