# Solving a Two-Dog Pulling Problem: Magnitude & Angle of Resultant Force

In summary, the force of 254 N is exerted by dog A, while the force of 328 N is exerted by dog B. The angle between the ropes is 59.0 degrees.
Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 59.0 degrees. Dog A exerts a force of 254 N and dog B exerts a force of 328 N.

Find the magnitude of the resultant force.
Find the angle the resultant force makes with dog A's rope.

I'm having trouble picturing the diagram in order to solve this problem.
I tried adding the sum of the x components and the y components but I don't know whether to use sin or cos.

I set the equation up as:
Fx = 254N + 328cos59 = 422.9N

Fy = 328sin59 = 281.15

I have a feeling these aren't correct.

I'd do it the way you've done it. If I draw it I get the exact same expressions for the x- and y-components as you do.

"I'd do it the way you've done it. If I draw it I get the exact same expressions for the x- and y-components as you do."

It's not giving me the correct answer.

That is.. very weird.

Perhaps I'm looking at the problem in the wrong way or something. I really don't know.. What's your resultant force?

I was having trouble finding that as well.

Oh.. okay. If you have the components it's easy to find the resultant force knowing about superposition and simple geometry.

I'm not sure what to tell you, because according to me your components are correct at least. And I'm not 100% sure where exactly it is that you're stuck, too. (Probably I'm too tired for thinking, it's rather late.)

I set the equation up as:
Fx = 254N + 328cos59 = 422.9N

Fy = 328sin59 = 281.15

I have a feeling these aren't correct.
Looks good to me. Keep going.

I agree. I thought the method of calculating it wasn't symmetrical.

I deleted my post.

I'll delete mine!

Now I'm really confused! =(
What do I do?

OK, so I figured out how to find the resultant force, but how do I find the angle it makes with dog A's rope?

You have the x and y components of the resultant. Use them to find the tangent of the angle, then the angle.

I used c^2 =a^2 + b^2 - 2abcostheta to solve for the resultant. How would I solve for the components? I was trying to before and I couldn't seem to get the correct answer.

I used c^2 =a^2 + b^2 - 2abcostheta to solve for the resultant. How would I solve for the components? I was trying to before and I couldn't seem to get the correct answer.
You found the components in your first post! The resultant is found using F2 = F2x + F2y.

(No need for the law of cosines, since you already found the components. You'd use that law if you didn't want to find the components.)

## 1. What is a two-dog pulling problem?

A two-dog pulling problem refers to a situation where two dogs are pulling on a rope or leash in different directions, causing a tension force to be applied to the rope. This can make it difficult for the person walking the dogs to control their movement and can also lead to discomfort or injury for the dogs.

## 2. How is the magnitude of the resultant force calculated in a two-dog pulling problem?

The magnitude of the resultant force in a two-dog pulling problem can be calculated using vector addition. This involves finding the sum of the individual forces acting on the rope, taking into account the direction and magnitude of each force. The resulting force will be the magnitude of the tension on the rope caused by the two dogs pulling in different directions.

## 3. Why is the angle of the resultant force important in solving a two-dog pulling problem?

The angle of the resultant force is important because it determines the direction in which the combined force is acting. This information is crucial for understanding how the dogs are pulling on the rope and can help in finding a solution to the problem. For example, if the resultant force is pulling to the left, this could indicate that one of the dogs is pulling harder than the other, causing an imbalance in the force.

## 4. What factors can affect the magnitude and angle of the resultant force in a two-dog pulling problem?

Several factors can affect the magnitude and angle of the resultant force in a two-dog pulling problem. These include the weight and strength of the dogs, their individual pulling tendencies, the length and material of the leash or rope, and any external forces such as wind or obstacles. The angle of the leash or rope can also play a role in determining the resultant force.

## 5. How can a two-dog pulling problem be solved?

A two-dog pulling problem can be solved by adjusting the magnitude and angle of the resultant force. This can be done by changing the length of the leash, training the dogs to walk in a specific formation, or using equipment such as a double leash or a no-pull harness. It is important to find a solution that is comfortable and safe for both the dogs and the person walking them.

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