Mass supported by two strings

NIn summary, the problem involves a 17kg mass supported by two strings, with T2 having a magnitude of 150N at an angle of 45° to the right of the vertical. The first part of the problem involves calculating the vector T1, which was found to be 122.1N at an angle of 60.31° to the left of the vertical. The second part requires finding T1 when T2 is acting vertically downwards with a magnitude of 150N, resulting in T1 acting vertically upwards with a force of 330.57N.
  • #1
ggmissmolly
2
0

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.
 
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  • #2
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 !
 
  • #3
I'm still not sure how you go about solving for T1 then.
 
  • #4
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
 
  • #5


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.
 

1. What is a mass supported by two strings?

A mass supported by two strings refers to a physical system in which a mass is suspended by two strings or ropes in a gravitational field. The two strings provide equal and opposite forces to support the weight of the mass, creating a stable equilibrium.

2. How does the mass affect the tension in the strings?

The mass of the object has no direct effect on the tension in the strings. As long as the mass is in equilibrium, the tension in each string will be equal to half of the weight of the mass. However, if the mass is not in equilibrium, the tension in the strings will change accordingly to support the weight and restore equilibrium.

3. What is the relationship between the angles of the strings and the mass?

The angles of the strings are directly related to the weight of the mass and the tension in the strings. As the weight of the mass increases, the angles of the strings will decrease, and vice versa. Additionally, as the tension in the strings increases, the angles will increase as well.

4. Can the mass be supported by only one string?

Yes, a mass can be supported by only one string if the string is strong enough to support the weight of the mass. However, this would not create a stable equilibrium, as any small disturbance could cause the mass to fall.

5. How does the distance between the strings affect the system?

The distance between the strings has a direct effect on the tension in the strings and the angles at which they are positioned. As the distance between the strings increases, the tension in the strings will decrease and the angles will become more acute. On the other hand, as the distance between the strings decreases, the tension will increase and the angles will become more obtuse.

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