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Ch 09: Work and Kinetic Energy
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 09: Work and Kinetic EnergyProblem 69a
Chapter 9, Problem 69a

Write a realistic problem for which this is the correct equation(s).
T−(1500kg)(9.8m/s2)=(1500kg)(1.0m/s2)T-(1500\,\(\text{kg}\))(9.8\,\(\text{m/s}\)^2)=(1500\,\(\text{kg}\))\(\left\)(1.0\,\(\text{m/s}\)^2\(\right\))
P=T(2.0m/s)P=T(2.0\,\(\text{m/s}\))

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Step 1: Analyze the given equations and identify the physical quantities involved. The first equation, T - (1500 kg)(9.8 m/s²) = (1500 kg)(1.0 m/s²), represents a force balance equation, likely describing a scenario involving tension (T), gravitational force, and net acceleration. The second equation, P = T(2.0 m/s), relates power (P) to tension (T) and velocity (2.0 m/s).
Step 2: Recognize the context of the problem. The first equation suggests a situation where a 1500 kg object is being lifted or pulled vertically, with a net acceleration of 1.0 m/s². The tension in the rope or cable is counteracting the gravitational force and providing the net force for acceleration. The second equation indicates that power is being calculated based on the tension and the velocity of the object.
Step 3: Formulate a realistic problem scenario. For example, consider a crane lifting a 1500 kg load vertically at a constant velocity of 2.0 m/s, but initially accelerating the load at 1.0 m/s². The tension in the cable must overcome the gravitational force acting on the load and provide the necessary force for acceleration. Additionally, the power output of the crane can be calculated based on the tension and the velocity of the load.
Step 4: Relate the equations to the scenario. The first equation calculates the tension in the cable during the acceleration phase, while the second equation calculates the power output of the crane once the load is moving at a constant velocity of 2.0 m/s.
Step 5: Ensure the problem is clear and realistic. A possible problem statement could be: 'A crane is lifting a 1500 kg load vertically. During the initial phase, the load accelerates upward at 1.0 m/s². Calculate the tension in the cable during this phase. Once the load reaches a constant velocity of 2.0 m/s, determine the power output of the crane.'

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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 fundamental in understanding how forces affect the motion of objects, allowing us to calculate the net force when multiple forces are acting simultaneously.
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Intro to Forces & Newton's Second Law

Tension in a Rope

Tension is the force transmitted through a rope or cable when it is pulled tight by forces acting from opposite ends. In problems involving pulleys or hanging objects, tension plays a crucial role in determining the forces acting on the system, often balancing gravitational forces and providing the necessary acceleration.
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Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time, allowing us to solve for unknown variables in motion problems. These equations are essential for analyzing scenarios where an object is accelerating, such as in the context of the given problem.
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Related Practice
Textbook Question

A 12 kg weather rocket generates a thrust of 200 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 550 N/m, is anchored to the ground. Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?

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Textbook Question

Astronomers using a 2.0-m-diameter telescope observe a distant supernova - an exploding star. The telescope's detector records 9.1 x 10-11 J of light energy during the first 10 s. It's known that this type of supernova has a visible-light power output of 5.0 x 1037 W for the first 10 s of the explosion. How distant is the supernova? Give your answer in light years, where one light year is the distance light travels in one year. The speed of light is 3.0 x 108 m/s.

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Textbook Question

A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the engine and the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the weight is over the drive wheels. How long does it take the Porsche to reach the maximum power output?

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Textbook Question

Draw a pictorial representation.

T−(1500kg)(9.8m/s2)=(1500kg)(1.0m/s2)T-(1500\,\(\text{kg}\))(9.8\,\(\text{m/s}\)^2)=(1500\,\(\text{kg}\))\(\left\)(1.0\,\(\text{m/s}\)^2\(\right\))

P=T(2.0m/s)P=T(2.0\,\(\text{m/s}\))

Textbook Question

Finish the solution of the problem.

T−(1500kg)(9.8m/s2)=(1500kg)(1.0m/s2)T-(1500\,\(\text{kg}\))(9.8\,\(\text{m/s}\)^2)=(1500\,\(\text{kg}\))\(\left\)(1.0\,\(\text{m/s}\)^2\(\right\))

P=T(2.0m/s)P=T(2.0\,\(\text{m/s}\))

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Textbook Question

A farmer uses a tractor to pull a 150 kg bale of hay up a 15° incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractor's power output?

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