Example Problem with Complete Solution

1A-2 : Conversion of Kinetic Energy into Spring Potential Energy 5 pts
The potential energy stored in a spring is given by 1/2 K x2, where K is the spring constant and x is the distance the spring is compressed.  Two springs are designed to absorb the kinetic energy of a 2000 kg vehicle.  Determine the spring constant necessary if the maximum compression is to be 100 mm for a vehicle speed of 10 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 : Equation. Eqn 1 K = spring constant
x = displacement of the spring, in this case compressi
m
2000
 kg
v
10
 m/s
gc
1
 kg-m/N-s2  
x
0.1
 m
Solution : 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 vehicle.
  Equation. Eqn 2
Because there are two identical springs : Equation. Eqn 3
          Ekin 100000 J
          Espring 50000 J
Next, we can solve Eqn 1 algebraically for the spring constant, K. Equation. Eqn 4
First, let's work on the units. Equation. Eqn 5
Answer : Now, let's calculate the value of the spring constant.
K
1.00E+07
 N/m