/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 BIO Animal Energy. Adult cheetah... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 17

BIO Animal Energy. Adult cheetahs, the fastest of the great cats, have a mass of about \(70 \mathrm{~kg}\) and have been clocked to run at up to \(72 \mathrm{mi} / \mathrm{h}(32 \mathrm{~m} / \mathrm{s}) .\) (a) How many joules of kinetic energy does such a swift cheetah have? (b) By what factor would its kinetic energy change if its speed were doubled?

Short Answer

Expert verified
a) The kinetic energy of the cheetah is \( 35840 \) joules. b) If its speed were doubled, its kinetic energy would increase by a factor of 4.

Step by step solution

01

Plug in the given values into the Kinetic Energy formula

The kinetic energy of the cheetah can be calculated using the Kinetic Energy formula, which is \( KE = \frac{1}{2} m v^{2} \). Here, 'm' is the mass and 'v' is the velocity. So our mass \( m = 70 \mathrm{~kg} \) and velocity \( v = 32 \mathrm{~m/s} \) are given in the problem. So KE = \( \frac{1}{2} \times 70 \mathrm{~kg} \times (32 \mathrm{~m/s})^{2} \).
02

Find the value for KE

After calculations, the value of KE comes out to be \( 35840 \mathrm{~J} \) joules.
03

Determine the change in kinetic energy if speed were doubled

Next, we look at how the kinetic energy would change if the cheetah's speed were to be doubled. We know the Kinetic energy depends on the square of the velocity - therefore, if the speed doubles, the kinetic energy would increase by a factor of \( 2^{2} \) or 4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cheetah Speed
When we talk about cheetah speed, we're diving into one of the most fascinating realms of the animal kingdom. Cheetahs are not just fast, they're masters at accelerating and reaching incredible speeds in mere seconds.
These magnificent creatures can run up to 72 miles per hour, equivalent to 32 meters per second! This speed allows them to be formidable predators in the wild, capable of chasing down swift prey.
To put this in perspective, the average human can sprint at about 15 miles per hour, highlighting just how remarkable the cheetah's ability is.
  • Cheetahs accelerate quickly, reaching their peak speed in about 3 seconds.
  • They use their strong and flexible spine for longer strides.
  • Exceptional vision helps them spot targets at great distances.
The aerodynamics of their bodies, lightweight frame, and muscular build all contribute to their unparalleled speed. It's a true marvel of evolution!
Joules
Joules are the units we use to measure energy, named after the physicist James Prescott Joule. When we say an object has a certain number of joules of kinetic energy, we're talking about how much work it can do due to its motion.
In the exercise, a cheetah carrying 70 kg of mass and running at 32 m/s is reported to have 35,840 joules of kinetic energy. This is a large amount of kinetic energy, highlighting how much energy is involved in its high-speed chase.
  • One joule is the energy transferred when a one-newton force moves an object one meter.
  • Kinetic energy is obtained by the formula \( KE = \frac{1}{2} m v^{2} \).
  • In context, 35,840 joules is equivalent to the energy needed to run a 60-watt light bulb for about 10 minutes.
Therefore, understanding joules helps us grasp the energy dynamics in various motions, from a cheetah's sprint to everyday appliances.
Velocity
Velocity is a key concept in physics that relates to the speed of an object in a given direction. It's a vector quantity, meaning it has both magnitude and direction.
In the exercise, the velocity of the cheetah is given as 32 m/s. This speed is what enables the cheetah to exert enough kinetic energy to chase and catch prey.
The relationship between velocity and kinetic energy emphasizes just how important speed is. As the cheetah doubles its velocity, since kinetic energy is dependent on the square of velocity, the kinetic energy increases by a factor of four.
  • Velocity takes into account direction, unlike speed which is only about how fast something moves.
  • In calculations, the standard unit of velocity is meters per second (m/s).
  • Doubling the velocity quadruples the kinetic energy because of the formula \( KE = \frac{1}{2} m v^{2} \).
Understanding velocity is crucial for realizing how different factors in motion interact to define energy and movement.

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Most popular questions from this chapter

A luggage handler pulls a \(20.0 \mathrm{~kg}\) suitcase up a ramp inclined at \(32.0^{\circ}\) above the horizontal by a force \(\vec{F}\) of magnitude \(160 \mathrm{~N}\) that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is \(\mu_{\mathrm{k}}=0.300 .\) If the suitcase travels \(3.80 \mathrm{~m}\) along the ramp, calculate (a) the work done on the suitcase by \(\overrightarrow{\boldsymbol{F}} ;\) (b) the work done on the suitcase by the gravitational force; (c) the work done on the suitcase by the normal force; (d) the work done on the suitcase by the friction force; (e) the total work done on the suitcase. (f) If the speed of the suitcase is zero at the bottom of the ramp, what is its speed after it has traveled \(3.80 \mathrm{~m}\) along the ramp?

A ski tow operates on a \(15.0^{\circ}\) slope of length \(300 \mathrm{~m}\). The rope moves at \(12.0 \mathrm{~km} / \mathrm{h}\) and provides power for 50 riders at one time, with an average mass per rider of \(70.0 \mathrm{~kg}\). Estimate the power required to operate the tow.

A \(5.00 \mathrm{~kg}\) block is moving at \(v_{0}=6.00 \mathrm{~m} / \mathrm{s}\) along a frictionless, horizontal surface toward a spring with force constant \(k=500 \mathrm{~N} / \mathrm{m}\) that is attached to a wall (Fig. P6.79). The spring has negligible mass. (a) Find the maximum distance the spring will be compressed. (b) If the spring is to compress by no more than \(0.150 \mathrm{~m},\) what should be the maximum value of \(v_{n} ?\)

On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 30.0 N and direction \(37.0^{\circ}\) counterclockwise from the \(+x\) -axis. How much work does this force do during a displacement of the pig that is (a) \(\vec{s}=(5.00 \mathrm{~m}) \hat{\imath}\) (b) \(\vec{s}=-(6.00 \mathrm{~m}) \hat{\jmath}\) (c) \(\vec{s}=-(2.00 \mathrm{~m}) \hat{\imath}+(4.00 \mathrm{~m}) \hat{\jmath} ?\)

A 12.0 kg package in a mail-sorting room slides \(2.00 \mathrm{~m}\) down a chute that is inclined at \(53.0^{\circ}\) below the horizontal. The coefficient of kinetic friction between the package and the chute's surface is 0.40 . Calculate the work done on the package by (a) friction, (b) gravity, and (c) the normal force. (d) What is the net work done on the package?
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