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Ch 09: Work and Kinetic Energy
Chapter 9, Problem 9

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. (c) How long does it take the Porsche to reach the maximum power output?

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1
Calculate the effective power reaching the wheels by taking 70% of the total engine power. Use the formula: Effective Power = 0.70 imes Total Power.
Convert the effective power from horsepower to watts for easier calculation in subsequent steps. Use the conversion factor where 1 horsepower is approximately equal to 746 watts.
Determine the force exerted by the drive wheels using the formula: Force = Power / Velocity. Note that the velocity should be the maximum speed at which the car can maintain its maximum power output.
Calculate the acceleration using Newton's second law, where Acceleration = Force / Mass. The mass to use here is the total mass of the car and driver.
Estimate the time it takes to reach maximum power output by using the kinematic equation: Time = Velocity / Acceleration, assuming the car starts from rest and reaches its maximum speed under constant acceleration.

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Key Concepts

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

Power and Work

Power is the rate at which work is done or energy is transferred over time. In the context of vehicles, engine power is often measured in horsepower (hp), which indicates how quickly the engine can perform work. Understanding the relationship between power, work, and time is crucial for calculating how long it takes for a car to reach its maximum power output.
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Force and Acceleration

Newton's second law states that force equals mass times acceleration (F = ma). In this scenario, the force exerted by the car's wheels, derived from the engine's power, is responsible for its acceleration. Knowing the mass of the car and how power translates into force allows us to determine how quickly the car can accelerate to its maximum speed.
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Energy Loss in Systems

In mechanical systems, energy losses occur due to friction, heat, and other inefficiencies. In this case, 30% of the engine's power is lost before reaching the wheels, meaning only 70% is available for acceleration. Understanding how to account for these losses is essential for accurately calculating the effective power that contributes to the car's performance.
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Related Practice
Textbook Question
A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing?
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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. (a) What is the maximum acceleration of the Porsche on a concrete surface where μₛ = 1.00 ? Hint: What force pushes the car forward?
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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. (b) If the Porsche accelerates at aₘₐₓ, what is its speed when it reaches maximum power output?
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Textbook Question
How much work does tension do to pull the mass from the bottom of the hill (θ = 0) to the top at constant speed? To answer this question, write an expression for the work done when the mass moves through a very small distance ds while it has angle θ, replace ds with an equivalent expression involving R and dθ , then integrate.
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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. (a) 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
A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s . During the same time interval, a 30 kg greyhound can go from rest to 20 m/s . What is the average power output of each? Average power over a time interval ∆t is ∆E/∆t .
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