Unit 7: Work, Power, and Energy 

   
Lesson 7.3 
Conservative and Nonconservative Forces 
 
Contents 
Introduction 1 

Learning Objectives 2 

Warm Up 2 

Learn about It! 3 

Conservative Forces 3 
Conservation of Mechanical Energy 5 
Nonconservative Forces 6 

Key Points 11 

Key Formula 11 

Check Your Understanding 12 

Challenge Yourself 14 

Bibliography 14 

Key to Try It! 15 

 
   

 
  
Unit 7: Work, Power, and Energy 
 

Lesson 7.3 
Conservative and Nonconservative Forces 
 

  Introduction 
The  photo  illustrates  both  the  escalator  and  elevator.  Both  machines’  purpose  is  to  move 
people.  But  which  of  the  two  machines  generate  more  work  in  moving  a  person  from  the 
upper  level  to  a  lower  one?  We  know  that  different  forces  play  essential  roles  in  a  moving 
body.  And  force  will  generate  work  if  it  results  in a displacement of the body. For example, 
an  elevator  moving  up  and  down  on  its  path  carrying  a  loaded  cart.  Also,  moving  the  cart 
using  a  ramp  of  the  same  height.  Although  the  scenarios  will  generate  the  same  result  of 
moving  the  cart  from  the  upper  level  to  a  lower  level,  each  scenario  has  a  different 
characteristic  of  the  forces  interacting  on  the  motion  of  the  cart.  Thus,  the  work  done  on 
the  cart  should  be  considered.  Forces  can  either  be  conservative  or  nonconservative 
depending on the determined work done by the body.  
 
7.3. Conservative and Nonconservative Forces  1 
 
  
Unit 7: Work, Power, and Energy 
 
 
 

Learning Objectives  DepEd Competencies 

● Identify conservative and 
In this lesson, you should be able to do the  nonconservative forces 
(STEM_GP12WE-lg-51). 
following: 
● Explain the properties and the 
● Identify conservative and  effects of conservative forces. 
nonconservative forces.  (STEM_GP12WE-lg-50) 

●
 

Explain the properties and the effects 

of conservative forces. 

  Warm Up       
  Clean the Board    10 minutes 
 
This  activity  will  help  you  understand  nonconservative  forces  and  how  it  affects  work  done 
by the body. 
 

Materials 
● board space with the same smiley drawing 
● eraser 

 
Procedure 
1. Two students were to erase two identical smiley drawings but with restrictions. At the 
drawing space there will be defined points A and B. 
2. The  first  student  will  move  the  eraser  from  point  A  to  B  on  a  straight  line  while  the 
second student will move in any directions from point A until it reaches point B. 
3. Ask  the  students  about  the  relationship  of  the  work  done  by  the  students  to  the 
erased drawing.  
 
Guide Questions 
1. Between the two, who exerted more effort in doing the activity? 
 
7.3. Conservative and Nonconservative Forces  2 
 
  
Unit 7: Work, Power, and Energy 
 
2. How does your work relate to the area of the erased image you have done? 
3. Why does it need more work to erase more area on the drawing? 

  Learn about It! 

When  applying  force  to  a  spring  and  pulling  the  string  horizontally at a certain length, it will 
return  to  its  original  position  upon  release.  In  the  same  scenario,  doing  the  activity  on  a 
book  on  the  table  will  not  yield  the  same  result.  Although,  same  amount  of force is applied 
and  work  is  generated  in  both  scenarios,  the  nature  of  the  forces  acting  on  the  setup  are 
different.  The  spring force that acts on the first setup represents what we call a conservative 
force,  on  the  other  hand,  the  second  setup  shows  friction  force  which  is  a nonconservative 
force. 
 

How does conservative force affect the work of a 

  system? 
 
Conservative Forces  
Work  that  is  generated  by  a  force  like  weight  has  its  special  characteristics.  The  force  such 
as  the  gravitational  force  is  an  example  of  a  conservative  force.  Conservative  force,  are 
forces  that  generate  work  that  only  depends  on  the  initial  and  final  position  of  the  body. 
Thus,  the  work  done  by  the  force  is  independent  on  the  path  it  has  taken.  This  means 
that  regardless  of  which  path  of  which  the  force  is  applied in a body will move from point A 
to  point  B,  as  long  as  its  final  position  is  point  B,  the  amount  of  work  done  will  still  be  the 
same.  Examples  of  conservative  forces  are  spring  force,  gravitational  force,  electrostatic 
force and magnetic force. 
 

Which will generate more work: moving a ball 

downward once or moving the ball downward, 
 
upward and finally downward again?  
 
To  further  analyze  this,  assuming  a  1  kg  ball  were to move downward by 10 m from point A 

 
7.3. Conservative and Nonconservative Forces  3 
 
  
Unit 7: Work, Power, and Energy 
 
to point B, as shown in Fig. 7.3.1. 

