Solving Vectors: Resolve T With 2 Equations & G = 9.8

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In summary, the problem involves two equations that need to be solved for T, with two different variables. The equations are 10 + T2cos25−T1cos45 = 0 and T1sin 45+ T2sin 25−8g = 0. The attempted solution involved using the values of cos 25/45 and sin 25/45, but the person was unable to make progress. Another person suggests multiplying the first equation by sin25º and the second equation by cos25º, then subtracting to get an equation in T1.
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olee
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Homework Statement


I have two equations in which I need to solve for T, involving two different variables and I'm not too sure how to solve.
(G = 9.8)
10 + T2cos25−T1cos45 = 0
T1sin 45+ T2sin 25−8g = 0


Homework Equations



10 + T2cos25−T1cos45 = 0
T1sin 45+ T2sin 25−8g = 0

The Attempt at a Solution



I tried solving where i used the values of cos 25/45 and sin 25/45 and I couldn't get anywhere.
 
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  • #2
Hi olee! :smile:
olee said:
10 + T2cos25−T1cos45 = 0
T1sin 45+ T2sin 25−8g = 0

uhhh? multiply the first equation by sin25º, and the second equation by cos25º, and subtract, to get an equation in T1.
 

FAQ: Solving Vectors: Resolve T With 2 Equations & G = 9.8

How do you resolve a vector using 2 equations?

To resolve a vector, you need to break it down into its components. This can be done by using two equations, one for the x-component and one for the y-component. These equations can be derived from the given magnitude and direction of the vector.

What is the significance of G = 9.8 in solving vectors?

G = 9.8 is the acceleration due to gravity on Earth. This value is used in solving vectors that involve gravitational forces, such as projectile motion or free fall.

3. Can you use other values for G if you are not on Earth?

Yes, the value of G can vary depending on the location and mass of the celestial body. For example, on the moon, G = 1.62 m/s^2. It is important to use the correct value of G when solving vectors in different environments.

4. What happens if you only have one equation to solve a vector?

If you only have one equation, you can still solve for the unknown variables, but the solution may not be unique. This means that there could be multiple combinations of values that satisfy the given equation, making it more difficult to accurately determine the vector's components.

5. Are there any shortcuts or tricks for solving vectors with multiple equations?

Yes, there are various techniques, such as the graphical method or the parallelogram method, that can help simplify the process of solving vectors with multiple equations. These methods involve visualizing the vectors and their components, making it easier to understand and solve the equations.

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