A freight train consists of two 8.00 x 104-kg engines and 45 cars with average masses of 5.00 x 104 kg. (a) What force (in N) must each engine exert backward on the track to accelerate the train at a rate of 4.00 x 10-2 m/s² if the force of friction is 7.20 x 105 N, assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. N (b) What is the force (in N) in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines? N

A car weighing 2.5 metric tons and traveling at 90 km/h hits a 500 m long stretch of black ice. Unfortunately, due to skidding, neither accelerating nor braking has any effect on the speed! The driver manages to maintain steady straight direction of motion and the only impact is provided by the ice friction force, which is numerically equal to 4v² Newtons, where the velocity v of the car is measured in m/sec. (a) Using Newton's Second Law F = ma, set up a mathematical model for the position x(t) and velocity v(t) of the car as functions of time t. Start by drawing a diagram and choosing a consistent system of units based on kg, m, sec (1 ton = 1000 kg, 1 m/sec = 3.6 km/h, 1 N = 1 kg · m/sec²). Introduce and label the variables, show the units and write down the differential equations and the intial conditions. (b) Use the model in part a to calculate v(t) and x(t). Fully show the process of solving the initial value problems. (c) Based on your work so far, how long will it take to pass…

The Omani "Noor Majan" car is of mass (M) kg is going up Jabal Akhdar, at angle (θ), with (N) people inside the car each of (mp) kg. The car model provides (L) Newtons of lift, and it is accelerating up at (a) m/s2. The road provides a coefficienct of kinetic friction (μk). What is the force exerted by the engine? [Hint: This question has no numbers. Your answer needs to be an equation.]

A freight train has a mass of 1.1 ✕ 107 kg. If the locomotive can exert a constant pull of 7.4 ✕ 105 N, how long does it take to increase the speed of the train from rest to 74 km/h?