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 cars B and C, causing them to slide on the track. The brakes are not applied on the wheels of car A. 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 13.129P
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 total frictional force acting on the whole train
Substitute 0 for
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.
Use the principle of impulse-momentum to the entire train to find the time taken by the train to stop by application of brakes.
The expression or the principle of impulse-momentum as follows:
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 13.129P
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
Want to see more full solutions like this?
Chapter 13 Solutions
VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
- 2- The two blocks shown are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and assuming that the coefficients of friction between block A and the horizontal surface are µz = 0.25 and u = 0.20, determine (a) the acceleration of each block, (b) the tension in the cable.arrow_forwardThe two blocks shown are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and knowing that the coefficients of friction between the blocks and the inclines are ls = 0.25 and = 0.2, determine (a) the acceleration of each block, (b) the tension in the cable. 200 lb 90° 20° 300 lb Вarrow_forwardA tractor-trailer rig with a 2000-kg tractor, a 4500-kg trailer, and a 3600-kg trailer is traveling on a level road at 90 km/h. The brakes on the rear trailer fail, and the antiskid system of the tractor and front trailer provide the largest possible force that will not cause the wheels to slide. Knowing that the coefficient of static friction is 0.75, determine (a) the shortest time for the rig to a come to a stop, (b) the force in the coupling between the two trailers during that time. Assume that the force exerted by the coupling on each of the two trailers is horizontal.arrow_forward
- The system shown is at rest when a constant 150-N force is applied to collar B. Neglecting the effect of friction, determine (a) the time at which the velocity of collar B will be 2.5 m/s to the left, (b) the corresponding tension in the cable.arrow_forwardBoxes A and B are at rest on a conveyor belt that is initially at rest. The belt is suddenly started in an upward direction so that slipping occurs between the belt and the boxes. Knowing that the coefficients of kinetic friction between the belt and the boxes are (μk) A= 0.30 and (μk)B= 0.32, determine the initial acceleration of each box.arrow_forwardIn order to determine the weight of a freight train of 40 identical boxcars, an engineer attaches a dynamometer between the train and the locomotive. The train starts from rest, travels over a straight, level track, and reaches a speed of 30 mi/h after three minutes. During this time interval, the average reading of the dynamometer is 120 tons. Knowing that the effective coefficient of friction in the system is 0.03 and air resistance is negligible, determine (a) the weight of the train (in tons), (b) the coupling force between boxcars A and B.arrow_forward
- The carnival ride from Prob 12.51 is modified so that the 80-kg riders can move up and down the inclined wall as the speed of the ride increases. Knowing that the coefficient of static friction between the wall and the platform is 0.2, determine the range of values of the constant speed v0 for which the platform will remain at h = 1.5 m.Reference to Problem 12.51:arrow_forwardA truck is hauling a 2200-lb log out of a ditch using a winch attached to the back of the truck. Knowing the winch applies a constant force of 2500 lb and the coefficient of kinetic friction between the ground and the log is 0.36, determine the time for the log to reach a speed of 5 ft/s. 20° The time is s.arrow_forwardA 2000-kg automobile starts from rest at point A on a 6° incline and coasts through a distance of 150 m to point B. The brakes are then applied, causing the automobile to come to a stop at point C , which is 20 m from B . Knowing that slipping is impending during the braking period and neglecting air resistance and rolling resistance, determine (a) the speed of the automobile at point B, (b) the coefficient of static friction between the tires and the road.arrow_forward
- The two blocks shown are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and knowing that the coefficients of friction between the blocks and the inclines are us = 0.25 and uk = 0.2, determine (a) the acceleration of each block, (b) the tension in the cable. 200 lb A 90° 20° 300 lb Barrow_forwardA block A of 60.0 lb is connected to a block B of 10.0 lb by means of a rope and an ideal pulley. The system is released from rest. Between block A and the surface, there is a coefficient of kinetic friction of 0.10. Block A has descended 5.00 ft. At this moment, determine: a. The displacement of block B.b. The magnitude of the tension in the rope.c. The speed of block B.d. The speed of block A.arrow_forwardA baggage conveyor is used to unload luggage from an airplane. The 10-kg duffel bag A is sitting on top of the 20-kg suitcase B . The conveyor is moving the bags down at a constant speed of 0.5 m/s when the belt suddenly stops. Knowing that the coefficient of friction between the belt and B is 0.3 and that bag A does not slip on suitcase B, determine the smallest allowable coefficient of static friction between the bags.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY