The distance between two telephone poles is 54 m. When a 2.0 kg bird lands on the telephone wire midway between the poles, the wire sags 0.16 m. How much tension in the wire does the bird produce? Ignore the weight of the wire. Answer in units of N.
To calculate the tension produced by the bird on the wire, we can use the formula for tension:
Tension = Weight + Sagging Force
First, let's calculate the weight of the bird:
Weight = mass * gravitational acceleration
mass = 2.0 kg
gravitational acceleration = 9.8 m/s^2 (approximate value)
Weight = 2.0 kg * 9.8 m/s^2
Weight = 19.6 N
Now, let's calculate the sagging force caused by the bird:
Sagging Force = (1/2) * bird's weight
Sagging Force = (1/2) * 19.6 N
Sagging Force = 9.8 N
Finally, let's calculate the tension in the wire:
Tension = Weight + Sagging Force
Tension = 19.6 N + 9.8 N
Tension = 29.4 N
Therefore, the bird produces a tension of 29.4 N on the wire.
To find the tension in the wire produced by the bird, we can use the concept of equilibrium. Since the bird is at rest on the wire, the total forces acting on the bird-wire system must add up to zero.
Let's analyze the forces acting on the bird-wire system:
1. Gravitational force (weight of the bird):
The weight of the bird can be calculated using the equation: weight = mass * gravity, where mass is given as 2.0 kg and gravity is approximately 9.8 m/s^2. So, the weight of the bird is 2.0 kg * 9.8 m/s^2 = 19.6 N. However, we can ignore the weight of the bird in this problem since we are only concerned with the tension in the wire.
2. Tension forces:
There are two segments of the wire, each pulling on the bird in opposite directions. The tension forces acting on the bird from the left and right sides are equal in magnitude and opposite in direction, resulting in a net force of zero. Let's denote the tension force as T.
Since the wire sags downward when the bird lands, the vertical components of the tension forces provide the upward force to balance the weight of the bird. So, there is a total upward force of 19.6 N acting on the bird.
Now, let's consider the horizontal components of the tension forces. Since the bird is positioned midway between the poles, the horizontal components of the tension forces are equal, and they balance each other out, leading to a net horizontal force of zero.
Since the wire sags 0.16 m, the vertical component of the tension force acting on the bird is equal to the weight of the bird, which is 19.6 N.
To find the tension force, we need to calculate the total tension force from both sides of the wire. Since the horizontal components from each side cancel each other out, we have:
Total tension force = 2 * vertical tension force = 2 * 19.6 N = 39.2 N.
Therefore, the bird produces a tension force of 39.2 N in the wire.