[Falcon4.0]

By my calculations of 1/2 mass X velocity squared, the 2.67lbs foam with an impact speed of 1500 feet per second gives you a force of 3375000lbs or 1687.5 tons of force.
Sounds like a resonable explination for tile damage to me.

[leadpenny]

Imus was reading from a NY Times article earlier and, according to some NASA expert, the shuttle was going a little over 1500 MPH but the relative speed of the foam piece hitting the Columbia wing was something like 700 MPH. FWIW.

[Straight Vermonter]

What you are forgetting is that at the moment it broke off the was traveling at the same speed as the shuttle. Your equation should take into account not the speed of the shuttle but rather the relative speed of the shuttle to the foam.

[Cboldt]

By my calculations of 1/2 mass X velocity squared, the 2.67lbs foam with an impact speed of 1500 feet per second gives you a force of 3375000lbs or 1687.5 tons of force. Sounds like a resonable explination for tile damage to me.

First, your incorrect calculation of 0.5 x m x v**2 has a math error.

Second, you missed an important factor (I'll point it out below).

Third, Force is mass time acceleration, your equation is for kinetic energy. The amount of damage caused will certainly be affected by the amount of kinetic energy the object has, but this object did not give up all of its kinetic energy to the orbitor. Also, the amount of damage is sometimes dependent on the RATE the kinetic energy is given up.

OK, first, 1500*1500 = 2,250,000, times 2.67 is 6,007,500, and half of that is 3,003,750. But, this number is not a proper engineering calculation for kinetic energy. A common mistake made is to take a weight figure (2.67) and equate that to "mass." The two units (weight and mass) are not equivalent for calculating kinetic energy.

In order to convert between them (weight and mass), one uses the acceleration due to gravity, and using the units of choice, that unit is 32.2 feet per second per second. An object that exerts 2.67 pounds of force when resting on the earth has a mass of 0.0829 lb*sec*sec/ft (2.67 divided by 32.2). This same object is weightless in space, and would exert a heavier force if resting on Jupiter, etc.

Using the correct calculation of kinetic energy: 0.5 times 0.0829 lb*sec*sec/ft times 1500 ft/sec times 1500 ft/sec gives this moving object 93,300 foot-pounds of kinetic energy.

One can "figure" the units without using numbers, by the way, and it is a good thing to do to determine whether the calculation is giving an answer in the units you expect (e.g., are we looking for force, pressure, temperature, or something else?). In this case, the sec*sec in the numerator cancels the sec*sec in the denominator, the ft*ft in the numerator divided by the ft in the denominator leaves just ft in the numerator, so the final answer is expressed in ft-lb.

Check out The Physics Classroom.

[jlogajan]

By my calculations of 1/2 mass X velocity squared, the 2.67lbs foam with an impact speed of 1500 feet per second gives you a force of 3375000lbs or 1687.5 tons of force.

Ouch, as mentioned above by another poster, that's the kinetic energy equation, not the force of impact.

Force = mass times acceleration. The total kinetic energy is irrelevant -- only the change in kinetic energy, the acceleration or deceleration, is relevant. That would be highly influenced by strike angle.