Problems involving springs

A spring allows for a third form of energy: elastic potential energy. In problems with springs, the total energy has three terms: one each for gravitational potential energy, elastic potential energy, and kinetic energy. Read the text aloud
Consider a 2.0 kg ball that drops onto a vertical spring with a spring constant k of 1,000 N/m. From what height did the ball drop if the spring compresses by 25 cm? Read the text aloud Initial and final states for the compressed spring
To solve the problem we follow the same three steps. First, name the variables and write down the total energy of the system in the initial and final states, before and after the change. Then eliminate terms that are zero. The remaining equation contains the solution. Read the text aloud
Steps for solving the spring problem
h= k x 2 2mg = (1,000 N/m)(0.25 m) 2 2 (2.0 kg)(9.8 m/s 2 ) =1.6 m
Initial and final states for the compressed springA horizontal spring is used to launch a 2.0 kg ball. The spring is compressed by 0.25 m and has a spring constant k of 1,000 N/m. What is the maximum speed of the ball?
Asked: speed v
Given: k = 1,000 N/m; x = 0.25 m;
m = 2.0 kg
Relationships: total mechanical energy:
Etotal = mgh + ½mv2 + ½kx2
Read the text aloud
Solution to the spring problem
Answer: v = 5.6 m/s

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