Question

A student uses a spring-loaded launcher to launch a marble vertically in the air. The mass of the marble is 0.003 kg and the spring constant is 220 N/m. What is the maximum height the marble can reach when compressed by 2 cm?

Answer 1

Maximum heigh: 1.496 m

(This number is not exacte I truncated it)

Step-by-step explanation:

Data:

mass : m = 0.003 kg

spring constant : k = 220 N/m

amount of compression: x = 2 cm = 0.02 m

heigh : h = ?

accelaratiom due to gravity : g = 9.8ms^-2

Potential Energy : PE = ?

Since you'll be converting the PE to KE, you'll use 2 formulas.

Formulas:

`PE=(1)/(2)\cdot k\cdot x^2`
`PE_{\text{marble}}\text{ = }m\cdot g\cdot h_{}`

Solution:

`\begin{gathered} PE\text{ }=\text{ }(220\cdot0.02^2)/(2) \\ PE\text{ = }0.044\text{ J} \end{gathered}`
`\begin{gathered} 0.044\text{ J =}m\cdot g\cdot h \\ 0.044\text{ = 0.003 }\cdot\text{ }9.8\cdot\text{ h} \\ h\text{ = }\frac{0.044}{0.003\cdot\text{ 9.8}} \\ h\text{ }\approx\text{ 1.496 m} \end{gathered}`