# As part of a challenge lab, a student determines that a spring powered marble cannon will fire a...

## Question:

As part of a challenge lab, a student determines that a spring-powered marble cannon will fire a 0.03kg marble to a maximum height of 0.8m when the cannon is set to the second medium firing position and fired vertically

A. If setting the medium firing position requires that the spring in the cannon is compressed by 2.5 cm, what is the spring constant of the spring?

B. If the cannon is set to it's high firing position, the spring is compressed 4cm. What is the maximum height the marble will reach when fired vertically

## Energy Conservation Principle:

The energy conservation principle consists of a physical law that states that for a closed system, the total energy of the system will conserve. Energy does not create nor destroys, it only transforms. Energy transformations may exist within the current system, but the total energy of the system will remain constant. The total energy of the system can be determined by the sum of the kinetic energy and potential energy.

{eq}E_t=\dfrac{1}{2}mv^2+mgh {/eq}

#### Part a):

We use energy conservation mechanics to determine the spring constant of the cannon spring. The total elastic potential energy at the beginning of the compression will completely convert to gravitational potential energy at maximum height.

{eq}E_i=E_f\\ \dfrac{1}{2}kx^2=mgh\\ 0.5\times k(0.025)^2=0.03\times9.8\times0.8\\ k=\dfrac{0.2352}{0.5\times0.025^2}\\ k=752.64\ N/m {/eq}

#### Part b):

Again, we use energy conservation mechanics to determine the maximum height the marble can reach when it is fired.

{eq}E_i=E_f\\ \dfrac{1}{2}kx^2=mgh\\\ 0.5\times (752.64)\times(0.04)^2=0.03\times9.8\times h\\ h=\dfrac{0.602}{0.03\times9.8}\\ h=2.05\ m {/eq} 