Answer to Question #253560 in Mechanics | Relativity for Kristine

Question

Spring is compressed to a length of 20 cm by a 20 kg object on a 20 degrees inclined surface with coefficient of kinetic friction 0.30. What is the initial velocity of the object moving up the plane? The spring constant is 980 N/m

Answer 1

To release the object, the spring must overcome friction, perform work against gravity to lift the mass, and increase its potential energy:

$$\frac12kx^2=\frac12mv^2+\mu mgx\cos\theta+mgx\sin\theta,\\\space\\ v=\sqrt{x\bigg[\frac{kx}{m}-2g(\mu cos\theta+\sin\theta)\bigg]},$$

where

$$x\bigg[\frac{kx}{m}-2g(\mu cos\theta+\sin\theta)\bigg]<0.$$

Therefore, the object won't move up the slope.