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A sled is pulled along a level path through snow by a rope. A 30-lb force acting at an angle of $ 40^\circ $ above the horizontal moves the sled 80 ft. Find the work done by the force.

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1839 ft-lb

00:58

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

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Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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A sled is pulled along a l…

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A force of 80 pounds on a …

So if we want to find the work done, remember, work is going to be dot product of our force with our displacement, but we don't have those vectors yet, So what we can do instead is used the other definition, which is where it's just the magnitude of each of them multiply the other times the angle between them. So our force is 30. Our distance we moved was 80 and then we have co sine of the angle between them, which is 40 degrees. And then the units for our force were pounds. The units for our displacement were feet. So our units over wall will be feet pounds so that we can go to multiply these together. So it'll be 2400 co sign of 40 degrees, £8. So if you want the exact answer, you can leave it there or we can also approximate that so could sign of 40 times 2400 is something around 18 39 ft pounds. So either of these would be our solution

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