A sports car driver collided with a parked car. You have been hired to investiga

Question

A sports car driver collided with a parked car. You have been hired to investigate the accident. You found that the sports car driver left a 20m skid mark leading up to the parked car, then the cars became entangled in the collision (e=0) and they skidded together an additional 15m.

A) How fast was the sports car driver traveling when he applied the brakes? Was he exceeding the 80 km/hr speed limit?

B) What percentage of energy does the sports car lose due to impact? Only consider the energy dissipated during impact ( not the skidding before or after).

Explanation / Answer

using the impact method

m1 is the mass of the sport car

m1 V1 + m2 V2 = (m1+m2) V3

but V2 =0 because the second car wasnt moving

so

1000 V1= (1000 + 1000) V3

e=0

analysing forces during the impact

Ff (frcition)= 9.81x2000x0.5= 9810 N

F1= m1 v1/ t1

0=-9810+m1(v1/t1)=-9810+m1(v1/t1) is cero beacuse before the impact they dont move

v1/t1= 10 m

so we have

v1=9.904 m/s

t1=1 s

know we analyses the sport car as the same way before the impactt

m1(V1/t0) = m1(V0/t0)-Ff = 1000(9.9/t0)=1000(v0/t1) - (0.5)(1000)(9.81)

V0*t0=20 m

v0=16.0226 m/s = 57.67 km/h so is less than 80 km/h

t0=1.24824 s

know we return to

1000 V1= (1000 + 1000) V3

and using v1=9.9 m/s

v3= 4.95 m/s

analysing energy lost

Elost= (1/2)(m1)v0^2 -(1/2)(m1+m2)v3^2 / (1/2)(m1)v0^2 = 38.2%

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