In just 0.30 s , you compress a spring (spring constant 5000 n/m ), which is initially at its equilibrium length, by 4.0 cm. part a what is your average power output?
The average power output is the ratio between the work done to compress the spring, W, and the time taken, t: [tex]P= \frac{W}{t} [/tex] (1)
The work done is equal to the elastic energy stored by the compressed spring: [tex]W=U= \frac{1}{2}kx^2 [/tex] where [tex]k=5000 N/m[/tex] is the spring constant and [tex]x=4.0 cm=0.04 m[/tex] is the compression of the spring. If we substitute the numbers, we find: [tex]W= \frac{1}{2}(5000 N/m)(0.04 m)^2=4 J [/tex]
And now we can use eq.(1) to calculate the average power output: [tex]P= \frac{W}{t}= \frac{4 J}{0.30 s} =13.3 W[/tex]
