Unit 4 - Problem 7 ==> Basic Springs

Given:

• Mass of block = 5 kg
• Velocity of block = 2 m/s
,li>Spring constant = 1000

Calculate: Energy in moving block

• $$ E_{block} = \frac{1}{2} * m_{block} * V_{block}^2$$
• $$ E_{block} = 0.5 * 5 * 2^2 = 10_{joules}$$

Maximum deformation of spring results transfer of all energy to it.

• $$ E_{spring} = \frac{1}{2} * k * \Delta{x}^2 $$
• $$ E_{spring} = 10_{joules} = 0.5 * 1000 * \Delta{x}^2 $$
• $$ 10 = 500 * \Delta{x}^2 $$
• $$ \Delta{x}^2 = \frac{10}{500} = .02 $$
• $$ \Delta{x} = 0.1414213562373095 = 0.14 $$