 
Fig. 7.3.1. A 1 kg ball that will move 10 m downward due to gravity. 
 
The gravitational force acting on the ball is given by: 
 

 
 
Thus the work of done by gravitational force is: 
 
 

 
 
 
Comparing  the  first  setup to when you move the same ball downward by 10 m then upward 
by 10 m and finally downward again by 10 m, as shown in Fig. 7.3.2. 
 
7.3. Conservative and Nonconservative Forces  4 
 
  
Unit 7: Work, Power, and Energy 
 

Fig. 7.3.2. A 1 kg ball that will move 10 m downward then 10 m upward and finally 10 m 
downward again in a system with gravity. 

     

     

The net work of the ball is equal to . 

This  shows  that  the  work  done  by  gravitational  force  depends  only  on  the  initial  and  the 
final position. 
 
Conservation of Mechanical Energy 
There  is  a distinction for conservative forces, that is we can write an expression for potential 
energy  for  conservative  forces.  Conservative forces follow the conservation of mechanical 
energy,  that  states  that  the  total  mechanical  energy  on  a  system  remains  constant  as  long 
as  the  forces  acting  on  the  system  are  conservative  forces.  This  implies  that  the  total 

 
7.3. Conservative and Nonconservative Forces  5 
 
  
Unit 7: Work, Power, and Energy 
 
mechanical  energy  (ME)  on  the  system  is  equal  to  the  sum  of  its  potential  energy  (PE)  and 
kinetic  energy  (KE),  which  implies  that  potential  energy  can  only  be  converted  to  kinetic 
energy  and  vice  versa  on  any  point  on  the  motion  generated  by  conservative  forces  on  an 
isolated system. 
 

  Equation 7.3.1 

 
Where  potential  energy  (PE)  refers  to  the  energy  that  defined  the  conservative  force  like 
gravitational  potential  energy  for  gravitational  force.  The  kinetic  energy  (KE)  correspond  to 
the  instantaneous  speed  that  resulted  from  the  acceleration  of  an  object,  as  given  by 

. 

How does nonconservative forces affect the work 

  of a system? 
 
Nonconservative Forces  
While  conservative  forces  only  depend  on  the  initial  and  final  position  of  the  body, 
Nonconservative  forces  are  forces  that  depend  on  the  path  taken  by  the  body.  A  good 
example  of  this  force  is  friction  force.  Friction  force  depends  on  the  length  of  the  path 
covered  by  the  body  upon  reaching  its  destination.  Examples  of  these  forces  are  friction 
force and applied force.  
 
Since  nonconservative  forces  depend  on the path, there was no potential energy associated 
with  the  system.  Thus,  it  indicates  that  the  mechanical  energy  on  the  system  dissipates  or 
will  lose  over  its  motion.  Work  done  by  nonconservative  forces  may  remove  or  add 
mechanical energy on the system.  
 

Did You Know? 

Roller  coasters  are  driven  almost  entirely  by  basic  inertial, 

 
7.3. Conservative and Nonconservative Forces  6 
 
  
Unit 7: Work, Power, and Energy 
 

gravitational,  and centripetal  forces,  all  manipulated  in  the  service 

of  a  great  ride.  Using  these  forces,  the  roller  coaster  follows  the 
principle of conservative force, which means the maximum height it 
can  reach  without  the  aid  of  electricity  on  a  minimal  friction  is  the 
same  height  of  its  launching.  This  also  explains  why  most  of  the 
loop  of  the  roller  coaster  track  does  not  reach  the  height  of  its 
launching point. 

 
 

  Let’s Practice!  

Example 1    
A boy dropped a 1-kg ball on the window 5 m above the ground. What is the gravitational 
potential energy of the ball on the window? 

 
Solution 
 
Step 1: Identify the unknown. 
You are asked to calculate the gravitational potential energy (PEgravity) of the ball on 
the window before it drops.  
 
Step 2:  Identify the given. 
The mass (m) of the ball, height of the dropping point (h), and the acceleration due 
to gravity was implied (g).  
 
Step 3:  Identify the equation that can be used.  

 
Step 4:  Substitute the given to the equation to find the solution.  

 
7.3. Conservative and Nonconservative Forces  7 
 
  
Unit 7: Work, Power, and Energy 
 

 
 
Step 5:  Find the answer. 

 
 
The gravitational potential energy of the ball before dropping is 49.05J. 
 

1  Try It!  
Find the potential energy of a 300-kg roller coaster to be released on the track at a 
height of 20 m. 

Example 2  
A  boy  dropped  a  1-kg  ball  on  the  window  5  m  above  the  ground.  Find  the  kinetic energy of 
the ball upon hitting the ground. 
 
Solution 
Step 1:  Identify the unknown. 
You are asked to calculate the kinetic energy (KE) of the ball upon hitting the 
ground. 
 
