Homework 5 Due On 22/11/41: The Distance Between Two Telepho

Homework 5 Due On 221141the Distance Between Two Telephone Pole I

Homework-5 (due on 2.21..The distance between two telephone pole is 50m. When a 1kg bird lands on the telephone wire midway between the poles the wire sags 0.2m. Draw the free body diagram of the Bird. How much tension does the bird produce in the wire. 2.A hocky puck struck by a hocky stick in given an initial speed of 20m/s on a frozen pond. The puck remains on the ice and slides 1.2x102m slowing down until it comes to rest. Determine the coefficient of kinetic friction between the puck and the ice.

Paper For Above instruction

Physics Problems Related to Forces and Friction

In this paper, we explore two fundamental problems in mechanics: one involving the tension in a flexible wire supporting a load, and the other analyzing the kinetic friction acting on a sliding puck. These problems encapsulate important concepts such as free body diagrams, trigonometric resolution of forces, and the calculation of friction coefficients, which are critical in understanding real-world physics applications ranging from structural engineering to sports dynamics.

Problem 1: Tension in a Telephone Wire Supporting a Bird

The first problem examines the scenario in which a bird lands on a telephone wire suspended between two poles. The given parameters include the distance between the poles (50 meters), the mass of the bird (1 kilogram), and the amount by which the wire sags (0.2 meters) when the bird is centered. The main goal is to determine the tension in the wire caused by the bird's weight.

To analyze this situation, a free body diagram of the bird is essential. The diagram shows the gravitational force acting downward (the weight, W = mg), and two tension forces in the wire acting upward and at angles on either side of the bird. Because the bird is at equilibrium, the sum of forces in both the vertical and horizontal directions must be zero.

The key geometric aspect involves the sag of the wire, which creates a right-angled triangle where the horizontal distance from the wire's lowest point to the pole supports is half of the span (25 meters), and the vertical displacement is 0.2 meters. Using these, we determine the angle θ that the tension makes with the horizontal component.

The tension (T) in the wire can be found using the relation:

T = (W/2) / sinθ

where θ = arctangent of (vertical sag / horizontal half-span) = arctangent (0.2 / 25) ≈ 0.008 radians.

Given that the bird's weight W = 1 kg * 9.8 m/s² = 9.8 N, the tension T comes out to be approximately:

T ≈ (9.8 / 2) / 0.008 ≈ 612.5 N

Thus, the tension in the wire caused by the bird is roughly 612.5 newtons, indicating a significant load relative to the wire's capacity.

Problem 2: Friction Acting on a Sliding Hockey Puck

The second problem involves a hockey puck struck with an initial velocity of 20 m/s on an icy surface. The puck slides a distance of 120 meters before coming to rest, implying that kinetic friction is acting against its motion. The task is to compute the coefficient of kinetic friction (μk) between the puck and ice.

Applying the principles of work and energy or Newton's second law, we recognize that the initial kinetic energy of the puck is dissipated by the work done by friction:

Initial kinetic energy = (1/2)mv²
Work done by friction = friction force  distance = μk  m  g  d

Since the puck comes to rest, the initial kinetic energy equals the work done:

(1/2)mv² = μk  m  g * d

Mass (m) cancels out from both sides, leading to:

μk = v² / (2  g  d)

Substituting the values: v = 20 m/s, g = 9.8 m/s², d = 120 meters, we find:

μk = (20)² / (2  9.8  120) ≈ 400 / (2  9.8  120) ≈ 400 / 2352 ≈ 0.17

Therefore, the coefficient of kinetic friction between the hockey puck and the ice is approximately 0.17, consistent with typical values for ice and hockey pucks.

Conclusion

This analysis clearly demonstrates the application of fundamental physics principles to real-world scenarios. The calculation of tension in a wire under load emphasizes the importance of free body diagrams and trigonometric relationships in structural analysis. Meanwhile, examining the effects of kinetic friction on a puck illustrates energy conservation principles and the significance of friction coefficients in dynamic systems. Such understanding is vital in engineering, sports science, and various technological fields, highlighting the interdisciplinary relevance of physics.

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