A ball is tossed in the air and released. It moves up, reversesdirection, falls

Question

A ball is tossed in the air and released. It moves up, reversesdirection, falls back down again, and is caught at the same heightit was released.

a.     a. Considering the time interval after the ball is released andbefore it is caught, when does the    gravitationalpotential energy of the ball have its maximum value? Minimum value?Explain.

b.     b. When does the kinetic energy of the ball have its maximum value?Minimum value? Explain.

c.       c. What about the mechanicalenergy of the ball? What can you say about its value at thelocations described in your answers to (a) and (b)?

Explanation / Answer

Solution (a): Note: assume that the height at which it is caught is the referencelevel (i.e. zero height) Note: I am assuming air resistance is ignored The gravitational potential energy is at a maximum when it reachesits maximum height because it is at a height above the referencelevel (i.e. gravitational potential energy depends on the heightrelative to some reference height when the gravitational potentialenergy would be zero (i.e. in this case, it happens to be the levelwhere the ball is thrown and caught)) Solution (b): The kinetic energy of the ball will have its maximum at the levelwhere it was thrown/caught because all of the gravitationalpotential energy has been converted into kinetic energy. Thekinetic energy of the ball will be a minimum at maximum heightbecause at maximum height, the velocity of the ball is zero(temporarily) Solution (c): Assuming air resistance is ignored, the total mechanical energy ofthe ball will be conserved - the only thing happening is theconversion of one type of energy into another (i.e. gravitationalpotential energy into kinetic energy and vice-versa). For example,the moment it is thrown, it has kinetic energy because it is inmotion, however, as it reaches its maximum height, the kineticenergy slowly decreases because it is being converted intogravitational potential energy. Upon reach maximum height, all thekinetic energy is gone and now it is in the form of gravitationalpotential energy. Now, the ball will start its motion back downtowards the location where it came (i.e. due to gravity) and all ofthe gravitational potential energy is now being converted intokinetic energy (i.e. the ball speeds up on it way down).

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