# Example Problem with Complete Solution

1A-2 : Conversion of Kinetic Energy into Spring Potential Energy 5 pts
It takes energy to compress a spring. This energy is stored as spring potential energy, which can be calculated using: Espring = 1/2 K x2, where K is the spring constant and x is the distance the spring is compressed.
At a dock, a boat with a mass of 50,000 kg hits a bumper supported by two springs that stop the boat and absorb its kinetic energy.
Determine the spring constant of the springs that is required if the maximum compression is to be 60 cm for a boat speed of 2.4 m/s.

Read: It is important to note that two springs are used to stop the vehicle.
All of the initial kinetic energy of the vehicle must be absorbed by the springs and converted to spring potential energy.
Given: Eqn 1 K = spring constant
x = displacement of the spring, in this case compression.
m 50000 kg
v 2.4 m/s gc 1 kg-m/N-s2
x 0.6 m
Find: K ??? N/m
Assumptions: 1- The spring is a linear spring and therefore  the given equation applies.
2- All of the kinetic energy of the boat is absorbed by the springs.
Equations / Data / Solve:
The key to solving this problem is to recognize that the final potential energy of the two springs must be equal to the initial kinetic energy of the vehicle.  So, we should begin by calculating the initial kinetic energy of the boat. Eqn 2
Because there are two identical springs : Eqn 3
Plugging given values into Eqn 2 and Eqn 3 yields: Ekin 144000 J
Espring 72000 J
Next, we can solve Eqn 1 algebraically for the spring constant, K. Eqn 4
First, let's work on the units. Eqn 5
Now, let's calculate the value of the spring constant. K 4.00E+05 N/m 