The table ^* gives automobile performance data for a few types of cars: (a) During an accelerati

The table ^* gives automobile performance data for a few...

Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity over a given time interval. It provides a measure of how quickly an object's speed increases (or decreases) and is a fundamental concept in analyzing motion, especially when comparing performances such as how fast vehicles reach a certain speed from rest.

Mass and Force Relationship

The relationship between mass and net force is pivotal because, for a given acceleration, a more massive object will require a larger net force. This concept is crucial when comparing different vehicles, as their mass directly influences the magnitude of force needed to achieve the same acceleration.

Net Force on Passengers

The net force experienced by passengers during acceleration is determined by applying the same acceleration as the vehicle to the mass of the passenger. This approach demonstrates how the force scales with mass and underscores the importance of Newton’s Second Law not just for the vehicle but also for its occupants.

Top Speed and Equilibrium of Forces

A vehicle’s top speed is reached when the driving force provided by the engine exactly balances the resistive forces, such as aerodynamic drag and friction. At this point, the net force is zero, meaning there is no further acceleration, which explains why a car cannot exceed its top speed despite the engine’s capabilities.

Aerodynamic Drag and Resistive Forces

Aerodynamic drag and other resistive forces, such as rolling friction, play a major role in limiting a vehicle's top speed. These forces increase with speed and eventually counterbalance the engine's driving force, resulting in a state of equilibrium where no net force is acting on the vehicle, thereby capping its maximum achievable speed.

Newton’s Second Law

Newton’s Second Law states that the net force acting on an object is equal to the product of its mass and its acceleration (F = m × a). This law is essential for understanding how different masses and accelerations lead to variations in the net force acting on vehicles during acceleration phases.

Transcript

00:01 Once again, welcome to a new problem, and it just so happens that forces have a relationship to the mass and acceleration of different objects, and this has to do with newton's second law.

00:19 So when you think about newton's second law, you always reflect on the mass of the object and the acceleration that gives us forces.

00:27 So we end up computing what we call the net force or the average net force just based off of the masses.

00:37 And the acceleration, when you define the acceleration, this is final velocity minus initial velocity over time from a conceptual point of view.

00:49 Acceleration is the change in velocity with respect to time.

00:56 Changing velocity with respect to time.

01:04 And one of the things you want to remember is that both velocity and acceleration happen to be vector units or vector quantities.

01:15 Vector quantities have magnitude and they also have the so you have those two requirements.

01:25 They have magnitude and direction.

01:29 So in this new problem we have specific requirements.

01:34 First of all, we're given a table and through the table will have performance.

01:42 So we have a make in the first column and you know when we talk about the make and the model and you know by the model we mean the the year it was built so we have an alpha romale an alpha romale and that was 2013 and then we have a honda civic there were honda civic or honda civid this is a 2 2 oh i and the make is 2000 that's just the other way, the other day, sorry.

02:32 And then we have a ferrari and the ferrari is the ferrari f430, if i'm not mistaken.

02:43 So a ferrari is italian, honda is probably japanese and then half of a male, maybe italian also.

02:55 I might be wrong on that but those are just the manufacturers that you're dealing with.

03:00 So this is a 2004.

03:03 Don't forget the us with the ford focus, the ford focus, and that happens to be, or rather ford vocus, that happens to be arrest 500, which was a 2010 make, and a volvo, a lot of luxury going on right here.

03:30 So the volvo is 2013 and so those are the models you're dealing with.

03:40 Of course these models have other parameters that are helpful in determining which one of these makes is stronger than the other.

03:52 And the mass is in chilogneal.

03:54 The first one is alfa romeo, 895, the honda 1320.

04:02 The ferrari 1435 and then of course we also have the ford focus which is 1468 we do have the volvo 1650 kilograms so the habeas as you can see is the volvo and that includes the engine and all the other factors you know the bodian stuff that makes it asia also we do have the time that we're going to be driving from zero seconds up until or rather zero up until 60 miles per hour and you know the time it takes is in seconds so you know driving from zero to 60 miles per hour 4 .4 you can see how strong the honda is at 6 .4 seconds so the fastest is the alpha male because it takes that sign which takes on the 3 .9 seconds and then there are for romeo 4 votes suit.

05:13 We have 5 .4 but of course there's going to be other factors that are included in the parameters and we do have the final velocity.

05:25 We have the final velocity and in terms of the final velocity we have miles per hour and meters per second.

05:41 Miles per hour and meters per second so these are divided like that we have miles per hour and meters per second so we have 60 for the male up until 26.

06:04 And age 2 and then 60 so they're all similar 26.

06:10 Point h2 and then 60 then 26 .82 and then 60 26.

06:19 26 .82 and then 60 26 .86.

06:23 H2.

06:25 And then we have the average acceleration and the average acceleration.

06:33 That's going to be given as, you know, through these numbers.

06:41 6 .10.

06:44 6 .10.

06:45 We also have 4 .19 and then we're going to have 4 .19, we're going to have 4 .196 .88 and don't forget 4 .97, 4 .97 and then 3 .73.

07:31 And then we have the average net force and of course this is going to be in neutins, don't forget the acceleration is in meters per second squared and we get 54, 56.

07:52 We also get 55, 32.

07:58 We get 98, 69, 72, 92, 62, 62, 61, 47.

08:10 So those are the options you have right there.

08:15 And so in part a of this problem, the question that stands out is which model has the largest and smallest net force from 0 to 60 miles per hour during acceleration? the typical question that we're dealing with changing velocity is the same as the units is meters per second.

09:08 Of course we know one mile is the same as 1 ,609 .34 meters and then one hour is 3 ,600 seconds.

09:21 So average acceleration is obviously we, as you say, the final minus the initial, all of the design where the initial is zero and then the final is 60.

09:41 The average net force, average net force, as you can see, is computed as the average force or average net force, is the mass times the average acceleration.

10:00 This is the mark times the average acceleration.

10:05 So in this case if you look at the table after doing the computations, you get to see that the top top one is the ferrari and then the lowest one is the the alpha romay...

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