Two vehicles are approaching an intersection. One is a 2500 -kg pickup traveling at 14.0 m / s f

Two vehicles are approaching an intersection. One is a 2500...

Key Concepts

Linear Momentum

Linear momentum is a vector quantity defined as the product of an object's mass and its velocity. It is fundamental in mechanics, especially in analyzing the motion of objects, as it reflects both the magnitude and the direction of their motion.

Vector Components

Any vector, including momentum, can be broken down into its perpendicular components, typically along the x and y axes. This decomposition simplifies calculations by allowing the treatment of the motion in each direction separately and is essential in solving problems involving directions.

Vector Addition

When more than one momentum vector is involved, their net effect is determined by vector addition, which involves summing their respective components along each axis. This principle allows for the calculation of the overall momentum of a system by combining the individual momenta.

Magnitude and Direction Calculation

After finding the vector sum of the components, the overall momentum is expressed in terms of its magnitude and direction. The magnitude is determined using the Pythagorean theorem, and the direction can be found using trigonometric functions, particularly the arctan function, which gives the angle relative to a specified axis.

Transcript

00:01 In this question, a traveling pickup is moving to the left with a velocity of 14 meters per second and it has a mass of 2 ,500 kilograms.

00:10 At the same time, a sedan is traveling upwards to the north with a velocity of 23 meters per second and a mass of 1 ,500 kilograms.

00:21 In the first item of this question, we have to find the x and y components of the net momentum.

00:28 For that, you have to be quite careful now because we are dealing with a problem that happens in two dimensions.

00:35 That is, we have things moving in the y direction and we have things moving in the x direction.

00:42 So, we evaluate the net momentum as follows.

00:45 So the net momentum, purn, has two components.

00:49 It has an x component and it also has an y component.

00:54 And the x component of punat is composed only by.

00:58 The momentum of the pickup because only the pickup is moving in the x direction actually the minus x direction this is because the problem gives us a reference frame which is this one everything that is moving up is going to the positive direction and everything that is moving to the right is going to the positive direction so knowing that we are now in conditions of evaluating the components of the net momentum the x component is given by the momentum of the pickup only so we have a mass of 2 ,500 kilograms times a velocity of minus 40 meters per second.

01:35 We have that minus sign because that velocity points to the left to the negative direction of our x -axis.

01:42 Then, for the y component, we have the following.

01:45 The y component is given by the mass of the sedan 1 ,500 kilograms times the velocity of the cidon, which is 23 meters per second.

01:55 It's positive because it's moving in the positive y direction.

02:00 Now, by performing these calculations, we get the following.

02:03 The x component of the net momentum is given by minus 35 ,000 kilograms times meters per second.

02:13 And at the same time, the y component of the net momentum is given by 34 ,000 and 500 kilograms times meters per second.

02:25 And this was the first item of this question.

02:29 In the second item, we have to evaluate the magnitude and the direction of the net momentum.

02:35 For that, it's very, very helpful to actually draw the components of the momentum.

02:40 So, the y component of the momentum is a vertical arrow that points upwards, and it has a length, a magnitude that is given by 34 ,000 and 500.

02:56 Now we can draw the x component of the momentum.

03:00 The x component points to the left.

03:03 So it's an arrow that points to the left and it has a length that is 35 ,000 kilograms meters per second.

03:16 Now remember that we are dealing with vectors so we can move vectors around and this will not change anything.

03:22 So what i'm doing is the following.

03:24 I use put the beginning of each vector together just like this.

03:30 As you can see, there is an angle in between them and that angle is a 90 degree angle.

03:37 Therefore we can complete that triangle by doing something like that.

03:43 The hypotenuse of that triangle will be the magnitude of the net momentum...

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