Vector Components (resultants)

In summary, the conversation discusses how to determine the tension in two strings suspending a 5 kg mass. There is confusion over whether to consider the 40 cm length as the resultant or rearrange the 24 and 32 cm lengths as head to tail vectors. The force of gravity is calculated to be 49.05, but it is unclear how to incorporate the other two lengths into the problem. It is suggested to draw a free body diagram and use the sum of forces at the x and y directions to solve for the tensions. Further clarification is requested for the specific details and steps of the problem.
  • #1

Homework Statement




A mass of 5 kg is suspended by two strings, 24 cm and 32 cm long, from two points that are 40 cm apart and at the same level. Determine the tension in each of the strings.


Would the 40 cm length be the resultant or do you rearrange the 24 and 32 as head to tail vectors.

The force of gravity is (5)(9.81) = 49.05 but I don't know how to make the other two into vectors (if i have too?)

please helppp! :) :)
 
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  • #2
You don't need vector math for this, draw out the FBD of the intersect , you have two unknowns (T1, T2) and use the sum of forces at the x and at the y for this, you know they are in equilibrium as the ropes aren't breaking so their sums are always equal to zero.

I had more in here, but I'm not exactly sure what you are asking for or what you have already done, please elaborate.
 

What are vector components?

Vector components are the individual parts of a vector that point in different directions. They are typically represented as x and y components in a two-dimensional coordinate system, or x, y, and z components in a three-dimensional coordinate system.

How do you calculate vector components?

To calculate vector components, you need to know the magnitude and direction of the vector. The x component is calculated by multiplying the magnitude by the cosine of the angle between the vector and the x-axis. The y component is calculated by multiplying the magnitude by the sine of the angle between the vector and the y-axis.

What is the resultant vector?

The resultant vector is the vector that represents the sum of two or more vectors. It is the combination of all the vector components and represents the overall magnitude and direction of the combined vectors.

How do you find the resultant vector?

To find the resultant vector, you can use the Pythagorean theorem to calculate the magnitude and trigonometric functions to calculate the direction. Alternatively, you can use graphical or algebraic methods to add the individual vector components together.

What is the difference between vector components and scalar components?

Vector components have both magnitude and direction, while scalar components only have magnitude. Scalar components are represented by a single number, while vector components are typically represented as two or three numbers for different directions.

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