An engine pulls a train of 20 freight cars, each having a mass of 5.0 ×10^4 kg, with a constant

step 1 In this problem we have given the car moves from rest to a speed of 4 meter per second that mean

An engine pulls a train of 20 freight cars, each having a...

An engine pulls a train of 20 freight cars, each having a mass of $5.0 \times 10^{4} \mathrm{kg},$ with a constant force. The cars move from rest to a speed of $4.0 \mathrm{m} / \mathrm{s}$ in $20.0 \mathrm{s}$ on a straight track. Ignoring friction, find the force with which the tenth car pulls the eleventh one (at the middle of the train).

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Key Concepts

Kinematics

Kinematics involves the study of motion without considering its causes. In this context, it is used to compute the acceleration of the train by relating the change in velocity to the time over which the change occurs. The constant acceleration can be found by dividing the final speed by the time taken, providing a necessary ingredient for further analysis with dynamics.

Newton's Second Law

Newton's Second Law (F = m × a) is central to solving problems involving forces and motion. It relates the net force acting on an object to the product of its mass and acceleration. In this problem, it is used to determine the total force required to accelerate the entire train, as well as to analyze the force transmitted between individual connected cars.

Force Distribution in Connected Systems

When multiple objects are connected and accelerate together, the force applied is transmitted through the connections between objects. This concept is important in determining the force exerted by one car on the next. In the scenario described, the force that one car (the tenth) exerts on the subsequent car (the eleventh) is responsible for accelerating all of the cars behind it. This analysis involves applying Newton's Second Law to the subset of the train for which that force is responsible.

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