Guiding Questions
- How can we use math to determine the distance required to stop a train?
- How can we use math to determine the braking time required to stop a train?
- How can we use math to determine the braking force required to stop a train?
Key Terms
- Braking distance: The distance a vehicle takes to stop, from the moment the brakes are applied to the moment the vehicle comes to rest (zero velocity).
- Braking time: The time a vehicle takes to stop, from the moment the brakes are applied to the moment the vehicle comes to rest (zero velocity).
- Coefficient of friction: A ratio between frictional force and normal force. The coefficient of friction describes how much "stick" there is between two materials. A large value describes very high-friction contact (like rubber soles on a grippy gym floor). A small value describes very low-friction contact (like ice skate blades on ice). Since the frictional coefficient is a ratio of forces, it has no unit.
- Dependent variable: In a two-variable relation, the variable that is affected. It is "dependent" on the on variable that is manipulated, which is called the "independent variable." The dependent variable can also be thought of as the output from a function equation.
- Friction: The force that resists motion between objects in contact with each other. Locomotives depend on friction for traction (where the wheels meet the track) but are also inhibited by friction, including both rolling resistance (in axles, bearings, wheels) and air resistance.
- Independent variable: In a two-variable relation, the variable that is manipulated. The independent variable can also be thought of as the input to a function equation.
- Momentum: The product of the mass and the velocity of an object. The SI unit of momentum is the kilogram∙meter per second (kg∙m/s).
- Normal force: A force that acts on an object in a perpendicular direction relative to the surface the object rests on. Often this force will be equal to the object's weight (though in the opposite direction) because the normal force will oppose gravity so as to keep the object from falling.
- Perception-reaction time: The time required for the operator of a vehicle to recognize an abnormal situation and react to it.
- Stopping distance: The sum of the perception-reaction time of the operator of a vehicle and the braking distance of that vehicle.
- Velocity: Speed in a specified direction.
- Weight: The force that gravity exerts on an object. Weight is related to mass in that an object with a larger mass will have a larger weight. However, they are not the same quantity. On Earth, the weight of one pound is 4.45 newtons. The weight of one kilogram is 9.81 newtons.
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