The surface shown in the figure is frictionless. The block is released from rest. What will be the maximum compression of the spring? Provide three significant digits in the final answer.)
A) 0.793 m
B) 3.24 m
C) 1.57m
D) 0.989 m
E) 0.886 m

Question

The surface shown in the figure is frictionless. The block is released from rest. What will be the maximum compression of the spring? Provide three significant digits in the final answer.)
A) 0.793 m 
B) 3.24 m 
C) 1.57m 
D) 0.989 m 
E) 0.886 m

Quizplus · Accepted Answer

At the maximum compression of the spring, all the potential energy will be converted into the kinetic energy of the block. Using conservation of energy:
$\frac{1}{2} kx^2 = mgh$
where $k$ is the spring constant, $x$ is the compression of the spring, $m$ is the mass of the block, $g$ is the acceleration due to gravity, and $h$ is the height from which the block is released.
Solving for $x$, we get:
$x = \sqrt{\frac{2mgh}{k}}$
Plugging in the given values, we get:
$x = \sqrt{\frac{2	imes 5.4	imes 9.81	imes 1.08}{200}}$
$x \approx 0.989$ m
Therefore, the correct choice is D.

The Surface Shown in the Figure Is Frictionless