Car A that is moving at 5m/s slows down until it stops. Car B, on the other hand, from rest moves to a velocity of 5m/s. Both cars required work. Compare the amounts of work of Car A and Car B.
Answers
Answer:
The previous part of Lesson 2 discussed the relationship between work and energy change. Whenever work is done upon an object by an external force, there will be a change in the total mechanical energy of the object. If only internal forces are doing work (no work done by external forces), there is no change in total mechanical energy; the total mechanical energy is said to be conserved. Because external forces are capable of changing the total mechanical energy of an object, they are sometimes referred to as nonconservative forces. Because internal forces do not change the total mechanical energy of an object, they are sometimes referred to as conservative forces. In this part of Lesson 2, we will further explore the quantitative relationship between work and energy.
Relating Work to Energy
The quantitative relationship between work and mechanical energy is expressed by the following equation:
TMEi + Wext = TMEf
The equation states that the initial amount of total mechanical energy (TMEi) plus the work done by external forces (Wext) is equal to the final amount of total mechanical energy (TMEf). A few notes should be made about the above equation. First, the mechanical energy can be either potential energy (in which case it could be due to springs or gravity) or kinetic energy. Given this fact, the above equation can be rewritten as
KEi + PEi + Wext = KEf + PEf
The second note that should be made about the above equation is that the work done by external forces can be a positive or a negative work term. Whether the work term takes on a positive or a negative value is dependent upon the angle between the force and the motion. Recall from Lesson 1 that the work is dependent upon the angle between the force and the displacement vectors. If the angle is 180 degrees as it occasionally is, then the work term will be negative. If the angle is 0 degrees, then the work term will be positive.
The above equation is expresses the quantitative relationship between work and energy. This equation will be the basis for the rest of this unit. It will form the basis of the conceptual aspect of our study of work and energy as well as the guiding force for our approach to solving mathematical problems. A large slice of the world of motion can be understood through the use of this relationship between work and energy.
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Practice Problem #1
A 1000-kg car traveling with a speed of 25 m/s skids to a stop. The car experiences an 8000 N force of friction. Determine the stopping distance of the car.
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Practice Problem #2
At the end of the Shock Wave roller coaster ride, the 6000-kg train of cars (includes passengers) is slowed from a speed of 20 m/s to a speed of 5 m/s over a distance of 20 meters. Determine the braking force required to slow the train of cars by this amount.
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Practice Problem #3
A shopping cart full of groceries is sitting at the top of a 2.0-m hill. The cart begins to roll until it hits a stump at the bottom of the hill. Upon impact, a 0.25-kg can of peaches flies horizontally out of the shopping cart and hits a parked car with an average force of 500 N. How deep a dent is made in the car (i.e., over what distance does the 500 N force act upon the can of peaches before bringing it to a stop)?
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Work done in both cases will be equal in magnitude but opposite in sign.
Explanation,
- Due to its motion, car A will possess kinetic energy when we apply the brake and the car stops. Work is done at the expense of this kinetic energy. Therefore, the work done for Car A will be negative.
- On the other hand, Car B starts from rest and reaches a velocity of 5m/s. This shows that work done is being done to increase the kinetic energy. In simpler words work done, provides momentum to the car, further contributing to its kinetic energy. Therefore, the work done for Car B is positive.