# Vectors/Tension Word Problem Help

• May 17th 2011, 02:31 PM
IanCarney
Vectors/Tension Word Problem Help
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.

I found that the angles inside the "triangle" are 90, 53 and 37, but I'm not sure where to go after this. Any help appreciated!
• May 18th 2011, 02:24 AM
HallsofIvy
You can use those angles to find the horizontal and vertical components of the force. If \$\displaystyle T_1\$ is the tension in the string that makes 53 degrees with the horizontal the the horizontal component of force is \$\displaystyle T_1cos(53)\$ and the vertical component is \$\displaystyle T_1sin(53)\$. Do the same with the string that makes the 37 degree angle.

Obviously, depending on the which string is on the right and which is on the left, one of the horizontal forces will be positive and one will be negative- it doesn't matter which you take positive. Both vertical forces will be upward. The sum of the horizontal forces must be 0 and the sum of the vertical forces will be the weight of the mass, 5g Newtons (NOT 5 kg- that is not a force). That will give you two equations to solve for \$\displaystyle T_1\$ and \$\displaystyle T_2\$.
• May 19th 2011, 01:06 PM
IanCarney
Quote:

Originally Posted by HallsofIvy
You can use those angles to find the horizontal and vertical components of the force. If \$\displaystyle T_1\$ is the tension in the string that makes 53 degrees with the horizontal the the horizontal component of force is \$\displaystyle T_1cos(53)\$ and the vertical component is \$\displaystyle T_1sin(53)\$. Do the same with the string that makes the 37 degree angle.

Obviously, depending on the which string is on the right and which is on the left, one of the horizontal forces will be positive and one will be negative- it doesn't matter which you take positive. Both vertical forces will be upward. The sum of the horizontal forces must be 0 and the sum of the vertical forces will be the weight of the mass, 5g Newtons (NOT 5 kg- that is not a force). That will give you two equations to solve for \$\displaystyle T_1\$ and \$\displaystyle T_2\$.

I'm not sure if I follow. I haven't taken physics, and this is for an introductory vectors class so I'm a little confused on how I would calculate the tension.

The answer in the book states a tension of 39.2N for the 24 cm string and 29.4N for the 32 cm string.