A 10-kg block starts from rest at a vertical height of 1 m on a 30º frictionless inclined plane.If the block slides down the incline and then 20 m along a frictionless horizontal surface into a fixed spring with a force constant of 100 N/m,the spring is compressed approximately
A)1.4 m
B)2.0 m
C)0.33 m
D)0.98 m
E)2.5 m

Question

Quizplus · Accepted Answer

The energy conservation principle is applied here. The potential energy at the height is converted into kinetic energy, which then is converted into the spring's potential energy. The potential energy at the height is $mgh = 10 \times 9.8 \times 1 = 98 \, \text{J}$. This energy is equal to the spring's potential energy when compressed, given by $\frac{1}{2}kx^2$, where $k = 100 \, \text{N/m}$. Solving for $x$, we get $x = \sqrt{\frac{2 \times 98}{100}} \approx 1.4 \, \text{m}$.

A 10-Kg Block Starts from Rest at a Vertical Height