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Ch. 04 - Dynamics: Newton's Laws of Motion
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 04 - Dynamics: Newton's Laws of MotionProblem 4.82c
Chapter 4, Problem 4.82c

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66.
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(c) What force does the cable exert on the helicopter?

Verified step by step guidance
1
Identify the total mass being accelerated. This includes both the mass of the helicopter and the mass of the frame. Add these two masses together.
Calculate the total force needed to accelerate this combined mass upward. Use Newton's second law, F = ma, where 'm' is the total mass and 'a' is the acceleration.
Determine the force of gravity acting on the combined mass. This force can be calculated using the formula F_gravity = mg, where 'g' is the acceleration due to gravity (approximately 9.81 m/s²).
Calculate the total force exerted by the cable. This force must not only support the weight of the helicopter and the frame against gravity but also provide the additional force required for the upward acceleration. Add the force needed for acceleration to the gravitational force.
The force exerted by the cable on the helicopter is the total force calculated in the previous step, as this force is transmitted through the cable to lift both the helicopter and the frame.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is crucial for analyzing the forces acting on the helicopter and the frame, as it allows us to calculate the net force required for the upward acceleration.
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Weight

Weight is the force exerted by gravity on an object, calculated as the product of its mass and the acceleration due to gravity (W = mg). In this scenario, both the helicopter and the frame have weights that must be considered when determining the total force exerted by the cable.
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Tension in the Cable

Tension is the force transmitted through a cable or rope when it is pulled tight by forces acting from opposite ends. In this case, the tension in the cable must counteract the combined weight of the helicopter and the frame while also providing the additional force needed for the upward acceleration.
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Related Practice
Textbook Question

According to a simplified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?

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Textbook Question

A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 62 kg. How might the thief use this 'rope' to escape? Give a quantitative answer.

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Textbook Question

Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train's mass is 3.6 x 10⁵ kg, how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?

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