Tag Archives: kinetic energy

College Physics by Openstax Chapter 7 Problem 10

(a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals would relate to metabolic rates.

Solution:

The translational kinetic energy of an object of mass mm moving at speed vv is KE=12mv2KE=\frac{1}{2}mv^{2}.

Part A. The Velocity of the Elephant to have the same Kinetic Energy as the Sprinter

First, we need to solve for the kinetic energy of the sprinter.

KEsprinter=12(65.0 kg)(10.0 m/s)2KEsprinter=3250 J\begin{align*} KE_{\text{sprinter}} & = \frac{1}{2} \left( 65.0\ \text{kg} \right)\left( 10.0\ \text{m}/\text{s} \right)^{2} \\ KE_{\text{sprinter}} & = 3250\ \text{J} \end{align*}

Then, we need to equate this to the kinetic energy of the elephant with the velocity as the unknown.

KEelephant=KEsprinter12(3000 kg)v2=3250 J1500v2=3250v2=32501500v=32501500v=1.4720 m/sv=1.47 m/s  (Answer)\begin{align*} KE_{\text{elephant}} & = KE_{\text{sprinter}} \\ \frac{1}{2}\left( 3000\ \text{kg} \right) v^{2} & = 3250\ \text{J} \\ 1500 v^{2} & = 3250 \\ v^{2} & = \frac{3250}{1500} \\ v & = \sqrt[]{\frac{3250}{1500}} \\ v & = 1.4720\ \text{m}/\text{s} \\ v & = 1.47\ \text{m}/\text{s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

Part B. How Larger Energies Needed for the Movement of Larger Animals would Relate to Metabolic Rates

If the elephant and the sprinter accelerate to a final velocity of 10.0 m/s, then
the elephant would have a much larger kinetic energy than the sprinter.
Therefore, the elephant clearly has burned more energy and requires a faster
metabolic output to sustain that speed.   (Answer)\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)

College Physics by Openstax Chapter 7 Problem 9

Compare the kinetic energy of a 20,000-kg truck moving at 110 km/h with that of an 80.0-kg astronaut in orbit moving at 27,500 km/h.

Solution:

The translational kinetic energy of an object of mass mm moving at speed vv is KE=12mv2KE=\frac{1}{2}mv^{2}.

The Kinetic Energy of the Truck

For the truck, we are given the following:

m=20000 kgv=110 kmhr×1000 m1 km×1 hr3600 s=30.5556 m/s\begin{align*} m & = 20 000\ \text{kg} \\ v & = 110\ \frac{\text{km}}{\text{hr}} \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{1\ \text{hr}}{3600\ \text{s}} = 30.5556\ \text{m}/\text{s} \end{align*}

Substitute these values to compute for the kinetic energy of the truck.

KEt=12mv2KEt=12(20000 kg)(30.5556 m/s)2KEt=9336446.9136 JKEt=9.34×106 J\begin{align*} KE_{t} & = \frac{1}{2} mv^{2} \\ KE_{t} & = \frac{1}{2} \left( 20 000\ \text{kg} \right) \left( 30.5556\ \text{m}/\text{s} \right)^{2} \\ KE_{t} & = 9 336 446.9136\ \text{J} \\ KE_{t} & = 9.34 \times 10^{6} \ \text{J} \end{align*}

The Kinetic Energy of the Astronaut

For the astronaut, we have the following given values

m=80 kgv=27500 kmhr×1000 m1 km×1 hr3600 s=7638.8889 m/s\begin{align*} m & = 80\ \text{kg} \\ v & = 27 500\ \frac{\text{km}}{\text{hr}} \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{1\ \text{hr}}{3600\ \text{s}} = 7638.8889\ \text{m}/\text{s} \end{align*}

The kinetic energy of the astronaut is calculated as

KEa=12mv2KEa=12(80 kg)(7638.8889 m/s)2KEa=2334104945.0617 JKEa=2.33×109 J\begin{align*} KE_{a} & = \frac{1}{2} mv^{2} \\ KE_{a} & = \frac{1}{2} \left( 80\ \text{kg} \right) \left( 7638.8889\ \text{m}/\text{s} \right)^{2} \\ KE_{a} & = 2 334 104 945 .0617\ \text{J} \\ KE_{a} & = 2.33 \times 10^{9} \ \text{J} \end{align*}

Comparing the Kinetic Energies of the truck and the astronaut

KEaKEt=2334104945.0617 J9336446.9136 JKEaKEt=250KEa=250 KEt  (Answer)\begin{align*} \frac{KE_{a}}{KE_{t}} & = \frac{2 334 104 945 .0617\ \text{J}}{9 336 446.9136\ \text{J}} \\ \frac{KE_{a}}{KE_{t}} & = 250 \\ KE_{a} & = 250\ KE_{t} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

The kinetic energy of the astronaut is 250 times larger than the kinetic energy of the truck.

Solution Guides to College Physics by Openstax Chapter 7 Banner

Chapter 7: Work, Energy, and Energy Resources

Work: The Scientific Definition

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Kinetic Energy and the Work-Energy Theorem

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Gravitational Potential Energy

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Conservative Forces and Potential Energy

Problem 22

Problem 23

Nonconservative Forces

Problem 24

Problem 25

Conservation of Energy

Problem 26

Problem 27

Problem 28

Problem 29

Power

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Work, Energy, and Power in Humans

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

World Energy Use

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70