Two strings support a small 8kg body. find the tension in the strings if they both make 30° with the vertical.
45.26N
To find the tension in the strings, we can use the concept of equilibrium in a system.
In this case, since the body is supported by two strings, the vertical forces must balance the weight of the body.
First, let's understand the forces acting on the body. We have the weight acting downward, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the mass of the body is 8kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:
Weight = 8kg × 9.8 m/s² = 78.4 N
Next, let's consider the tension in the strings. Each string can be resolved into two components: one perpendicular to the vertical (the tension force) and one parallel to the vertical (the horizontal component).
Since both strings make an angle of 30° with the vertical, we can determine the tension in each string by considering the equilibrium of forces in the vertical direction.
Applying trigonometry, we can determine the vertical component for each string's tension:
Vertical Component = Tension × sin(30°)
Now, since there are two strings supporting the body, the vertical components of the tensions must add up to balance the weight:
2 × Vertical Component = Weight
Substituting the values, we have:
2 × Tension × sin(30°) = 78.4 N
Now, solving for Tension:
Tension = (78.4 N) / (2 × sin(30°))
Using a calculator, we can compute the value of the tension:
Tension ≈ 78.4 N / (2 × 0.5) ≈ 78.4 N / 1 ≈ 78.4 N
Therefore, the tension in each string is approximately 78.4 Newtons.