Question

1. A 560.0 N cyclist sits on a bicycle seat and compresses the two springs that support it.  The spring constant equals 2.2 X 104 N/m. 
2. How much is each spring compressed?
3. By how much does the compression increase in each spring’s elastic PE?

Answer 1

1.How much is each spring compressed?

$F =kx$

where x is the compression. Since there are two strings, the force will be distributed on them

$F =2kx$

$\displaystyle x = \frac{F}{2k} = \frac{560}{2 \cdot2.2 \cdot 10^4}= 12.73 \cdot 10^{-3}\, m = 12.73\; mm$

Each string is compressed by 12.73 mm.

2.By how much does the compression increase in each spring’s elastic PE?

The increase in each spring’s elastic potential energy is

$\displaystyle E = \frac{kx^2}{2}= \frac{2.2 \cdot 10^4 \cdot 12.73^2 \cdot 10^{-6}}{2} = 178.26 \cdot 10^{-2} = 1.78 \; J$

PE of each spring increases by 1.78 J.