Question

1. Spring launch Knightro is learning a new trick called the ''Spring Launch'', where he stands on a skateboard and is launched up a ramp by a giant spring. In the first test run, the spring is compressed a distance delta x Knightro moves across the horizontal portion of the ramp with speed v and reaches a maximum heigh at the end of the ramp. For the next trial, Knightro plans to compress the spring a distance 2 delta x. 1. For the second trial, will the Knightro's speed on the horizontal portion of the ramp be: (circle one) greater than 2v less than 2v equal to 2v

Answer 1

Here potential energy stored in the spring due to compression will transfered to Knightro in the form of kinetic energy.

First case,

$\frac{1}{2}k(\Delta x)^{2}=\frac{1}{2}mv^{2}$

$v^{2}=\frac{k}{m}(\Delta x)^{2}$

2nd case,

$V^{2}=\frac{k}{m}(2\Delta x)^{2}=4v^{2}$

$V=2v$