Answer to Question #162420 in Molecular Physics | Thermodynamics for Golardha Chhetri

Question

A body with the mass m 5 kg lies on an inclined plane and is connected to a solid cylinder with a mass M 10 kg by a massless rope (see sketch). The rope is wound on the solid cylinder. The inclined plane has a static friction of 0.12 and a sliding friction of 0.06. The body is at rest at the beginning.

a) At what critical angle can the body overcome static friction?

b) At the critical angle the body of mass m begins to slide down the plane. Its acceleration is slowed down by the rolling of the full cylinder. How big is the acceleration of the body and how big is the tensile force in the rope?

Answer 1

a)

$$tan \alpha=0.12$$

$$\alpha =atan 0.12=7^0$$

b)

I can only assume that the figure shows a right-angled triangle at one of the vertices of which a cylinder is reinforced.

$$- Mg+\mu mgcos \alpha+mg sin \alpha=ma$$

$$\alpha = acos (0.06)=87^0$$