A 1130 kg car traveling initially with a speed of 26.80 m/s in an easterly direc
ID: 1732179 • Letter: A
Question
A 1130 kg car traveling initially with a speed of 26.80 m/s in an easterly direction crashes into the back of a 9510 kg truck moving in the same direction at 20.0 m/s. The velocity of the car right after the collision is 18.0 m/s to the east.
(a) What is the velocity of the truck right after the collision? (Give your answer to at least four significant figures.)
(b) What is the change in mechanical energy of the car-truck system in the collision?
I put 19794.592 (incorrect)
Explanation / Answer
a)
m1 = 1130 Kg
m2 = 9510 Kg
v1i = 26.8 m/s
v2i = 20 m/s
v1f = 18 m/s
use conservation of momentum
initial momentum = final momentum
m1*v1i + m2*v1i = m1*v1f + m2*v2f
1130 * 26.8 + 9510 * 20.0 = 1130 * 18 + 9510 * v2f
30284 + 190200 = 20340 + 9510 * v2f
200144 = 9510 * v2f
v2f = 21.05 m/s
Answer: 21.05 m/s
b)
Initial KE = 0.5*m1*v1i^2 + 0.5*m2*v2i^2
= 0.5*1130*(26.8)^2 + 0.5*9510*(20)^2
= 2.3078*10^6 J
final KE = 0.5*m1*v1f^2 + 0.5*m2*v2f^2
= 0.5*1130*(18)^2 + 0.5*9510*(21.05)^2
= 3.93534*10^5 J
change = 2.3078*10^6 J - 3.93534*10^5 J
= 1.9143*10^6 J
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