Inelastic collisions in two dimensions

[jmw2112]

A light passenger vehicle weighing 1470 N collides with a train engine weighing 1.23 x 105
N, which was being moved from one rail siding to another. The train engine and the vehicle were entangled after the accident and from your measurements you have been able to determine they skidded 15 m before finally coming to rest at an angle of 68 degress to the crossing. The co-efficient of friction between the vehicle’s tyres and wet road surface
are 0.25. The eyewitness reports highlight the passenger vehicle drove straight through the stop sign and ignored the warning horn blasts of the train and continued onto the railway level crossing without due care. You need to ascertain the vehicle’s actual entrance speed to the crossing and whether the driver has exceeded the speed limit of 60 km/hr?

 

[jbsteele]

The frictional force acting between the vehicle and the road is equal to F = μmg = 0.25(1470)(9.8) = 3585.5 N.The initial kinetic energy of the vehicle is equal to 1/2mv^2 = 1/2(1470)(v^2)The final kinetic energy of the vehicle is equal to 1/2mv^2cos^2θ + 1/2Iω^2 = 0The total energy is conserved, so:1/2(1470)(v^2) = 1/2(1470)(v^2)cos^2θ + (1/2)(mv^2sin^2θ)v^2 = 2v^2cos^2θ + 2v^2sin^2θv^2 = v^2cos2θ + v^2sin2θv^2 = v^2(cos^2θ + sin^2θ)v^2 = v^2Therefore, v = √(2v^2cos^2θ) = √(2(3585.5)(cos^2 68)) = 60 km/hrTherefore, the driver has exceeded the speed limit of 60 km/hr.