Question

A small block of ice with mass $0.120$ kg is placed against a horizontal compressed spring mounted on a horizontal table top that is $1.90$ m above the floor. The spring has a force constant $k=2300$ N/m and is initially compressed $0.045$ m. The mass of the spring is negligible. The spring is released, and the block slides along the table, goes off the edge, and travels to the floor. If there is negligible friction between the ice and the table, what is the speed of the block of ice when it reaches the floor. $(g=9.8m/s^2)$

• A. $3.24m{s}^{-1}$
• B. $4.48m{s}^{-1}$
• C. $8.72m{s}^{-1}$
• D. $12.36m{s}^{-1}$

Answer 1

The correct option is C $8.72m{s}^{-1}$

$initialcompression=0.045m,usingconservatipnofenergy$
$\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2\Rightarrow v=x\sqrt{\frac{k}{m}}=0.045\sqrt{\frac{2300}{0.12}}=6.23m/s$

$istheveocityalongx-directionandwo{n}^{\prime }tchangeduringthecourseofmotion.velocityalongy-directionwillbe\sqrt{2gh}=6.16m/stotalvelocity=\sqrt{{6.23}^2+{6.16}^2}=8.72m/s$