Question

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

• A. $\sqrt{6} \, \text{m}$
• B. $2 \, \text{m}$
• C. $1 \, \text{m}$
• D. $\sqrt{5} \, \text{m}$

Answer 1

Answer: (B)

$2 \, \text{m}$

Answer 2

Using the work-energy theorem, the total work done by all forces is equal to the change in kinetic energy ($\Delta KE$) of the system. Here:
$w_g + w_{Fr} + w_s = \Delta KE.$
Substituting the given values:
$5 \times 10 \times 5 - 0.5 \times 5 \times 10 \times x - \frac{1}{2} Kx^2 = 0 - 0.$
Simplifying:
$250 - 25x - 50x^2 = 0.$
Rewriting:
$2x^2 + x - 10 = 0.$
Solving this quadratic equation gives:
$x = 2.$
Thus, the maximum compression in the spring is $x = 2$ m.