Need help preparing for the MCAT physics section? MedSchoolCoach expert, Ken Tao, will teach you what you need to know about the Work Kinetic Energy Theorem. Watch this video to learn how to do well on the physics section of the MCAT exam!
The work-kinetic energy theorem states that the total work done in an object is equal to the change in kinetic energy of that object. We’ll use the equation below to solve an example.
An 800 kg car is initially traveling at 10 m/s. The brakes are applied, producing a constant decelerating force of 2000 N. How far will the car travel before stopping? We can recognize this as a situation to apply the theorem because it’s a situation where an object has a reduction in kinetic energy, slowing down, due to a force doing work on the object over some distance. According to the theorem, the total work done on the car is equal to the cars change in kinetic energy. We know that the car is slowing down to a stop, and so it’s final kinetic energy is equal to 0. Therefore, the change in the kinetic energy of the car is equal to 0 minus the initial kinetic energy of the car.
We are able to calculate the change in kinetic energy of the car by substituting in the values for the mass and initial velocity of the car from the question stem. Thus, we can calculate the total work done on the car by setting Wtotal equal to the change in kinetic energy.
Remember that the formula for work is W = Fdcos(θ). Theta is the angle between the force applied to an object to perform work, and the direction of displacement of the object. Because the breaks are a decelerating force, they act in the direction opposite motion. Therefore, the breaks are acting in the direction 180 degrees from the direction of the car’s motion, so theta is 180. The force applied by the breaks is 2000 N. Therefore, the work performed by the breaks on the car can be set equal to -40,000 J, and if we substitute in 2000 N and 180o, we can solve for the distance over which work was performed.
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