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Understanding statics and dynamics is essential in solving many engineering mechanics problems. These areas examine the forces and moments acting on bodies and how they affect motion. Statics is about analyzing forces on objects that remain at rest, effectively balancing these forces so no movement occurs. Dynamics, conversely, focuses on objects in motion and accounts for how forces impact velocity and acceleration. In the context of a locomotive with a snowplow, dynamics plays a crucial role as it deals with forces acting on the moving train. Thus, understanding these principles helps engineer systems to control and utilize forces for desired motion outcomes, such as resisting added forces from accumulated snow.

The mass flow rate is a critical concept when dealing with fluids or mixtures, like snow being collected by a plow. It measures how much mass of a substance passes through a given area over a specified time. To find it, multiply the volume flow rate by the density or specific weight of the substance. For the locomotive, the mass flow rate equals the volume flow rate of snow collected (10 ft³/s) times the specific weight of snow (6 lb/ft³), giving 60 lb/s. This calculation helps determine the magnitude of the forces involved as the train scoops up the snow, affecting how it moves and reacts to resistive forces.

Resistance to motion refers to forces that oppose movement, requiring energy to overcome. In scenarios involving locomotives, various factors contribute to resistance, including friction, air drag, and external forces like snow plowing. When the locomotive's plow gathers snow, the resistance arises mainly from the momentum change in the snow. This resistance can be calculated by multiplying the mass flow rate of the snow by the speed of the train. Here, it's calculated as 60 lb/s times 12 ft/s, resulting in a resistance force of 720 lb. This opposing force must be offset by increasing engine power to maintain speed.

Specific weight is the weight per unit volume of a material. For snow, it describes how heavy a given volume is, essential for calculations involving mass and force. Typically, the specific weight of snow varies based on its density, which can change with moisture content and compaction. In this problem, the specific weight of snow (\( \gamma_{s}=6 \, \mathrm{lb/ft^{3}}\)) is crucial for determining the mass of snow collected by the train's plow. It ensures accurate computation of the forces acting against the train. Such calculations are indispensable in engineering applications where precise load and resistance estimations are needed.