A boy reaches out of a window and tosses a ball straight up with a speed of 10 m / s. The ball i

A boy reaches out of a window and tosses a ball straight up...

Key Concepts

Reference Level in Potential Energy Calculations

The choice of a reference level is important in gravitational potential energy calculations since potential energy is measured relative to this level. Selecting an appropriate reference simplifies computations and ensures that energy changes are calculated consistently across different positions in the gravitational field.

Conservation of Energy

This principle states that in a closed system with no non-conservative forces (like air resistance) performing work, the total mechanical energy remains constant. It is used to equate the initial sum of kinetic and potential energies of a system with the sum at any later point, allowing problems involving energy conversion to be solved without directly analyzing the motion details.

Gravitational Potential Energy

Gravitational potential energy represents the energy stored in an object due to its position in a gravitational field and is calculated using the formula mgh, where m is mass, g is gravitational acceleration, and h is the height relative to a chosen reference level. This concept is critical for understanding energy changes as objects ascend or descend.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion and is given by the formula 1/2 mv². In energy conversion problems involving projectile motion, the interplay between kinetic and potential energy determines values such as maximum height or impact speed, as the object’s kinetic energy reduces to potential energy during ascent and increases during descent.

Transcript

00:01 Hello everyone.

00:02 In this problem, we're asked to find various things about a, or as to find out various things about a bowl throw, where a boy throws of a ball with an initial speed of 10 meters per second from an initial height of 20 meters.

00:17 And we're asked to find what is the maximum height that the ball reaches.

00:20 What is the speed of the bowl as it comes back to the initial position falling down this time? and what is the impact speed? so what is the speed with which the bowl reaches or touches the ground? so apart from these two information, of the initial speed and the initial height, we're also noted the rotation acceleration is 9 .8 meters per second squared.

00:46 So first of all, how do we find the maximum height? okay, so to find a maximum height, what we really want to use is essentially the mechanical energy concept, so what we want is we want to find the initial kinetic energy of the process, the final kinetic energy in the process, and the initial potential energy and the final potential energies.

01:08 Okay, so we know that the initial kinetic energy is something like half times m times a b1 squared, where b1 is the initial speed.

01:18 And we know that at the height of the, at the maximum height that the bowl reaches, the velocity or the speed of the bowl is going to be zero.

01:26 So this tells us that the kinetic energy up there is going to be zero.

01:32 Right.

01:32 And so what this means is that essentially the change in potential energy is going to be equal to the change in kinetic energy.

01:41 Or a change in kinetic energy is going to be equal to the change in potential energy.

01:45 And so the simple way of writing that is to say that m times, g times the change in height is going to be equal to the kinetic energy of the object.

01:57 So you can imagine the object or the ball losing all of its kinetic energy and giving that up in order to climb up in the potential and the gravitational potential of the earth.

02:10 Okay, so this is the equation that we want to use.

02:14 So this just comes from saying that, you know, if i write, if i write the mechanical energy on one side for the initial process, which would be k .e .1 plus p .e .1 equal to the final energy of the process, which is k .e .2 plus p .e .2.

02:36 Right.

02:37 And so all i've done is i've said, you know, k .e2 is equal to zero because the speed up there is zero.

02:43 And so then i subtract pe1, and then i essentially just find literally this equation, right? so i have p .e2 minus p .e .1 is equal to k .e1, which is the box term over here.

02:55 And now i can drop the masses from both sides and then rearrange this to find what y2 is.

03:03 And so what i get is that y2 is equal to we1 squared over 2g plus y1 and plugging in the values we find that this is equal to 25 .1 meters.

03:13 Okay, so this is the maximum height that the bowl is going to reach...

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