Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\bullet$$\bullet$ An object is dropped from rest and encounters air resist-ance that is proportional to the square of its speed. Sketchqualitative graphs (no numbers) showing (a) the air resistanceon this object as a function of its speed, (b) the net force on theobject as a function of its speed, (c) the net force on the objectas a function of time, (d) the speed of the object as a functionof time, and (e) the acceleration of the object as a function oftime.

a) $F_{r}=D v^{2} \quad \mathrm{D}$ is constant b) $F=m g-D v^{2}$c) $m g-D v_{0}^{2}-2 D g t-D g^{2} t^{2}$d) Graph of speed versus timee) Graph of acceleration versus time is similar to that of force versus time

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

01:40

An object starts from rest…

04:43

(II) An object starts from…

02:46

04:11

03:35

00:42

The velocity-time graph of…

02:27

A ball is dropped from res…

01:05

Consider an objects that f…

00:58

When a net force acts on a…

02:11

When an object is thrown u…

00:25

01:41

Free fall of an object in …

03:19

An object falling under th…

01:14

In the absence of a net fo…

question 53 cents an object has dropped from rest and encounters, a resistance that's proportional to the square of the speed sketch, the quality of graphs. No numbers showing a few different scenarios. So go one by one and we'll figure out what we want. A plot for each graph is the first graph part. A asked us to plot the air resistance so the Air Force, due to resistance physical, aren't here, Let's say as a function of the speed. So you know, in a textbook, we're told that the, uh, sort of resistance for us is simply given by the D, the proportional constant for the object times V squared. So since I guess to have a quiet, quadratic formula as the speed is increasing in, the force increases Quadratic Lee as well repeat the net force on the object as a function of its speed. So it's a net, and he is, well again. So you know how an object that's falling for saying it's accelerating downwards. We're calling that direction positive. Why here, downward? Of course. Another dropping will have a weight downward and opposite of its motion, will have this drag force. Um, I told fR before, Just resistance, drag whichever is appropriate. So know that the net force, as we're looking for for this problem, is it's exciting downward. So you can call that just a which is equivalent to if any is positive that our weight pretty positive and we subtract off this drag force or resistance for us. So we have an expression for our F net as a function of the velocity TMG its weight minus r value for, um force previously d b swear this is our equation for part two. So we're starting initially. That's a value for the wait and we drop off Quadratic Lee such Yes, that looks actually kind of exponential. So it really is just 1/4 reports what is dipping quite a bit down. Not as drastic as I drew it. Originally part C. The net force on the object as a function of time. So going to F net here and now you have time. So we're looking at will be started at the previous equation. If next equals almost put, the weight is merely that one. But we represent the velocity in terms of its initial velocity and six elimination so we know it's accelerating with G, and we're saying it's trying downward to both. These terms will be positive. You hear this term falsies squared, They're just using kinetic expression for this term. Describe the change of velocity with respect to time. So we expanded. So yeah, the wait might as devi not squared Mine is d B not G t played right to Anri, adding in d g squared t squared. So again, based on this as a function of time, we have another quadratic formula. So are net force. Here is this term close the weight minus d B not squared although it is to see that the object does start from rest. Okay, that means we can eliminate a couple of terms here. This new we ever do not was RV knocks. Initial times cancel out. So we just start The function of this equation is just the weight plus de Oh, that's a minus. Because this is my studio in front, so that make sense, it shouldn't be increasing. So it's a relief that there, so this term is minus same here. It's my assign saver weight minus D g squared t squared. It was falling off with T squared here again, starting from rest. So there's no initial velocity and again decreases like a quadratic formula downward party, the speed of the object as a function of time, speed as a function of time. You know it starts from rest. So because this falling the creation of the equals B not plus GT because we're saying live velocity is increasing all those in the downward direction, it's increasing until certain point. Where basically becomes flat and at this point is where we reach each other's we flat not decreasing. This point is our terminal velocity and acceleration have. The object is a function of time celebration in time, you know, it's as it states and textbook in the example that's provided that the when the object does fall vertically through the air. The drag force opposing the motion increases as we see for some privacy and the downward acceleration decreases. It was a damn acceleration until eventually reaches zero. Because you know, this new R and me equals zero such that we can use the relationship from above, Um, this one here so f equals zero. Such that are wait, therefore equals R constant and time I'm velocity squared. When you reach that terminal velocity, so does a collision. Does 10 under this time frame. There you go. Well, I guess sorry, I should say Then if this is the scenario, I'm going to do it versus time. It's not quite linearly as I drew, it could be represented in the snares would be not plus geeky squared. Similarly, as you saw before, this term goes to zero And the acceleration does go like a quadratic so similares of force versus time curve that we perform previously. The recent Sorry. Just be clear. It is quadratic quadratic fall off to eventual zero, you know.

View More Answers From This Book

Find Another Textbook

02:47

Eavesdropping! You are trying to overhear a juicy conversation, but from you…

01:55

$\bullet$ Voiceprints. Suppose a singer singing $\mathrm{FH}$ (370 Hz, the

04:04

$\bullet$ $\bullet$ Solar energy. The sun transfers energy to the earth by r…

06:01

$\bullet$$\bullet$ The stretchy silk of a certain species of spider has a fo…

05:47

Compute the equivalent resistance of the network in Figure $19.56,$ and find…

07:32

Catch a piece of a comet. The Stardust spacecraft was designed to visit a co…

03:51

$\bullet$ The longest home run. According to the Guinness Book of World Reco…

01:18

$\cdot$ The eyepiece of a refracting astronomical telescope (see Figure 25.1…

03:57

$\bullet$ $\bullet$ At 7.35 cents per kilowatt-hour, (a) what does it cost t…

01:25

An errand of mercy. An airplane is dropping bales of hay to cattle stranded …