(A) Find the final speed after collision.Let m 1 and v 1 i represent the mass an
ID: 1461666 • Letter: #
Question
(A) Find the final speed after collision.Let
m1
and
v1i
represent the mass and initial velocity of the pickup truck, while
m2
and
v2i
pertain to the compact. Apply conservation of momentum.
Substitute the values and solve for the final velocity, vf.
(B) Find the change in velocity for each vehicle.
Change in velocity of the pickup truck.
v1 = vf v1i = 5.00 m/s 15.0 m/s = 10.0 m/s
Change in velocity of the compact car.
v2 = vf v2i = 5.00 m/s (15.0 m/s) = 20.0 m/s
(C) Find the change in kinetic energy of the system.
Calculate the initial kinetic energy of the system.
Calculate the final kinetic energy of the system and the change in kinetic energy, KE.
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REMARKS During the collision, the system lost almost 90% of its kinetic energy. The change in velocity of the pickup truck was only 10.0 m/s, compared to twice that for the compact car. This example underscores perhaps the most important safety feature of any car: its mass. Injury is caused by a change in velocity, and the more massive vehicle undergoes a smaller velocity change in a typical accident.
PRACTICE IT
(c) Find the change in the kinetic energy of the system consisting of both vehicles.
J
EXERCISEHINTS: GETTING STARTED | I'M STUCK!
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 5.42 m/s. If the pickup truck traveling at 17.0 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 5.42 m/s) to the instant right after the collision
KE = J
Explanation / Answer
PRACTICE IT
A) Apply conservation of momentum.
Substitute the values and solve for the final velocity, vf.
b)
Change in velocity of the pickup truck.
v1 = vf v1i = 5.00 m/s 14.8 m/s = 9.8 m/s
Change in velocity of the compact car.
v2 = vf v2i = 5.00 m/s (14.8m/s) = 19.8 m/s
c) KEi =0.5 ( m1v1i2 + m2v2i2) =0.5 * [ (1.81 103 kg)(14.8 m/s)2 +(9.08 102 kg)(14.8 m/s)2 ]=297675 J
KEf = 0.5 (m1 + m2)vf2
(1.81 103 kg + 9.08 102 kg)(4.911 m/s)2
=65552.5 J
KE = KEf KEi = 232122.5 J
GETTING STARTED | I'M STUCK!
A) Apply conservation of momentum.
Substitute the values and solve for the final velocity, vf.
b)
Change in velocity of the pickup truck.
v1 = vf v1i = 13.13 17 m/s = 3.87m/s
Change in velocity of the compact car.
v2 = vf v2i = 13.13 m/s (5.42m/s) = 7.17 m/s
c) KEi =0.5 ( m1v1i2 + m2v2i2) =0.5 * [ (1.81 103 kg)(17 m/s)2 +(9.08 102 kg)(5.42 m/s)2 ]=274881 J
KEf = 0.5 (m1 + m2)vf2
0.5*(1.81 103 kg + 9.08 102 kg)(4.911 m/s)2
=43725.79J
KE = KEf KEi = 231155.2 J
pi = pf m1v1i + m2v2i = (m1 + m2)vfRelated Questions
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