A flower pot with a mass of 3.8kg is hanging by 2 wires that make an angle of 48° from the horizontal.
what is the tension in each wire
To find the tension in each wire, we need to analyze the forces acting on the flower pot. Here's how you can approach it:
Step 1: Draw a diagram:
Draw a diagram representing the situation. Label the angle between the wires and the horizontal as 48°.
Step 2: Identify the forces:
There are two forces acting on the flower pot: the weight (mg) pulling downward and the tension in each wire (T1 and T2) pulling upward.
Step 3: Resolve the weight force:
The weight force can be resolved into two components: one parallel to the wires (T1) and the other perpendicular to the wires (mg * cos(48°)).
Step 4: Set up force equations:
Write separate force equations for the vertical and horizontal direction.
In the vertical direction:
The sum of the vertical forces is zero since the flower pot is not accelerating vertically.
T1 * sin(48°) + T2 * sin(48°) = mg * cos(48°)
In the horizontal direction:
There is no horizontal acceleration, so the sum of the horizontal forces is zero.
T1 * cos(48°) = T2 * cos(48°)
Step 5: Solve the equations:
Since the angle and mass are given, substitute the known values into the equations.
T1 * sin(48°) + T2 * sin(48°) = (3.8 kg) * cos(48°)
T1 * cos(48°) = T2 * cos(48°)
Step 6: Simplify and solve for T1 and T2:
Divide the second equation by cos(48°) to get T1 = T2.
Substitute this value into the first equation and solve for T1:
2T1 * sin(48°) = (3.8 kg) * cos(48°)
T1 * sin(48°) = (3.8 kg) * cos(48°) / 2
Finally, calculate the value of T1:
T1 = (3.8 kg) * cos(48°) / (2 * sin(48°))
T1 ≈ 2.25 N
Since T1 = T2, the tension in each wire is approximately 2.25 N.