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## Physics Tutorials

### Spring Potential Energy and Mountain Bikes

Today, mountain biking is a popular sport across the world. The bikes are used on all sorts of terrain, from city streets to mountain sides, by people with different levels of ability. For the more advanced bikers, having the newest technology incorporated into their bikes is important for speed and safety. To absorb shock, designers have developed high-quality suspension systems for the front and rear of the mountain bikes.  This allows a more comfortable ride for the biker, and less wear on the bike.

The suspension system uses springs that compress when the bike experiences a large impact. Not just any spring can be used. It has to be strong enough to bear the strain of the shock, but not so strong that it won't compress.

To calculate the energy being absorbed by the spring, we can use the formula for spring potential energy:

Es= (.5)kx2

Es= spring potential energy  (J)

k  = spring constant  (N/m)

x  = amount of compression  (m)

Spring potential energy is the amount of energy stored in a spring that has been either compressed or stretched. When a spring is in its natural state, meaning not compressed or extended, it does not have any potential energy.

#### Question

Jan's mountain bike has a spring with a constant of 64 N/m in the front-wheel suspension, and it compressed 0.17m when she hit a bump. How much energy does the front spring now store?

Es= (.5)kx2
= (.5)(64)(0.17)2
= 0.92 J

#### Question

A spring has 1.1 J of potential energy and was compressed 0.2m. What is its spring constant?