A car with mass m_c = 1074\ kg is traveling west through an inte

Arthur Pratt

Arthur Pratt

Answered question


A car with mass mc=1074 kg is traveling west through an intersection at a magnitude of velocity of vc = 15 m/s when a truck of mass mt=1593 kg traveling south at vt=10.8 ms fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficient of friction of μk=0.5.
a)Write an expression for the velocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and j.
b)How far, in meters, will the vehicles slide after the collision?

Answer & Explanation

Mary Herrera

Mary Herrera

Beginner2021-12-20Added 37 answers

Given information:
The mass of the car (mc)=1047 kg
The velocity of the car (vc)=15 ms=15 i ms (consider east as +ve x direction or +ve i)
The mass of the truck (mt)=1593 kg
The velocity of the truck (vt)=10.8 ms=10.8 j
According to law of conservation of momentum the momentum in all the direction is conserved, considering the along the "i" direction we can write:
Now, consider the momentum conservation along the "j" direction:
Therefore, the velocity of the vehicles after the collsion is:
By substituting the correspondingvalues, we get the velocity of the vehciles after the collision as:
V=6.04i^6.45j^|V|=8.836 ms
After the collision the cinetic energy of the both vehicles combined will be utilized to do work against the dricion force (given μk=0.5), The friction force both the vehicles is given by:
f=μk(mc+mt)g=0.5(1074+1593)9.81=13081.635 N
Now, according to work energy theorem the we can write:
Where "d" is the distance travelled by the wreckage after the collision. Substituting the corresponding values, we get:
d=1074+15932(13081.635)×(8,836)2=7.958 m
Hence, the distance travelled by the wreckage after the collsion is 7.958 m.

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