How Do You Calculate Tension in Different Configurations of Supporting Strings?

[ggmissmolly]

Homework Statement

A mass of 17kg is supported statically by two strings. T2 has a magnitude of 150N at β=45° to the right of the vertical. (a)Calculate the vector T1. (b) If T2 was acting vertically downwards with the same magnitude as in (a) calculate T1.

Homework Equations

0=T1sinα-T2sinβ
0=T2cosβ+T1cosα-mg

The Attempt at a Solution

I calculated T1 for the first part and found it to be 122.1N at 60.31° to the left of the vertical. I'm not sure how to do the second part.

 

[technician]

I got the same answers for part 1 as you did.
If T2 is acting vertically downwards with a tension of 150N then it seems to me that T1 must be acting vertically upwards if these are 2 STRINGS supporting a mass !

 

[ggmissmolly]

I'm still not sure how you go about solving for T1 then.

 

[technician]

I would say that T1 is now providing the upwards force to hold the 17kg mass plus the 150N downwards force caused by T2
So (9.81 x 17) + 150

 

[asteriatic]

I would suggest breaking down the forces acting on the mass in question. In this scenario, we have two strings, T1 and T2, supporting the mass, as well as the force of gravity acting downwards. The first part of the question asks for the vector T1, which can be found by using the equations given and solving for T1. However, in the second part, T2 is now acting vertically downwards instead of at an angle. This means that the angle β is now equal to 90°, and the equation for the vertical component of T2 will be different. By breaking down the forces and using the equations given, we can solve for T1 in this new scenario. It is important to carefully consider the direction and magnitude of all forces when solving for T1 in this situation.