Magnitude and angles of a force

In summary: But your calculations are correct.In summary, the force given by F= 20i - 60j + 90k N has a magnitude of 110 N and forms angles of 79.5 degrees, 123.1 degrees, and 35.1 degrees with the x, y, and z coordinate axes, respectively. If a different answer is given, it may be due to a difference in measurement units.
  • #1
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Homework Statement


a force is given by F= 20i - 60j + 90k N. Find its magnitude and the angles it forms with the coordinate axis.

Homework Equations


F = magnitude of F times the unit vector
magnitude is square root (Fx squared + Fy squared + Fz squared)
and the unit vector can be written as (cos(theta)x)i + (cos(theta)y)j + (cos(theta)z)k
x for x component
y for y component
z for z component

to find the angle of the x component: inverse cosine of Fx/magnitude

The Attempt at a Solution


For the magnitude I got 110
for the angles with respect to x, y, z: 79.5, 123.1, 35.1

please tell me if i did something wrong! thanks
 
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  • #2
That should be correct.
 
  • #3
IHave said:

Homework Statement


a force is given by F= 20i - 60j + 90k N. Find its magnitude and the angles it forms with the coordinate axis.

Homework Equations


F = magnitude of F times the unit vector
magnitude is square root (Fx squared + Fy squared + Fz squared)
and the unit vector can be written as (cos(theta)x)i + (cos(theta)y)j + (cos(theta)z)k
x for x component
y for y component
z for z component

to find the angle of the x component: inverse cosine of Fx/magnitude

The Attempt at a Solution


For the magnitude I got 110
for the angles with respect to x, y, z: 79.5, 123.1, 35.1

please tell me if i did something wrong! thanks

Agree. All looks good.
 
  • #4
If a textbook or something gives a different answer, it's possible the angle is in another measurement, for example radians.
 
  • #5


Your solution looks correct. However, it would be helpful to provide more context or explanation for the solution, such as explaining the use of the unit vector and the inverse cosine function. Additionally, it would be helpful to provide the units for the angles, as angles are typically measured in degrees or radians. Overall, your solution shows a good understanding of vector components and their relationship to magnitude and angles.
 

FAQ: Magnitude and angles of a force

1. What is meant by the magnitude of a force?

The magnitude of a force is the measure of the strength or intensity of the force. It is typically expressed in units of Newtons (N) in the metric system or pounds (lb) in the imperial system.

2. How is the magnitude of a force calculated?

The magnitude of a force is calculated by multiplying the mass of an object by its acceleration. This is represented by the formula F = ma, where F is the force, m is the mass, and a is the acceleration.

3. What is the significance of the direction of a force?

The direction of a force is important because it determines the effect the force will have on an object. Forces in the same direction will add together, while forces in opposite directions will cancel each other out.

4. How is the direction of a force represented?

The direction of a force can be represented using a vector, which is an arrow pointing in the direction of the force. The length of the arrow represents the magnitude of the force.

5. How are the magnitude and direction of a force related?

The magnitude and direction of a force are both required to fully describe the force. They are represented by the length and direction of a vector, respectively. In order to fully understand the effect of a force on an object, both the magnitude and direction must be taken into account.

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