Concept explainers
Three identical cars are being unloaded from an automobile carrier. Cars B and C have just been unloaded and are at rest with their brakes off when car A leaves the unloading ramp with a velocity of 5.76 ft/s and hits car B, which hits car C. Car A then again hits car B. Knowing that the velocity of car B is 5.04 ft/s after the first collision, 0.630 ft/s after the second collision, and 0.709 ft/s after the third collision, determine (a) the final velocities of cars A and C, (b) the coefficient of restitution for each of the collisions.
Fig. P14.105
(a)
Find the final velocity of the car A and C.
Answer to Problem 14.105RP
The final velocity of the car A and C are
Explanation of Solution
Given information:
Consider the mass of car A, car B, and C is denoted by m.
The initial velocity of the car is
The initial velocity of the car B and C is zero.
The velocity of the car B after the first, second and third collisions are
Calculation:
The Horizontal momentum of the system is conserved as no horizontal force is acting on the system.
Show the Event
Refer to Figure 1.
Show the conservation of horizontal momentum as follows:
Substitute
Show the Event
Refer to Figure 2.
Show the conservation of horizontal momentum as follows:
Substitute
Thus, the final velocity of the car C is
Show the Event
Refer to Figure 3.
Show the conservation of horizontal momentum as follows:
Substitute
Thus, the final velocity of the car A is
(b)
Find the coefficients of restitution of each collision.
Answer to Problem 14.105RP
The coefficients of restitution of first, second and third collision are
Explanation of Solution
Given information:
Calculation:
Refer Part (a).
Consider the coefficient of restitution corresponding to collision Event
Calculate the coefficient of restitution corresponding to collision Event
Substitute
Calculate the coefficient of restitution corresponding to collision Event
Substitute
Calculate the coefficient of restitution corresponding to collision Event
Substitute
Thus, the coefficients of restitution of first, second and third collision are
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