(a) In Problem 3, what is the speed of the book when it...

Name: Problem 10, Chapter 8: Fundamentals of Physics
Uploaded: 2019-07-08T23:57:34-08:00
Duration: 4 min 54 s
Channel: Eric Xue
Description: (a) In Problem 3, what is the speed of the book when it reaches the hands? (b) If we substituted a second book with twice the mass, what would its speed be? (c) If, instead, the book were thrown down, would the answer to (a) increase, decrease, or remain the same?

(a) In Problem 3, what is the speed of the book when it reaches the hands? (b) If we substituted a second book with twice the mass, what would its speed be? (c) If, instead, the book were thrown down, would the answer to (a) increase, decrease, or remain the same?

Key Concepts

Conservation of Mechanical Energy

This is the principle that in a system without non-conservative forces (such as friction or air resistance), the total mechanical energy remains constant. In the context of a falling object, gravitational potential energy is converted into kinetic energy, allowing the determination of speed solely based on the height of the fall.

Mass Independence in Free Fall

Under the influence of gravity, in the absence of air resistance, all objects accelerate at the same rate regardless of their mass. This means that the final speed reached by an object falling from a given height is independent of its mass, as the mass cancels out in the energy conservation equations.

Influence of Initial Velocity on Final Speed

The final speed of an object in free fall can be affected by its initial kinetic energy. If the object is thrown downward, it starts with additional kinetic energy compared to being dropped from rest, which leads to a higher speed upon reaching the destination.

Transcript

00:01 Okay, everyone.

00:02 So we're gonna look at problem number 10 now, and so this problem is basically a repeated one with different concepts.

00:10 So what do we have? so basically, we have a building, right? and there's a book being dropped from the building now at the bottom, we have a man over here and his hands are outstretched so that they're very linear.

00:28 And these arms are at a certain height, de whereas this book is at a certain height big d and now this book has a mass of two kilograms.

00:45 Two kilograms.

00:47 This big d is equal to 10 meters wire as this small d is equal to one point five meters on the problem wants to know what is the speed when it reaches this person's hand.

01:03 This is very simple, right? this is simply a a conservation of energy problem.

01:08 So let's look at it.

01:09 So we have an initial energy and we have a final we have.

01:14 Ah, why? why did you write it like that? and we have a final energy.

01:21 So what is our beginning? energy? well, all we have is gravitational potential energy.

01:28 And what is our ending energy? well, we have kinetic energy because the book is falling and we have gravitational potential energy because it does not read cromwell.

01:39 Very simple.

01:40 So we have m g d big d and then we have 1/2 em the final square, plus m g little t.

01:57 Okay, so what do we do now? very simple.

01:59 We solved for velocity and so mg big d minus m g little d is equal to 1/2 on the final square.

02:11 And so it's two times mg big d, minus mg small d is equal to em the final square and you just solve for v divide.

02:25 I am divide by an and then you square root it so the final is equal to the square root of two mg big d minus mg little d all over em.

02:43 Right? so that's how you would find the speed and wave you from here...

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