The system shown in the Figure is in equilibrium. The mass of block 1 is 2.2 kg and the mass of block 2 is 3.5 kg. String 1 makes an angle = 28o with the vertical and string 2 is exactly horizontal.
what is the angle between the string that connects the masses and the string that hold m2?
What is the tension in the string between the two masses?
To find the angle between the string that connects the masses (string 1) and the string that holds m2 (string 2), we need to analyze the forces acting on the system.
Let's consider the forces acting on block 2 (m2). There are two forces acting on block 2: the tension in string 2 and the force of gravity. As the system is in equilibrium, these two forces must balance each other out.
The force of gravity on block 2 can be decomposed into two components: one perpendicular to string 2 and one parallel to it. The component parallel to string 2 will be balanced by the tension in string 2 since the block is not moving in that direction. Therefore, the angle between string 1 and string 2 is equal to the angle between the gravitational force component and string 1.
To find this angle, we can use trigonometry. The opposite side of the angle is the component of the gravitational force perpendicular to string 2, which is equal to m2 * g * cosθ (where θ is the angle at which string 1 is inclined with the vertical, which is given as 28°). The adjacent side is the component of the gravitational force parallel to string 2, which is equal to m2 * g * sinθ.
Therefore, the tangent of the angle between string 1 and string 2 is given by:
tan(θ angle) = (m2 * g * cosθ) / (m2 * g * sinθ)
Simplifying, we get:
tan(θ angle) = cosθ / sinθ
Using the trigonometric identity tan(θ) = sin(θ) / cos(θ), we can rewrite the equation as:
tan(θ angle) = 1 / tan(θ)
Solving for θ angle, we get:
θ angle = arctan(1 / tan(θ))
Using the given angle θ = 28°, we can calculate the angle between string 1 and string 2 using this formula.
To find the tension in the string between the two masses, we need to consider the forces acting on block 1. The tension in string 1 is responsible for balancing the gravitational force on block 1. Therefore, the tension in string 1 is equal to the weight of block 1, which is given by m1 * g.
Using the known masses (m1 = 2.2 kg, m2 = 3.5 kg) and the acceleration due to gravity (g = 9.8 m/s^2), we can calculate the tensions in the strings.