Question

22. A block of mass 3.0 kg slides with uniform velocity down a plane inclined 25o with the horizontal. If the angle of inclination is increased to 40o , what will be the acceleration of the block?

Answer 1

From the fact that it descends uniformly at 25°, find the coefficient of friction:

$$mg\sin\theta=\mu mg\cos\theta,\\\space\\ \mu=\tan\theta.$$

The acceleration on another slope can be found from Newton's second law:

$$ma=mg\sin\phi-\mu mg\cos\phi,\\ a=g(\sin\phi-\mu\cos\phi)=g(\sin\phi-\tan\theta\cos\phi)=\\ =9.8(\sin40°-\tan25°\cos40°)=2.8\text{ m/s}^2.$$