Final answer:
To calculate the tension in a telephone wire when a 2.7 kg bird lands in the middle, causing a 40.0-degree angle with the horizontal, use the formula T = (m*g) / (2*sin(θ)). By balancing the weight with the vertical component of the tension, the exact tension can be found through calculation.
Step-by-step explanation:
A bird with a mass of 2.7 kg lands on the middle of a horizontal telephone wire, causing it to make an angle of 40.0 degrees with the horizontal.
To find the tension in the wire, we'll follow the concept that the vertical component of the tension must balance the bird's weight, and the horizontal components are equal and opposite since the bird is at the midpoint. The weight of the bird (force due to gravity) is given by W = m × g, where m is the mass of the bird and g is the acceleration due to gravity (approximately 9.81 m/s2).
Let's denote the tension in the wire as T, and since the bird is in equilibrium, the sum of forces in the vertical direction should be zero. We can set up the following equation:
2Tsin(θ) = mg,
where θ is the given angle. Therefore, the tension in the wire can be calculated as:
T = ⅔mg / sin(θ).
Plugging in the values, we get:
T = ½ × 2.7 kg × 9.81 m/s2 / sin(40.0°).
After calculating the sine of 40.0 degrees and applying the equation, we can determine the tension in the wire.