Physics

Problem

A research trolley of mass

1.2\times10^{3}\,\text{kg}

is connected to two instrument wagons of masses

6.0\times10^{2}\,\text{kg}

and

4.0\times10^{2}\,\text{kg}

respectively. The three vehicles move together on a straight horizontal test track. During a trial run the trolley’s propulsion system delivers a constant forward force

F

while the total horizontal resistive force acting on the whole system is measured as

3.0\times10^{3}\,\text{N}

. The resulting acceleration of the train is found to be

1.5\,\text{m\,s}^{-2}

. (a) Write an expression for the net horizontal force acting on the system in terms of

F

. (b) Using the measured acceleration, derive an equation to obtain the value of

F

. (c) Calculate the magnitude of the propulsion force

F

. (d) Engineers intend to add an extra wagon of mass

8.0\times10^{2}\,\text{kg}

while keeping the same propulsion force

F

and with the resistive force unchanged. Compute the new acceleration that would result, showing all steps clearly.

Intuitive explanation

This problem is about applying Newton's second law to a system of connected objects moving together. The key insight is that you can treat the entire train as one combined mass when finding the net force and acceleration, then use $F_{\text{net}} = ma$ to relate the driving force, resistance, and motion. Once you find the propulsion force from the initial scenario, you can predict how adding mass changes the acceleration while keeping the driving force constant.

Intuitive explanation

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