The Work Energy Principle Explained

Since energy can be neither created nor destroyed, external work performed on a system changes the system’s total energy.

$W = {\Delta}E = E_2 - E_1$

The work energy principle introduces some simplifications into many mechanical problems, such as:

• You don’t need to know the acceleration of a body to calculate the work performed on it.
• Forces normal to the direction of motion (i.e. don’t contribute to work) are not considered.
• You don’t need to work in vector quantities. Only scalars are involved.
• You can analyze the system as a whole, not in individual parts.

Example

An elevator starts from rest, accelerates uniformly to a constant speed of 2.5 m/s, and then decelerates uniformly to a stop 100 m higher than its initial position. The elevator weighs 3000 kg. What work was done on the elevator?

Solution

$W = E_2 - E_1\newline \-\hspace{7mm}= mg(h_2 - h_1)\newline \-\hspace{7mm}=(3000 kg)(9.81 m/s^{2})(100 m) = 2,943 kJ$

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