Question

A mass of 0.5kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 \mathrm {~N} / \mathrm { m }$. The maximum compression of the spring would be

• A. 0.15 m
• B. 0.12 m
• C. 1.5 m
• D. 0.5 m

Answer 1

Answer: (A)

0.15 m

Answer 2

The kinetic energy of mass is converted into potential energy of a spring

$\frac { 1 } { 2 } m v ^ { 2 } = \frac { 1 } { 2 } k x ^ { 2 }$⇒ $x = \sqrt { \frac { m v ^ { 2 } } { k } } = \sqrt { \frac { 0.5 \times ( 1.5 ) ^ { 2 } } { 50 } } = 0.15 \mathrm {~m}$