Solve for vectors needed to cancel out given sets of forces

In summary, the conversation is about solving for the last vector, vector D, in a set of forces by finding its x and y components, magnitude, and direction. The speaker is unsure about the direction they calculated for vector D and asks for clarification. The other speaker suggests double checking the angle, which should be a small negative angle close to 360 degrees due to the components being in the fourth quadrant. The first speaker mistakenly thought the angle should be added to 270 degrees instead of subtracted from 360 degrees.
  • #1
aron silvester

Homework Statement


For this assignment, I am given sets of forces and asked to solve for the force(s) needed to cancel them out. For this case, I am asked to solve for the last vector, which is vector D. I've successfully found its x and y component, magnitude, and mass (kg). I've also checked if all of their combined x and y components added up to zero by adding the x and y components for all vectors A, B, C, and D. What I don't understand is the answer I got for the direction of vector D. When I drew a diagram for vector D, it's located in quadrant 4, since x-component is 1.23 N, and y-component is -0.37 N. The direction I got was 253 degrees, clearly, it means that the vectors should be in quadrant 3, but according to my x and y component, it's pointing in quadrant 4. Did I make a mistake when calculating the direction of vector D?

Homework Equations


It's all in my work down below in part 3.

The Attempt at a Solution


Case 5.jpeg


 
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  • #2
Your math looks good to me as far as the components go. I would double check your angle however. From the two components, it should be a small negative angle that is close to 360 degrees rather than 270 degrees. Definitely in the fourth quadrant.
 
  • #3
magoo said:
Your math looks good to me as far as the components go. I would double check your angle however. From the two components, it should be a small negative angle that is close to 360 degrees rather than 270 degrees. Definitely in the fourth quadrant.
Isn't that how to find the angle by using the inverse of tangent, and we add 270 degrees because it's in the 4th quadrant?
 
  • #4
The inverse tangent will give you the angle of -16.8 degrees. Because it's in the fourth quadrant, you need to subtract it from 360 degrees. I'm not sure where you got the equation that adds it to 270 degrees.
 

FAQ: Solve for vectors needed to cancel out given sets of forces

1. What is the concept of vector addition and cancellation in solving for forces?

Vector addition and cancellation is a mathematical concept that involves combining multiple forces acting on an object to determine the overall resulting force. In order to do this, the direction and magnitude of each force must be taken into account, as well as the angle at which they act.

2. How do you determine the vectors needed to cancel out a given set of forces?

In order to determine the vectors needed to cancel out a given set of forces, you must first break down each force into its x and y components. Then, add together all of the x components and all of the y components separately. The resulting sums will be the x and y components of the overall resulting force. Finally, use the Pythagorean theorem to calculate the magnitude and trigonometry to determine the direction of the resulting force.

3. Can vectors in opposite directions cancel each other out?

Yes, vectors in opposite directions can cancel each other out. This is known as vector subtraction, where a force in one direction is subtracted from a force in the opposite direction. The resulting force will have a smaller magnitude or may even be zero if the two forces are equal.

4. What happens when there are more than two forces acting on an object?

When there are more than two forces acting on an object, the same principles of vector addition and cancellation apply. Each force must be broken down into its components and added together to determine the overall resulting force. This can be done iteratively, combining two forces at a time until all forces have been accounted for.

5. Are there any real-life applications of solving for vectors needed to cancel out forces?

Yes, there are many real-life applications of solving for vectors needed to cancel out forces. This concept is used in engineering to design structures that can withstand external forces, in physics to analyze the motion of objects, and in navigation to determine the direction and magnitude of travel. It is also used in sports and athletics to optimize performance and minimize the impact of external forces on the body.

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