Ch. 08 - Conservation of Energy

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 08 - Conservation of Energy

Problem 57b

Chapter 8, Problem 57b

An 85-kg football player traveling 5.0 m/s is stopped in 1.0 s by a tackler. What average power is required to stop him?

Verified step by step guidance

Determine the initial kinetic energy of the football player using the formula for kinetic energy:

K_{i} = (1/2)mv

², where

m

is the mass (85 kg) and

v

is the velocity (5.0 m/s).

Since the player is stopped, the final kinetic energy is zero. The change in kinetic energy is equal to the initial kinetic energy:

ΔK = K_{i} - K_{f}

, where

K_{f} = 0

The work done to stop the player is equal to the change in kinetic energy:

W = ΔK

. Substitute the value of

ΔK

from the previous step.

The average power required to stop the player is given by the formula:

P = W / t

, where

t

is the time interval (1.0 s). Substitute the value of

W

from the previous step.

Simplify the expression to find the average power. Ensure all units are consistent (mass in kg, velocity in m/s, time in seconds) to get the power in watts (W).

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Key Concepts

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

Momentum

Momentum is the product of an object's mass and its velocity, represented by the equation p = mv. In this scenario, the football player's momentum before being tackled can be calculated using his mass (85 kg) and his speed (5.0 m/s). Understanding momentum is crucial for analyzing the changes in motion and the forces involved in stopping the player.

Impulse

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. It can be calculated using the formula Impulse = Force × Time. In this case, the tackler applies a force over 1.0 second to stop the player, and calculating the impulse will help determine the average force exerted during the tackle.

Power

Power is the rate at which work is done or energy is transferred, expressed as Power = Work / Time. In this context, the work done to stop the football player can be related to the impulse and the time taken (1.0 s). Calculating the average power required to stop the player involves determining the work done in stopping him and dividing it by the time interval.

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Related Practice

Textbook Question

A driver notices that her 950-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

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Textbook Question

The graph of Fig. 8–43 shows the potential energy curve of a particle moving along the 𝓍 axis under the influence of a conservative force. Note that the total energy E > U(𝓍), so that the particle’s speed is never zero. In which interval(s) of 𝓍 is the force on the particle to the right?

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Textbook Question

Early test flights for the space shuttle used a “glider” (mass of 980 kg including pilot). After a horizontal launch at 480 km/h at a height of 3200 m, the glider eventually landed at sea level with a speed of 210 km/h. What would its landing speed have been in the absence of air resistance?

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Textbook Question

The position of a 280-g object is given (in meters) by x = 4.0t³ - 8.0t² - 44t, where t is in seconds. What is the average net power input during the interval from t = 0s to t = 2.0 s, and in the interval from t = 2.0 s to 4.0 s?

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Textbook Question

Determine the escape velocity from the Sun for an object at the average distance of the Earth (1.50 x 10⁸ km). Compare (give factor for each) to the speed of the Earth in its orbit.

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Textbook Question

Determine the escape velocity from the Sun for an object at the Sun’s surface ( r = 7.0 x 10⁵ km , M = 2.0 x 10³⁰ kg).

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