| Basic Thermodynamics ~ J. Pohl © | www.THERMOspokenhere.com (120-C259) |
On Feb 18, 1885, a train engine moving at high speed collided with a second, stationary engine. Their engines were identical, having been manufactured by the same company.
The aftermath of the collision was engine A (stationary upon impact) situated near vertically on top of engine B.
The engine crews were killed but one witness judged the speed of engine B prior to the crash to have been at least 100 miles per hour. A second observer claimed engine B was not speeding; he was sure the engine's speed was "...more like ten miles per hour."
Take the system as both engines together. Write the energy equation and simplify it by applying facts and reasonable assumptions.
♦ The event is an increment type. The energy equation is:
| (1)
Events that include impact and destruction involve changes of internal energy and heat. |
We take the event to initiate a moment prior to collision and to end a minute or so later. Heat takes time, so the approximation, ΣQ = 0, is reasonable. With the exception of the loud noise, ΣW = 0. There are large forces of the impact but they are all interior to the system. The velocity of engine A is initially and finally zero. Engine B experiences no change of elevation. Hence ΔKEA and ΔPEB are zero.
| (2) The energy equation simplfies to this. |
Next write the terms explicitly,
| (3) Represent the energies explicitly. |
To proceed, some approximate information can be retrieved from the photograph. Assume the man, pictured standing beside the wreck (front left), is 6 feet tall. In proportion to the height of his image the bottoms of the wheels of engine A appear to be about 8 feet above the rails. Hence the center of mass of engine A was elevated about 8 feet when engine B went under it. Thus we can write the equation as:
| (4) 4 |
The engine masses are equal. If the tracks are not torn up, zero work for the event is reasonable. The noise of the collision is work but we ignore it - it is small. No heat is reasonable because the event is quick. Also the 8 feet of elevation change is a reasonable number. Thus the energy equation has ΔUA, ΔUB,and vB,1 as unknowns.
| (5) 5 |
This is the limit to which we can simplify the energy equation. Some cases can be investigated.
Calculate the maximum increase of internal energy of the system.
♦ This would happen were engine B moving initially at 100 miles per hour (~ 150 ft/s).
| (6) Take care of units! |
Calculate the least possible speed of engine B.
♦ Ten Miles per Hour (~15 ft/s) sounds ridiculously slow. If we assume in the event the engines had no increase of internal energy whatsoever, that solution of the energy equation would yield the very least theoretical initial velocity of Engine B. We rewrite the reduced form:
|
| (7) 7 |
We see that as the sum, ΔUA+B, becomes smaller, so also does the predicted initial speed of engine B. As it should!
| (8) Leave algebra until the last step. |
Thus the very least possible velocity of Engine B is 33 miles/hour.
On Feb 18, 1885, a train engine moving at high speed collided with a second, stationary engine. Their engines were identical, having been manufactured by the same company.
The aftermath of the collision was engine A (stationary upon impact) situated near vertically on top of engine B.