Force Vector Magnitude Distance

You will need to find the angle between F and D, which is not 45 degrees.In summary, the problem involves calculating the work done by a force of F = i + 2j - 3k on a particle that moves 10 feet in the direction of i + j. The correct formula for work is W = ||F|| * ||D|| * cosθ, where θ is the angle between F and D. After finding the magnitude of F and D, the angle between them can be calculated and plugged into the formula to find the work done, which is not 20√7 as calculated in the attempt.
  • #1
Justabeginner
309
1

Homework Statement


A force of f= i + 2j- 3k is applied to a particle that moves 10 feet in the direction of i + j. How much work is done?


Homework Equations


W= ||F|| dot product d


The Attempt at a Solution


D= 10 cos 45 i + 10 sin 45 j
D= 5sqrt(2) i + 5 sqrt(2) j
F= i + 2j - 3k

W= ||F|| dot product d
W= sqrt(14) dot product (5sqrt(2)i + 5sqrt(2)j)
W= 5sqrt(28) + 5 sqrt(28)
W= 10sqrt(28)
W= 20sqrt(7)
Is this even right? Thanks!
 
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  • #2
Justabeginner said:

Homework Statement


A force of f= i + 2j- 3k is applied to a particle that moves 10 feet in the direction of i + j. How much work is done?


Homework Equations


W= ||F|| dot product d

##\| F\|## is a scalar and you can't dot a scalar and a vector.

The Attempt at a Solution


D= 10 cos 45 i + 10 sin 45 j
D= 5sqrt(2) i + 5 sqrt(2) j
F= i + 2j - 3k

W= ||F|| dot product d
W= sqrt(14) dot product (5sqrt(2)i + 5sqrt(2)j)
W= 5sqrt(28) + 5 sqrt(28)
W= 10sqrt(28)
W= 20sqrt(7)
Is this even right? Thanks!

No, it is not correct. You have F and D correct. Look up the correct formula for work.
 

Related to Force Vector Magnitude Distance

1. What is force vector magnitude distance?

Force vector magnitude distance is a measurement that describes the strength and direction of a force, as well as the distance over which the force acts. It is a vector quantity, meaning it has both magnitude (size) and direction.

2. How is force vector magnitude distance calculated?

To calculate force vector magnitude distance, one must determine the magnitude of the force and the distance over which it acts. The magnitude is often measured in Newtons (N) and the distance in meters (m). The calculation involves multiplying the magnitude by the distance, resulting in a unit of Newton-meters (Nm).

3. What is the importance of understanding force vector magnitude distance?

Understanding force vector magnitude distance is important in many areas of science, such as physics and engineering. It allows us to accurately describe and predict the effects of forces on objects, and to design structures and machines that can withstand and utilize these forces.

4. How does force vector magnitude distance differ from scalar distance?

Force vector magnitude distance differs from scalar distance in that it takes into account both the strength and direction of a force, whereas scalar distance only considers the numerical value of the distance traveled. Force vector magnitude distance also has a unit of measurement (Nm), while scalar distance is simply measured in units of length (m).

5. Can force vector magnitude distance be negative?

Yes, force vector magnitude distance can be negative. This occurs when the force is acting in the opposite direction of the displacement, resulting in a negative value for the force vector magnitude distance. This negative value indicates that the force is doing work in the opposite direction of the displacement.

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