M1, Physics
posted by John .
Two hooks A and B are fixed to a ceiling, where AB is 2.5 m. A small object of mass 3 kg is suspended from A and B by two light inextensible strings so that it is 2 m from A and 1.3 m from B. calculate the tension in strings

so looking at the triangle formed by the ceiling and strings, you know three sides.
Angle A= angle from ceiling to 2 m string.
Law of cosines:
1.3^{2}=2^{2}+2.5^{2}2*2*2.5CosA
solve for angle A. Then, do the same to get angle B,
Now draw a perpendicular frm the weight to the ceiling. You have two new triangles, with 90 degree angles at the top, and two angles at the bottom from the verticals to the strings. Label them C and D (C on the long side). Labele the distance from A to the perpendicular x, and the other horiztonal distance, 2.5x
Your objective is to find angles C, D, and x
angle C= 90A
angle D=90B
Now x/2=cosA solve for x.
Finally, you are almost there to write the physics..
The sum of vertical forces is zero:
3gTension2*sinATension1.3*sinB=0
now the second equation:
sum of horizontal forces is zero.
Tension2*cosATension1*cosB=0
two equations, two unknowns.
Respond to this Question
Similar Questions

Physics
Two small spheres of mass 451 g and 695 g are suspended from the ceiling at the same point by massless strings of equal length 10.9 m . The lighter sphere is pulled aside through an angle of 65 degrees from the vertical and let go. … 
physics
Two small pith balls, each of mass m = 16.6 g, are suspended from the ceiling of the physics lab by 1.8 m long fine strings and are not moving. If the angle which each string makes with the vertical is è = 19°, and the charges on … 
Physics
Two small pith balls, each of mass m = 10.1 g, are suspended from the ceiling of the physics lab by 0.8 m long fine strings and are not moving. If the angle which each string makes with the vertical is è = 42.1°, and the charges … 
Physics
Two small pith balls, each of mass m = 16.6 g, are suspended from the ceiling of the physics lab by 1.8 m long fine strings and are not moving. If the angle which each string makes with the vertical is è = 19°, and the charges on … 
Physics
The ends of a light string are tied to two hooks A and B in a ceiling which are 100 cm apart horizontally so that the length between hooks is 140 cm. A 650g mass is then attached by a second length of string to a point C on the first, … 
physics
An object of weight 50 N is suspended vertically by two strings. The strings are of the same lenght and the angle between them is 60 degree. Draw a free body diagram of the forces acting on the object. Calculate the tension in the … 
Physics, Electricity and Magnetism, Sciences
Two small pith balls, each of mass m = 17.4 g, are suspended from the ceiling of the physics lab by 1.2 m long fine strings and are not moving. If the angle which each string makes with the vertical is = 17.9°, and the charges on … 
Physics
Two small pith balls, each of mass m = 17.4 g, are suspended from the ceiling of the physics lab by 1.2 m long fine strings and are not moving. If the angle which each string makes with the vertical is = 17.9°, and the charges on … 
Elective maths
A particle P of mass 7kg is suspended by two inextensible strings AP,BP of lengths 40cm and 75cm respectively. The ends, AP of the strings are attached to two point at the same level, whose distance apart is 85cm. Find angle APB and … 
Physics
A lamp of mass 5kg is hung from two hooks 2.5cm apart on the horizontal ceiling of room by strings of length 1.5m and 2m.Find tension in the strings?