Calculating Mass and Tension: Classical Mechanics Problems Solved

[eeeps333]

Hi, If these questions have been asked before, then please point me in the right direction.

1) Find the Mass of an object that is suspended by two strings. The tension on String one is 34 N and is held at a 40 degree angle with the horizontal (i.e., if a line was drawn through the center of the object, string one would form 40 degree angle between the vertical line and the horizontal). The tension in string 2 is 24 N and the angle is unknown.

2) Find the tension of a string that is parallel to the horizontal. The end of the string is attached to ANOTHER string, that creates a 60 degree angle with the horizontal. both strings are carying a 2 KG object at the point of connection

_______________________________
                     |    /
                     |   / 
                     |  /             
----------------  | /             <-------------------60 degree angle and this point
                     |
                    [M]

3)3 masses of mass M, 2M and 3M, are attached on a frictionless surface, look like this:

<--------2F---[M]---2----[ 2M ]----1---[ 3M ]------3F---->

if F= 12N what is the tension in string 1

 

[eeeps333]

correction.

Ques 1, the string (34n) forms a 40 degree angle with the vertical line. the veritcal line that is drawn from the horizontal above, through the suspended mass.

 

[baba89]

1) To find the mass of the object, we can use the equation T=mg, where T is the tension, m is the mass, and g is the acceleration due to gravity (9.8 m/s^2). In this case, we have two equations, one for each string: T1=34 N and T2=24 N. We also know that the angle between string one and the horizontal is 40 degrees. Using trigonometry, we can find the vertical component of the tension for string one, which is T1sin(40)=m1g. Similarly, for string two, we can find the vertical component of the tension as T2sin(theta)=m2g. Since both strings are supporting the same object, the mass will be the same for both equations. We can set these two equations equal to each other and solve for the mass: T1sin(40)=T2sin(theta) --> m1g=m2g --> m1=m2. Therefore, the mass of the object is the same as the mass of the object being supported by string two. We can use either equation to find the mass: m1=T1sin(40)/g=34sin(40)/9.8=4.5 kg.

2) To find the tension of the string parallel to the horizontal, we can use the same equation as before, T=mg. In this case, we have two equations, one for each string: T1=mg and T2=mg. We also know that the angle between the two strings is 60 degrees. We can use trigonometry to find the vertical component of the tension for both strings: T1cos(60)=mg and T2sin(60)=mg. Since both strings are carrying the same object, we can set these two equations equal to each other and solve for the tension: T1cos(60)=T2sin(60) --> T1=T2. Therefore, the tension in both strings is the same, and we can use either equation to find the tension: T1=mg=2(9.8)=19.6 N.

3) In this situation, we have three masses attached to a frictionless surface and connected by strings. We are given the force, F=12 N, and we need to find the tension in string one. To do this, we can use Newton's second law, F=