Problem 2: [20 points] (Car crash.) You are driving in a subcompact car (mass of

Question

Problem 2: [20 points] (Car crash.) You are driving in a subcompact car (mass of 1000 kg) at a speed of 15.0 m/s when you have the misfortune to experience a head-on collision with an SUV of mass 2000 kg traveling at a velocity of 22.5 m/s. As a result of the collision, the vehicles stick together. a) Determine the velocity of the stuck-together vehicles immediately after the collision. b) Determine the change in kinetic energy due to this collision. Where did the missing energy go? c) Fortunately for you, the subcompact car is equipped with airbags and you were wearing a seatbelt. Take your mass to be 50.0 kg. The duration of the collision (during which the front ends of both vehicles get crushed) is 0.250 s. What average force do you experience during the collision? (This force is provided by the seatbelt and airbag working together.)

Explanation / Answer

a)we use law of conservation of linear momentum,

m1v1i+m2v2i=(m1+m2)*vf

vf= [m1v1i+m2v2i]/(m1+m2)

Plugging values,

vf=(1000*15.0-2000*22.5)/(1000+2000)

vf= -20m/s ……………..directed in the direction of initial velocity of SUV(m2) or v2i

b)

KE =KEf-KEi= ½*(m1+m2)*vf^2 – [½*m1*v1i^2+1/2*m2*v2i^2]

Plugging values,

KE = ½*(1000+2000)*-10^2 – [1/2*1000*15^2 -1/2*2000*22.5^2]

KE = -4.7*10^5 J

Missing heat is converted into heat.

c)

Let us first find acceleration, vf=-10m/s, vi=15m/s, t=0.250s

a=(vf-vi)/t =

a=(-10.0-15.0)/0.250

a= -100m/s^2

F=ma= 50.0*-100 = -5000m/s^2

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