Driving Mathematics Question

[CL8]

Using the formula for kinetic energy, 1/2 mass x velocity squared

using a car with a mass of 100, going at :

1. 10mph: 50x100= 5000

2.15mph: 50x225=11250


First am I correct in saying the impact of a collision is 2 1/4 times greater at 15mph than at 10mph using this formula?

And does anyone know what the unit of energy is called in this formula
(would it be 5000 joules of energy @ 10mph or something else?)

reason for the question is a page I'm building on suburban driving:

http://www.drivingtips.org/suburban-streets.html


Thanks,
cl8

[CL8]

I guess no one is interested in, or no one knows the answers to this physics of driving question.
Anyone know where I could find the answer?

cl8

[Blt2Lst]

Originally Posted by CL8

I guess no one is interested in, or no one knows the answers to this physics of driving question.
Anyone know where I could find the answer?

cl8

Have you tried a college physics textbook?

[RahX]

Or google. I would think the outcome would be exponential but not by that much. The basic formula is correct but it just seems like something is missing.

[MagicRat]

Originally Posted by CL8

Using the formula for kinetic energy, 1/2 mass x velocity squared

using a car with a mass of 100, going at :

1. 10mph: 50x100= 5000

2.15mph: 50x225=11250


First am I correct in saying the impact of a collision is 2 1/4 times greater at 15mph than at 10mph using this formula?

And does anyone know what the unit of energy is called in this formula
(would it be 5000 joules of energy @ 10mph or something else?)

You are absolutely correct. Your formula is accurate, as is your conclusion.
The easiest way to express it is" when your speed doubles, the energy increases four times".

Fundamentally this explains why your car accelerates much more slowly at highway speed than from a standing stop, and why stopping distances at high speed are so much longer than at low ones.

It also explains why car crashes at highway speeds are so much more deadly than those at lower speeds. If you double the speed of the car, the car has 4 times the amount of kinetic energy which must be dissipated either in a crash or by the brakes.

Finally, joules is the best measurement of kinetic energy, imo.

[jdmccright]

Units of speed are miles/hr...mass is lbs. If E=1/2mv^2, your units for E in your calculation are lbs-miles^2/hr^2

The more common English units would be foot-pounds-force (ft-lbf). Joules is metric based so you'd have to convert your starting values appropriately.

Staying in English, 10 mph converts to 14.67 ft/sec (multiply by 5,280, divide by 3600)

Thus, E= 1/2(100 lbs) x (14.67 ft/sec)^2 = 10,755 lb-ft^2/sec^2

Divide by gravitational acceleration and you get to 334.0 ft-lbf for a 100-lb body moving at 10 mph.

Similarly for the same body moving at 15 mph you get 751.6 ft-lbf.

It's the squared term that makes the difference. It rises exponentially with speed.

[curtis73]

Math... hurting... brain. Must... drink .... beer

Carry on

[CL8]

Originally Posted by Blt2Lst

Have you tried a college physics textbook?

I just ordered a physics text book from Amazon!

[CL8]

Originally Posted by jdmccright

Divide by gravitational acceleration and you get to 334.0 ft-lbf for a 100-lb body moving at 10 mph.

Similarly for the same body moving at 15 mph you get 751.6 ft-lbf.

It's the squared term that makes the difference. It rises exponentially with speed.

Thanks jdmccright and all the rest of you for your input.


I have never heard of "foot-pounds-force" before.
I'll have to research that one!

[jdmccright]

*Places bucket on Curtis' head to contain explosion*

Pounds is the mass of the object. Pounds-force is self-explanatory...it is the force exerted by a mass due to gravitational acceleration. A 1-lb mass resting on the ground exerts 32.2 lbf on the ground (gravitational acceleration being 32.2 ft/sec^2). Place that weight on a 1-ft long torque wrench and you'd exert 32.2 ft-lbf on the bolt. This is what is measured by a torque wrench.

1 lbf is equal to 4.45 Newtons (for you SI thinkers).
1 ft-lbf is equal to 1.356 Joules, 0.323 calories, or 1.29x10-3 BTUs

*Hands Curtis sponge to clean up mess, places bucket in biohazard bin*

This is the s**t I deal with alot...lost my brain long ago...yes, beer helps alot.

[curtis73]

I have learned 6 bazillion things after reading Milliken's Race Car Vehicle Dynamics. It is a physics/engineering textbook that contains a monstrous amount of calculus, but it also contains easily understandable text and graphic demonstration. Its 860-some pages, but I actually read it cover to cover over a 5-day period on a train ride. Talk about brain hurt.

Its out of print, but you should be able to find it on Amazon used. I think I paid $150 for mine, but it was something ridiculous like $500 new. Worth every penny. Put it this way... it gave me a firm enough grasp of the physics of suspension geometry that I was recruited to consult on a design for the suspension on a Chinese electric car.*

*that's not saying much... the suspension was terrible to start with - I could have added duct tape and improved it

[Alastor187]

Originally Posted by jdmccright

Pounds is the mass of the object. Pounds-force is self-explanatory...it is the force exerted by a mass due to gravitational acceleration. A 1-lb mass resting on the ground exerts 32.2 lbf on the ground (gravitational acceleration being 32.2 ft/sec^2). Place that weight on a 1-ft long torque wrench and you'd exert 32.2 ft-lbf on the bolt. This is what is measured by a torque wrench.

I would add that Imperial/US Customary units really are a lot of work (no pun intended) to use.

From a technical stand-point 1-lb mass can be represented in either pound-mass, lbm, or slugs. Slugs would really follow the equation noted above, where 1 slug * 32.2 ft/s² = 32.2 lbf.

While 1 lbm = 1 lbf and it is assumed that gravity equals the gravitational constant (i.e. ~32.2 ft/s²).

This is very convenient for a lot problems because it makes converting from lbm to lbf very easy, basically substituting units. However, the trade off is that if you need to calculate the mass or force when acceleration isn't equal to the gravitational constant, you have to scale accordingly [i.e. F = m*a doesn't work, you have to use F = m*(a/g_constant)]

It should also be noted that for the torque that is generated by the weight, the 32.2 ft-lbf is a measure of torque (which is a special kind of force) and does not represent energy or work even though the units appear to be the same. This is clarified in the SI system where a meter*newton = joule (energy/work) but Newton-meter = units of torque (force). No clarification has been standardized, that I know of, for the Imperial/US Customary system of units.

[jdmccright]

Point taken...ft-lbf is a unit for work (Force x Distance) or torque not energy, which is what was originally asked. My oops. And I avoided using slugs to keep it simple...English units are maddening enough to keep track of as it is. Carry on....

[RahX]

I'm not sure you caught that right jdmccright. Force over a distance is a representation of torque and is not work or energy. Torque applied to something does nothing, does not move anything, it just is force applied.

[jdmccright]

Another oops. Torque translates to work only after a wrench is moved though an angle. Once you move a mass, work has been done. Until then it is only a force. Good catch.