# How do I solve this vector problem involving three ropes and a rough surface?

• y90x
In summary, the conversation discusses a problem involving adding three vectors to find the resulting acceleration of a 30 kg mass on a rough surface. The book suggests using the component method and finding the angle of the y and x components, which is initially -1.25 but later changes to -51. The conversation also includes the attempt at a solution, which involves calculating the x and y components for each rope and finding the resultant magnitude and angle. However, it is noted that there may be a mistake in the angle calculation for rope B, and the question is raised about including the friction force in the solution.
y90x

## Homework Statement

I’m working on a problem that requires adding 3 vectors . And while I was following the book, it said to find the angle to divide the y over the x components of the resistant , and showed the angle to be -1.25 but then follow d to change to -51 .
How did it change ? The book doesn’t explain I’ll inclide a photo of the textbook so you can see what I’m talking about
Here’s the problem I’m working on just in case:

Three horizontal ropes are tied to a 30 kg mass resting on a rough surface. The coefficient of friction between the mass and the surface is 0.12. Rope A has tension 60 N directed Northwest, rope B has tension 70 N directed 20° East of South, and rope C has tension 80 N directed 35 North of West. Find the resulting acceleration of the 30 kg mass.

## Homework Equations

The component method for adding vectors

## The Attempt at a Solution

Rope A :
-60cos(45) + 60sin(45)= A
-42.426 + 42.426 = A
Rope B :
70cos(20) + -70sin(20) = B
65.778 + -23.94
Rope C:
-80cos(35) + 80sin(35) = C
-65.532 + 45.886 = C

To find the resultant magnitude :
Square root of ( all the X components added up) (-42,1800)^2 + 64.3711^2 ( all the Y components added up)
= 76.959

To find the angle :
Pheta = tan^(-1)(Y/X)
= tan^(-1) (64.3711/-42.1800)
= -56.8 Solution of the actual problem :
1.72 m/s^2 at 15.0 north of westhttps://www.physicsforums.com/attachments/215616

y90x said:
rope B has tension 70 N directed 20° East of South,

## The Attempt at a Solution

Rope B :
70cos(20) + -70sin(20) = B
65.778 + -23.94
Note that 20° East of South is not the same as 20° South of East

Also, do you need to add in the friction force?

TSny said:
Note that 20° East of South is not the same as 20° South of East

Also, do you need to add in the friction force?

You’re right , thanks

## 1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is represented graphically by an arrow, with the length of the arrow representing the magnitude of the vector and the direction of the arrow indicating its direction.

## 2. How do you calculate the magnitude of a vector?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, to calculate the magnitude of a vector, you square each component of the vector, add them together, and then take the square root of the result.

## 3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, whereas a vector has both magnitude and direction. For example, speed is a scalar quantity (e.g. 50 miles per hour), while velocity is a vector quantity (e.g. 50 miles per hour north).

## 4. How do you add or subtract vectors?

To add or subtract vectors, you simply add or subtract the corresponding components of the vectors. For example, if vector A has components (3,2) and vector B has components (1,4), the sum of A and B would be (3+1, 2+4) = (4,6).

## 5. What are some real-world applications of vectors?

Vectors are used in many fields, such as physics, engineering, and computer graphics. Some real-world applications of vectors include navigation systems, force and motion calculations, and 3D modeling and animation. They are also used in sports, such as determining the trajectory of a baseball or calculating the velocity of a soccer ball.

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