(a) Find the speed of the entangled vehicles after the collision. m/s (b) Find t
ID: 2037139 • Letter: #
Question
(a) Find the speed of the entangled vehicles after the collision.
m/s
(b) Find the change in the velocity of each vehicle.
(c) Find the change in the kinetic energy of the system consisting of both vehicles.
J
Use the values from PRACTICE IT to help you work this exercise. Suppose the same two vehicles are both traveling eastward, the compact car leading the pickup truck. The driver of the compact car slams on the brakes suddenly, slowing the vehicle to 5.75 m/s. If the pickup truck traveling at 18.2 m/s crashes into the compact car, find the following.
(a) the speed of the system right after the collision, assuming the two vehicles become entangled
m/s
(b) the change in velocity for both vehicles
(c) the change in kinetic energy of the system, from the instant before impact (when the compact car is traveling at 5.75 m/s) to the instant right after the collision
?KE = J
Explanation / Answer
1)
let,
m1=1.74*10^3 kg and u1=15.5 m/sec
m2=9.5*10^2 kg and u2=-15.5 m/sec
a)
by using conservation momentum,
m1*u1+m2u2=(m1+m2)*v
1.74*10^3*15.5 + 9.5*10^2*(-15.5) = (1.74*10^3 + 9.5*10^2)*v
====> v=4.55 m/sec
speed of the entangled vehicles, v=4.55 m/sec
b)
dv_truck=v-u1
dv_truck=4.55-15.5 = -10.95 m/sec
and
dv_car=v-u2
dv_car=4.55-(-15.5) = 20.05 m/sec
c)
change in K.E=K2-K1
=1/2*(m1+m2)v^2 - (1/2*m1*u1^2+1/2*m2*u2^2)
=1/2*(1.74*10^3+9.5*10^2)*4.55^2 - (1/2*1.74*10^3*15.5^2 + 1/2*9.5*10^2*(-15.5)^2)
=-295291.387 J
2)
let,
m1=1.74*10^3 kg and u1=18.2 m/sec
m2=9.5*10^2 kg and u2=5.75 m/sec
a)
by using conservation momentum,
m1*u1+m2u2=(m1+m2)*v
1.74*10^3*18.2+ 9.5*10^2*5.75 = (1.74*10^3 + 9.5*10^2)*v
====> v=10.147 m/sec
speed of the entangled vehicles, v=10.147 m/sec
b)
dv_truck=v-u1
dv_truck=10.147-18.2 = -8.053 m/sec
and
dv_car=v-u2
dv_car=10.147-5.75 = 4.397 m/sec
c)
change in K.E=K2-K1
=1/2*(m1+m2)v^2 - (1/2*m1*u1^2+1/2*m2*u2^2)
=1/2*(1.74*10^3+9.5*10^2)*10.147^2 - (1/2*1.74*10^3*18.2^2 + 1/2*9.5*10^2*(5.75)^2)
=-165400.123 J
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