Concept explainers
The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the wheels of car A, causing it to slide on the track. The brakes are not applied on the wheels of cars B or C. Knowing that the coefficient of kinetic friction is 0.35 between the wheels and the track, determine (a) the time required to bring the train to a stop, (b) the force in each coupling.
(a)
Find the time required to bring the train (t) to a stop.
Answer to Problem 13.130P
The time required to bring the train (t) to a stop is
Explanation of Solution
Given information:
The initial speed of the train
The coefficient of kinetic friction
The weight of the rail car A
The weight of the rail car B
The weight of the rail car C
The acceleration due to gravity (g) is
Calculation:
Show the impulse momentum diagram for the entire train as Figure (1).
Convert the initial speed of the train
Here,
Substitute
Calculate the masses of the rail cars A
Substitute
Calculate the mass of the rail car B
Substitute
Calculate the mass of the rail car C
Substitute
Calculate the frictional force acting on the car B after application of brakes
Substitute
Calculate the frictional force acting on the car C after application of brakes
Substitute
The brakes are not applied on the wheels of car A
Calculate the total mass of the train
Substitute
Calculate the frictional force acting on the car A after application of brakes
Substitute
The brakes are not applied on the wheels of car B and car C, so there is no frictional force acting on the car B and car C, that is
Here,
Calculate the total frictional force acting on the whole train
Substitute
The expression for the impulse acting on the train due to frictional force
Here, t is the time taken by the train to come to rest.
Substitute
Substitute
Therefore, the time required to bring the train (t) to a stop is
(b)
Find the force in each coupling.
Answer to Problem 13.130P
The force in AB
Explanation of Solution
Given information:
The initial speed of the train
The coefficient of kinetic friction
The weight of the rail car A
The weight of the rail car B
The weight of the rail car C
The acceleration due to gravity (g) is
Calculation:
Show the impulse-momentum diagram of rail car A as in Figure (2).
The expression for the impulse acting on the rail car A
Here,
The expression for the principle of impulse-momentum to rail car A alone as follows:
Substitute
Substitute
Show the impulse-momentum diagram of rail car C as in Figure (3).
The expression for the impulse acting on the rail car C
Here,
The expression for principle of impulse-momentum to car C alone as follows:
Substitute
Substitute
Therefore, the force in AB
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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