Force and Energy to Move a Pickup Truck?

The calculations must be watertight to stick in a court of law. All factors must be included in the formula.

Was the handbrake on?

Condition of brakes?

Was it in a gear?

Was it a single bump or sticky (continues , pushing ) bump?

Any brake or skid marks before or after contact?

Amount of deformation on both trucks? (energy absorbed?)

Did the nose of the small truck went underneath the loading area of big truck?

Was some of the wheels lifted?

Gradient of area?

Type of road surface?

Interesting problem of the type that is conceptually easy but practically difficult. Since some of the small vehicle's energy is lost due to metal deformation, the sliding friction is probably non linear and some movement may have been vertical. It's probably impossible to solve with out some real world testing. Jeff

Forget about calculations. Take a look at the aggressor's truck speedometer - maybe was broken during the crash and froze it's speed.

The kind of information you're looking for is available at the truck manufacturer where various crash tests are performed. Show them your pictures and they may give you the best estimate of those parameters. Hendrik is perfectly right - try to provide those answers too.

Some vehicles have a "Black box" in them, that will record vehicle statistics prior to a crash. It might be worth looking into retrieving this data if the vehicles had them.

Try this thought experiment. Lock up your brakes on gravel or on a new bitumen road, you'll slide different distances. Crash your car into a wall square on or at an angle, you'll experience a different decceleration profile. Kick a football straight up or flat, It'll go a different distance for the same energy in.

Any estimate of the small vehicle's initial velocity will have assumptions built in that render it suspect. Especially if it's in a court, where a lawyer will add a further layer of doubt and confusion. Jeff

Greg,

I don't have the formulas or at least I'm not sure. But unlike the last proposed "thought experimenter", I think you'll be able to apply the appropriate classic physics formulas to get a reliable answer, that is within 5%. I think one is F=MA. One has to do with force increasing by velocity squared. The coefficient of friction, with the appropriate mass and distance will equal the applied force, or something to that effect, and since you can probably measure the coefficent of friction for that truck on that road under the conditions it was under it shouldn't be that difficult.

My seat of the pants guess is that whoever it was driving the small car, was going way to fast and by way more than 5%. Basically check the stopping distance tables that you can find for various vehicles,...(his vehicle?) is one third the weight so to move (yours?) at the speed that is required for you to stop (37ft) he has to be moving at a speed ( obviously faster so that your mass times your (velocity sq ?)=his mass times his velocity sq?),...and add to his velocity the energy not transfered to yours by non-resilient crunching, which can also be reasonably determined by manufacturers crash tests. The time your vehicle was skidding 37 feet was probably under 3 sec....(again thats just a no math guess), but the pretty exact time won't be hard to determine either.

The factors that the previous post mentions, even taken to extremes, should be pretty provable, to be quite minor. Anyway the conditions of the road can probably be factually determined. classic Newtonian Physics (IF THEY CAN LAND A MAN ON THE MOON???!!!).

gEOFFREY rEED

Geoff

The chances are that immediately after impact the two vehicles will continue moving together, so the joint speed immediately after impact will be about quarter of the original speed of the smaller vehicle. This can usually be confirmed from the damage profile on the vehicles.

But we also need to find the post-impact speed from the distance the pair take to stop after that. If they separate before coming to rest, it is likely that the smaller vehicle had its brakes on fully, but the larger vehicle did not. The original speed can be determined by how firmly the brakes were set and the types of tyres. One common method to verify this is to look at the skidmarks created by the vehicles and the type and condition of the tyres (and the road conditions at the time).

BTW, if the vehicles moved together, and both vehicles' brakes were applied on all wheels, the ground was flat, and the conditions were good, the smaller vehicle could have been travelling at over 100-m.p.h. But that is probably a worst case, as there could have been some rebound, and hand-brakes do not always lock all four wheels. (Presumably you have taken the loads of the vehicles into account when assessing their weights)