An amount of work equal to 2.0 J is required to compress the spring in a spring-gun.What is the "launch speed" of a 26.0-g marble?
A)12.4 m/s
B)13.4 m/s
C)8.8 m/s
D)3.92 m/s
E)0.392 m/s

Question

Quizplus · Accepted Answer

The launch speed can be found using the conservation of energy principle. The work done to compress the spring (2.0 J) is converted into the kinetic energy of the marble. The kinetic energy (KE) is given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass in kilograms and $v$ is the velocity in meters per second. Rearranging for $v$, we get $v = \sqrt{\frac{2KE}{m}}$. Substituting the given values ($KE = 2.0 J$, $m = 26.0 g = 0.026 kg$), we find $v = \sqrt{\frac{2 \times 2.0}{0.026}} \approx 12.4 m/s$.

An Amount of Work Equal to 2