Part A To keep her dog from running away while she talks to...

Part A To keep her dog from running away while she talks to a friend, Susan pulls gently on the dog's leash with a constant force given by \(\vec{F} = (2.2\text{ N})\hat{x} + (1.1\text{ N})\hat{y}\). For the steps and strategies involved in solving a similar problem, you may view the following Example 7-10 video: HOW FAST? How much work does she do on the dog if its displacement is \(\vec{d} = (0.22\text{ m})\hat{x}\)? Express your answer in joules. \(W = \) Submit Request Answer Part B How much work does she do on the dog if its displacement is \(\vec{d} = (0.23\text{ m})\hat{y}\), or Express your answer in joules. \(W = \)

Transcript

00:01 This question talks about a dog walker walking three different dogs, and they're all pulling in different directions.

00:07 We know that if this is the point where all the leashes diverge, and this is true north, we know that one is pointing, is pulling with eight units of force, 60 degrees west of north.

00:23 Another one is pulling with six units of force, 45 degrees east of north, and the third is pulling with 12 degrees exactly, or 12 units of force exactly north.

00:41 So there's going to be some resultant vector of all these dogs pulling, and the dog walker is going to have to counteract all three with one force, and we want to figure out what that force is that will keep this system stationary.

00:56 So our first step is going to be finding what that resultant vector is of all three dogs pulling.

01:03 The way we're going to do this is we're just going to add up all of these different vectors.

01:09 We're going to break them into components and add them up that way.

01:13 Now, it would be sort of easy to do it in the horizontal and vertical directions.

01:20 What i want to do to make it a little bit easier is break it up into the north component and the west component.

01:28 That will help us quite a bit.

01:30 So we're going to be treating north as our x -axis and west as our y -axis.

01:37 So sort of put your head on the tilt, and we'll think about it like this.

01:41 So the 12 -unit vector very clearly is all in the north direction.

01:47 So we don't have to worry about that.

01:48 It's just going to be 12 -north -zero -west.

01:52 Let's then do the 6 -unit vector.

01:55 So what that's going to be is actually, 45 degrees below the x -axis.

02:02 So our north component, or our x component, is going to be 6 times the cosine of 45 degrees, and our west component is going to be, oh, excuse me, six times the cosine of negative 45 degrees because it's 45 degrees below the x -axis, and our west component will be 6 cosine, or excuse me, 6 sine of negative 45 degrees.

02:27 There we go...

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