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Efficiency of Energy Conversion

Often we have energy in one form and we want to convert it into another form, for example, from chemical energy in gasoline to kinetic energy of a car. It may be the case that energy cannot be destroyed, but it can end up in an inconvenient form such as heat. In this case we define the efficiency of energy conversion as follows:



A car (800 kg) goes slowly up a hill from the base to a height of 300 meters. It uses 245 grams of fuel in the form of 2,2,4-trimethylpentane. The following overall reaction occurs in the car:
What is the efficiency of the engine? Assume no energy loss due to air resistance. Use 1 kcal = 4184 J.

First we calculate the energy in desired form, which is the potential energy:

Edes = mgh
= (800 kg)(10 m/s2)(300 m)
= 2.4 x 106 J

Next we calculate the energy used:


The efficiency is


(See Figure 9-8.)


..\art 9 jpg\figure 9-th.jpg
Figure 9-8

We can speak of efficiency in a collision as well. In a collision, kinetic energy is often converted to heat and chemical energy. If this is not the case, that is, if kinetic energy before the collision is the same as after, then the collision is called elastic. Otherwise it is called inelastic. If everything is stuck together in the end, the collision is called completely inelastic.


Two cars collide in one dimension in a completely inelastic collision. One car is 1000 kg, initially going east at 10 m/s. The other car is 1500 kg, initially going west at 15 m/s.
  1. What is the velocity of the twisted metal afterward?
  2. What is the efficiency of the collision?
  1. Did you remember that crunching or smashing generally means we must use the conservation of momentum? Let us take east to be positive (see Figure 9-9) and we write

p1 = p2,


(1000 kg)(10 m/s) + (1500 kg)(–15 m/s) = (2500 kg)vf


vf = –5 m/s

  1. Now we need to know the kinetic energy both before and after the collision.

EK1 = 1/2 (1000 kg)(10 m/s)2 + 1/2 (1500 kg)( –15 m/s)2
= 2.19 x 105 J,
EK2 = 1/2 (2500 kg)( –5 m/s)2
= 3.1 x 104 J

Thus the efficiency is



..\art 9 jpg\figure 9-ti.jpg
Figure 9-9

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