6.3. Energy Conservation http://www.ck12.org
FIGURE 6.21
Illustrative Example 5
In this example, we will introduce the effect of a dissipative force. Though the mechanical energy will not be
conserved, the total energy will be conserved. To solve problems that involve friction, we have to keep track of the
energy that is transformed into heat. InFigure6.22, the 20.0-kg block is pushed 0.50 m against a spring with a
spring constant of 500 N/m. The ground underneath the spring is frictionless, but at the point the mass is free of the
spring, the coefficient of kinetic friction,μkbetween the mass and the ground is 0.20. Find the distancexthe mass
travels before stopping.
FIGURE 6.22
Answer:
As in the last example, the initial energy is all potential energy and it is stored within the spring. As soon as the
block is free of the spring it has its greatest kinetic energy, but it also begins to immediately transform that energy
into heat. When all of the block’s kinetic energy has been transformed into heat, it will no longer have kinetic energy
and it will come to a stop. We write the initial energy,Eiof the system (spring plus mass) as:KEi+PEi= 0 +^12 kx^2
and the final energyEfof the system asKEf+PEf+Q, whereQis the mechanical energy lost to heat.Qis the
work done by friction:W=Q=f x, wheref=μN=μmg.
Thus,