Here are the essential concepts you must grasp in order to answer the question correctly.
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In the context of the roller coaster, the initial kinetic energy at point 1 will be converted into kinetic energy at point 2, accounting for work done against friction.
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Work-Energy Principle
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this scenario, the work done by friction will reduce the roller coaster's kinetic energy as it travels from point 1 to point 2, affecting its final speed.
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Frictional Force
Frictional force is the resistance encountered when one surface moves over another, calculated as F_friction = μN, where μ is the coefficient of friction and N is the normal force. In this problem, the average force of friction is given as a fraction of the weight, which will impact the net force acting on the roller coaster and thus its acceleration and final speed.
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