So what does physics say about the event, "a person is hsnged."

GOD Lifted Earth In Massachusetts (1710) an accused witch was hanged in the public square. At the moment of her death, when the rope snapped taut, it seemed to all that an earthquake had occurred. Later, in full darkness, as friends cut her down, a rumor got started. "When she died, God lifted Earth to receive her" a bystander whispered. Within days the entire village came to believed she was innocent. The next Sunday, the Bishop explained, "She was guilty. God did not casue the tremor. It was gravity: as she fell down, Earth fell up." He provided the solution shown below. Is the Bishop's solution correct?

♦  The exaggerated sketch shows the "before" and "after" of the event. We will use the momentum equation with the system being both Earth and the woman. The momentum equation written with a (discrete) summation sign is:

The velocities for this event have only "K" components. So when we multiply by "• K the velocities become - v_z's. So we make that multiplication, theseparate variables, integrate and apply limits. This same simple process gets done again and again.

Next we recognize that v_z = d z( t ) / dt. Make that substitution, separate variables again. Then integrate.

The two masses, taken as a system, experience no surface forces during the event. Therefore the center of mass of the system does not move. It is sufficient for us to assumw the elevation, Z_c.m. and then set it as a zero datum for the event. Thus the elevations of the above equation are "relative" to the location (zero value of z). We enter the elevations with some algebra:

The Bishop is correct that mutual gravity caused Earth to move up. However we see that the amount of movement is very small. Many people felt the tremor, it must have been a minor Earthquake.

A Second Solution:  They had better obtain the same answer.