Question

A spring with constant k = 78 N/m is at the base of a frictionless, 30.0°-inclined plane. A 0.50-kg block is pressed against the spring, compressing it 0.20 m from its equilibrium position. The block is then released. If the block is not attached to the spring, how far up the incline will it travel before it stops?

Answer 1

Explanation:

The given data is as follows.

   Spring constant (k) = 78 N/m,     $\theta = 30^{o}$

 Mass of block (m) = 0.50 kg

According to the formula of energy conservation,

                mgh sin $\theta = \frac{1}{2}kx^{2}$

       h = $\frac{1}{2} \times \frac{kx^{2}}{mg Sin \theta}$

          = $\frac{78 \times 0.04}{2 \times 0.5 \times 9.8 \times 0.5}$

          = 0.64 m

Thus, we can conclude that the distance traveled by the block is 0.64 m.