# How to Calculate the Force Needed to Move a Railroad Car ••• Thinkstock Images/Comstock/Getty Images

Railroad cars are used to move a wide range of materials across the United States. Hopper cars carry coal from the mines in Wyoming to coal-fired plants on the East Coast. Automobile transport cars move new vehicles from assembly plants to distribution centers across the country. Passenger cars carry commuters and long-distance travelers between cities and across states. Railroad cars can carry a significant amount of weight, but railroads have to determine how many and what types of engines to use, based on the weight of the cargo being hauled. Calculating the force needed to move a railroad car from rest is a straightforward process, using a few calculator keystrokes.

## Calculate the Force Needed to Move a Railroad Car

Determine the coefficient of friction between the car wheels and the rail. This coefficient (?) can either be selected theoretically from a table, or it can be measured experimentally. The coefficient of rolling friction is much lower than the coefficient of static friction, which would apply if the wheel were not allowed to rotate and would have to slide. The coefficient of rolling friction for a wheel-rail interface is approximately 0.001, while the coefficient of static friction for a steel-on-steel interface is approximately 0.5. Therefore, it requires far less force to move a rail car with freely moving wheels than one with the wheels locked.

Determine the friction force (F) that the rail car has to overcome to move. The friction force is based on the following formula: F = ?W, where ? is the coefficient of rolling friction between the wheel and the rail and W is the weight of the rail car. If the weight of a fully loaded rail car is 280,000 pounds, then F = (0.001 x 280,000) = 280 pounds.

Because the only horizontal force that the railroad car produces is the friction force, the force to move the rail car (P) is equal to the friction force (F). Therefore, using the previous example, an input force of 280 pounds is needed to move the rail car.

#### Things You'll Need

• Weight of the railroad car
• Coefficient of friction between the car wheels and the rail
• Calculator

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