Before we look at the physics behind a push up we must first establish a standard. We must choose how to define a push up. There are many different types of push ups with varying form and execution. For the purposes of this experiment we will define a push as starting in a plank position with hands directly under shoulders, fingers forward and ending with back straight arms fully extended. 

We must now create an example subject. Suppose the subject is 90kg (200 lb) 1.75 m (5'9") with a center of mass (2/3)h up from the feet. assume that the angular difference between the two positions is 20 degrees.

http://2.bp.blogspot.com/-2tEmrsXWo6U/UFdubAyGYYI/AAAAAAAAAPk/4ZeqECaMGWM/s1600/push-up1.jpg