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

According to the energy conservation, the initial kinetic energy of the object is equal to the potential energy stored in the fully compressed spring:

$$K = W\\ \dfrac{mv^2}{2} = \dfrac{kx^2}{2}$$

where $m = 20kg$, $k = 980N/m$, $x = 20cm = 0.2m$ and $v$ is the initial velocity. Thus, obtain:

$$v = x\sqrt{\dfrac{k}{m}} = 0.2m\cdot \sqrt{\dfrac{980N/m}{20kg}} = 1.4m/s$$

Answer. 1.4m/s.