Solve Vector Word Problem with Tow Truck: Work Done in Joules

In summary, the problem involves a tow truck pulling a stalled car along a horizontal road. The tension in the chain is F Newtons and the chain makes an angle of θ degrees with the road. The goal is to find the work done by the truck in pulling the car a distance D = 1km(1000m). Using the definition of work, the problem can be approached by considering the force perpendicular to the direction of travel. The equation used in this problem is w = f*d or ##w = \vec f \cdot \vec d## with the result expressed in joules using scientific notation and three significant figures.
  • #1
hungrymouth
5
0
1. Let F = 1050N & θ = 24°. A tow truck drags a stalled car along a road. The chain makes an angle of θ degrees with the road, and the tension in the chain is F Newtons. How much work W is done by the truck in pulling the car a distance D = 1km(1000m) along a horizontal road? Express the result in joules using scientific notation and three significant figures.



2. w = f*d



3. I don't have a clue how to approach this problem. I need some guidance as in approaching the problem so that I can solve the problem.
 
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  • #2
Start from the definition of work.
(In words - possibly.)

i.e. if the force were perpendicular to the direction of travel - how much work would it do?
 
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  • #3
hungrymouth said:
2. w = f*d

And don't you mean ##w = \vec f \cdot \vec d##? (Vectors and dot product)
 

FAQ: Solve Vector Word Problem with Tow Truck: Work Done in Joules

What are vector word problems?

Vector word problems involve the use of vectors, which are quantities that have both magnitude and direction. These problems often require solving for an unknown vector or finding the magnitude or direction of a given vector.

What are some common applications of vector word problems?

Vector word problems are commonly used in physics, engineering, and mathematics to describe the motion of objects in space or to analyze forces acting on a system. They can also be used in navigation, such as finding the direction and magnitude of a plane's velocity.

What are the key steps to solving vector word problems?

The key steps to solving vector word problems include drawing a diagram to visualize the problem, breaking down the vectors into their component parts, applying trigonometric functions to find the magnitude and direction of the vectors, and using vector addition and subtraction to solve for the unknown vector.

How can I improve my skills in solving vector word problems?

Practice is key to improving your skills in solving vector word problems. Start with simpler problems and gradually increase the difficulty level. It's also helpful to understand vector operations, such as addition, subtraction, and scalar multiplication, and to have a strong grasp of trigonometry.

Are there any common mistakes to watch out for when solving vector word problems?

One common mistake is forgetting to break down vectors into their components. It's also important to use the correct sign for each component, as well as keeping track of units for magnitude and direction. Another mistake is not properly applying trigonometric functions, which can lead to incorrect solutions.

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