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

1. A ball is tossed in the air and released. It moves up, reverses direction, falls back down again, and is caught at the same height it was released. a. Considering the interval after the ball is released and before it is caught, when does the gravitational potential energy of the ball have its maximum value? Minimum value? Explain. b. When does the kinetic energy of the ball have its maximum value? Minimum value? Explain. c. What about the total energy of the ball? What can you say about its value at the locations described in your answers to (a) and (b)? d. Draw graphs of potential energy, kinetic energy, and total energy as a function of position.

Transcript

00:01 Hello! now we have said that a bowl is being toast in the air and then released.

00:06 It moves up, reverses the direction and falls back down again and is caught at the same height it was released.

00:12 Okay, then if we look at the motion, we can see that here the height, from where it is toast, we will take the height edge to be zero.

00:22 Okay.

00:23 Now at the topmost point, the height edges, edge maximum and when it comes down, here its height is again zero okay now we know that the potential energy u is given by the equation m g multiplied by h since m and g are two constants h will be the only determining factor here and the kinetic energy k e would be equal to half m b square okay now this body is chose to be the velocity v from this point and it reaches the maximum height here.

01:06 So the velocity here would be equal to zero and when it comes back down again, its velocity will be the maximum.

01:14 Okay.

01:14 So here from this diagram, we can see that the kinetic, sorry, the potential energy will be maximum at the maximum height and will be minimum when the ball is being released.

01:30 At the point from where the bowl is being released.

01:34 Now, when it comes to the kinetic energy, the kinetic energy will be maximum at the points where the bowl is being released as well as the bowl comes back down to the same point from where it was released, and the kinetic energy will be minimum at the topmost point.

01:53 Okay.

01:56 Now, if t is the time of flight for this whole motion, time of flight, then for the upward and the downward motion, it will take the same time.

02:12 Okay, so we can say that the potential energy is maximum at t divided by 2.

02:21 Okay, and the potential energy is minimum at the starting of the flight, flight as well as at the end of the flight.

03:15 This is because at time t is equal to t divided by two, we can say that the height h is equal to h maximum.

03:25 That is, it reaches the peak point.

03:27 Okay.

03:27 And the potential energy would be equal to mg h maximum and hence the potential energy value will be maximum at this point.

03:41 Okay.

03:41 Now at the starting and the ending points, the height h is equal to zero, and hence the potential energy pe would be equal to zero, and hence we can say that there the potential energy will be minimum.

03:56 Now, the kinetic energy, k .e, is maximum, maximum at the starting and the end of the flight.

04:32 Now, the kinetic energy is minimum halfway through the flight.

04:50 Okay, halfway through the flight.

05:04 Why? because at the starting and the ending points, the velocity v is equal to v maximum.

05:13 Okay.

05:14 And hence the kinetic energy, ke would be equal to half, m multiplied by v maximum square...

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