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?
I do not believe your lengths. are they all in meters?
Pls send the answers
To find the tension in the strings, we need to consider the forces acting on the lamp. There are two forces: the weight of the lamp and the tension in the strings.
Let's denote the tension in the shorter string as T1 and the tension in the longer string as T2. The weight of the lamp can be calculated as the mass multiplied by the acceleration due to gravity. In this case, the mass of the lamp is 5 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
So, the weight of the lamp is given by:
Weight = mass × acceleration due to gravity
= 5 kg × 9.8 m/s^2
= 49 N
Now, let's consider the forces acting on the lamp in the horizontal direction. Since the lamp is hanging vertically, the vertical component of the weight is balanced by the tension in the strings. Therefore, the tension in the strings is equal to the vertical component of the weight.
To calculate the vertical component of the weight, we need to find the angles between the strings and the vertical direction. Considering the triangle formed by the lamp, the vertical direction, and the string, we can use trigonometry to determine these angles.
For the shorter string with a length of 1.5 m, let's call the angle between the shorter string and the vertical direction as θ1. Using the given distance between the hooks (2.5 cm = 0.025 m), we have:
sin(θ1) = 0.025 m / 1.5 m
θ1 = sin^(-1)(0.025 / 1.5)
Similarly, for the longer string with a length of 2 m, let's call the angle between the longer string and the vertical direction as θ2. Using the given distance between the hooks (2.5 cm = 0.025 m), we have:
sin(θ2) = 0.025 m / 2 m
θ2 = sin^(-1)(0.025 / 2)
Now, we can calculate the tension in the strings using the following formula:
Tension = weight / cos(θ)
For the shorter string:
T1 = 49 N / cos(θ1)
For the longer string:
T2 = 49 N / cos(θ2)
By plugging in the calculated values for θ1 and θ2, we can find the tension in the strings.