# Angle of Vector: Find Resultant Force & Direction

• delfam
In summary, to find the resultant force and direction between -180 and 180 degrees of two forces (406N at 17 degrees and 256N at -26 degrees) applied to a 3400kg car, we first calculate the x-components of the forces (388.26N and -230.09N). Then, using the arctan function, we find that the resultant force has a magnitude of 618.35N and a direction of approximately 0.6 degrees. This falls within the feasible region of -4.5 to 17 degrees, indicating that our answer is reasonable. It is important to follow the rules of trigonometry when calculating resultant forces.
delfam

## Homework Statement

two forces, 406N at 17 degrees and 256N at -26 degrees are applied to a a 3400kg car. Find resultant of these two forces and the direction of the resultant force between -180 and 180 degrees.

## The Attempt at a Solution

406cos(17) = 388.26, 256cos(26) = 230.09, 230.09 = 388.26 = 618.35N
arctan(230.09/388.26) = 30.65 degrees

because it's a car and it doesn't move on the y-axis. I'm still not sure how to get the angle though.

delfam said:
because it's a car and it doesn't move on the y-axis. I'm still not sure how to get the angle though.

The car has nothing to do with anything. And changing -26 degrees to 26 was a nice trick, but you need to follow the rules because the next step requires the actual angle.

Does your answer make sense that the highest forces pulling at 17 degrees somehow generates a force vector that is 30 degress? Your answer is obviously somewhere between (17+26)/2=21.5 degree spread between the two forces. You have 1.58 times the force at 17 degrees than at -26 degrees, so you should be slightly higher off a midpoint mark (17-21.5 = -4.5 deg). So your answer should be above 0 degree mark at least, but not at 30 degrees! Your feasible region is thus between (-4.5, 17) degrees

Look at it this way.. if 17 degree force has (406/256)= 1.5859375 times more weight than the negative force, then your resultant should be around 1.5859375*17 + 1*(-26) ~ 0.96 degrees. Or more closely to the answer now, 1*17 + 0.60591138*(-26) ~ 0.60 degrees

You need to calculate all resultant forces and follow rules of trigonometry.

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## 1. What is the angle of vector?

The angle of vector is the measurement of the direction in which a vector is pointing. It is measured in degrees or radians and is typically denoted by the Greek letter theta (θ).

## 2. How do you find the resultant force using the angle of vector?

To find the resultant force, you can use the trigonometric functions sine, cosine, and tangent. These functions involve the angle of vector and the magnitude of the vector. By using the Pythagorean theorem and these trigonometric functions, you can determine both the magnitude and direction of the resultant force.

## 3. Can the angle of vector be negative?

Yes, the angle of vector can be negative. This occurs when the vector is pointing in the opposite direction of a designated reference direction. In this case, the angle would be measured in the opposite direction, resulting in a negative value.

## 4. What is the difference between the angle of vector and the direction of the vector?

The angle of vector refers to the measurement of the direction in which a vector is pointing, while the direction of the vector refers to the compass direction or bearing in which the vector is pointing. The angle of vector is typically measured in degrees or radians, while the direction is measured in degrees, minutes, and seconds.

## 5. How does the angle of vector affect the resultant force?

The angle of vector plays a crucial role in determining the magnitude and direction of the resultant force. If the angle is small, the resultant force will be close to the magnitude of the original vector. However, if the angle is large, the resultant force will be significantly smaller than the original vector. The direction of the resultant force will also be affected by the angle of vector, as it determines the direction in which the force is acting.

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