Question

A 36500 lb engine is pulling two freight cars up a 2.4 % incline. The weight of the first freight car is 36500 lbs, and the weight of the second freight car is 10000 lbs. The train is accelerating at 0.43 ft/s2 as it goes up the hill.

Oooooooo A 36500 lb engine is pulling two freight cars up a 2.4 % incline. The weight of the first freight car is 36500 lbs, and the weight of the second freight car is 10000 lbs. The train is accelerating at 0.43 ft/s2 as it goes up the hill. NOTES IMAGES DISCUSS UNITS STATS HELP PREFERENCES Answer Chk Part Description History 16.67 pts. 100% What is the force in the coupling between the engine and freight car #1? (include units with answer) # tries: 0 Show Details Format Check 2% try penalty Hints: 0,0 16.67 pts. 100% What is the force in the coupling between freight car #1 and freight car #2? (include units with answer) # tries: 0 Show Details Format Check 2% try penalty

Answer 1

First let us convert the units to SI units-

The 2.4 % inclination means tan (theta) = 0.024 => theta = 1.375 deg

35500 lbs = 16556 kg

10000 lbs = 4536 kg

0.43 ft / s² = 0.13 m /s².

A) If we consider the first and second freight car as one unit, the total mass = 16556 + 4536 kg = 21092 kg

The forces acting on this unit are- the tension in the link between engine and first freight car up the slope, and the gravitational force component down the slope. Net force is-

F_net = T1- mg sin (theta) = T1 - 21092 x 9.8 x sin (1.375) = T1 - 4960 N

This causes an acceleration of 0.13 to the combined mass of the freight cars. Thus from newton's second law-

F_net = mass x acceleration

T1- 4960 = 21092 x 0.13

Therefore, T1 = 2742 N

B) Using similar steps as in the previous part-

We consider the forces on the second freight car only, and apply Newton's 2nd law-

F_net = (mass of freight car #2) x acceleration

F_net = T2 - mg sin (theta) = T2 - 4536 x 9.8 x sin (1.375) = mass x acc = 4536 x 0.13

Therefore, T2 = 590 + 1067

T2 = 1656 N