Step 2:  Identify the given.  
The potential energy on the highest point which is the gravitational potential 
energy of the ball in the window has been computed on Example 1. 
 
Step 3:  Identify the equation that can be used. 
 
 
Step 4:  Analyze the problem and substitute the given values. 

, where since the ball is not 

 
7.3. Conservative and Nonconservative Forces  8 
 
  
Unit 7: Work, Power, and Energy 
 
moving. 
 
Then, 

 
 
Using  the Principle of Conservation of Mechanical Energy, the mechanical energy is 
conserved  on  any  point  of  the  drop.  Thus,  since  we  are  looking  for  the  kinetic 
energy  upon  hitting  the  ground  which  is  the  lowest  point  we  can  imply  that  all 
potential energy converted into kinetic energy upon hitting the ground. Thus; 

 
 
 
Step 5:  Find the answer. 

 
 
The kinetic energy of the ball upon hitting the ground is 49.05 J. 
 

2  Try It!  
Find the value of the kinetic energy at the lowest point of the track of the 300-kg 
roller coaster that was released on the track at a height of 20 m.  

Example 3  
A  boy  dropped  a  1-kg  ball on the window 5 m above the ground. Find the velocity of the ball 
upon hitting the ground. 
 
Solution 
Step 1:  Identify the unknown. 
You are asked to calculate the velocity of the ball upon hitting the ground. 
 
Step 2:  Identify the given. 

 
7.3. Conservative and Nonconservative Forces  9 
 
  
Unit 7: Work, Power, and Energy 
 
The kinetic energy of the ball upon hitting the ground was acquired on Example 2. 

 
 
Step 3: Identify the equation needed. 

 
Step 4:  Substitute the given to the equation.  

 
 
Step 5:  Find the answer. 

 
 
The velocity of the ball upon hitting the ground is 9.90 m/s. 
 

3  Try It!  
Find the velocity of the coaster at the lowest point of the 300-kg roller coaster that 
was released on the track at 20 m.   

What is the difference between conservative and 

  nonconservative force? 
 
 

 
7.3. Conservative and Nonconservative Forces  10 
 
  
Unit 7: Work, Power, and Energy 
 

Key Points 
___________________________________________________________________________________________ 
 
● Conservative forces are forces that generate work that depends on the initial and 
final position of the object. Conservative forces conserve mechanical energy. 
● Nonconservative  forces  are  forces  that  generate  work  which  is  dependent  on 
the path taken by the object. It may dissipate the mechanical energy in the system. 
● Conservation  of  mechanical  energy states that the total mechanical energy on a 
system  remains  constant  as  long  as  the  forces  acting  on  the  system  are 
conservative  forces.  Thus  the  total  mechanical  energy  of  the  system  is the sum of 
its potential and kinetic energy. 
___________________________________________________________________________________________ 
 
Key Formula 
___________________________________________________________________________________________ 
 

Concept  Formula  Description 

Conservation of    Use this formula to analyze 

Mechanical Energy    conservative forces that 
where:  follow the conservation of 
● ME is the total mechanical  mechanical energy. 
energy in joules (J)   
● PE is potential energy of 
the conservative force in 
joules (J) 
● KE is kinetic energy in 
joules (J) 

 
___________________________________________________________________________________________ 
 
 
 

 
7.3. Conservative and Nonconservative Forces  11 
 
  
Unit 7: Work, Power, and Energy 
 

  Check Your Understanding 

 

A. Identify the word or phrase described by each statement.  

___________________  1. What  do  you  call  the  forces that generate work which depends 

  only on the initial and final position of the object?  
___________________  2. What  do  you  call  the  forces that generate work which depends 
  on the path taken by the object?  
___________________  3. What  principle  states  that  the  total  mechanical  energy  on  a 
  system  remains  constant  as  long  as  the  forces  acting  on  the 
  system are conservative forces? 
___________________  4. What  energy corresponds to the instantaneous speed resulting 
  from the acceleration of a moving object? 
___________________  5. It  is  the  sum of potential energy and kinetic energy when acted 
on by conservative force. 

 
 
 

B. Write  true  when  the  statement  is  correct  false  if  otherwise.  If  the 
statement  is  false  correct  the  underlined  word  to  make  the 
statement true. 

________________  1. Nonconservative  forces  generate  work  that  only  depends 

  on the initial and final position of the object. 
________________  2. Gravitational force is an example of conservative force. 
________________  3. The  work  done  by  the  gravitational  force  when  lifting  a 
  mug  on  a  certain  height  then  returning  it  to  its  original 
  position is zero. 
________________  4. The  total  mechanical  energy  on  a  system  acted  upon  by 

 
7.3. Conservative and Nonconservative Forces  12 
 
  
Unit 7: Work, Power, and Energy 
 

  conservative  force  is  equal  to  the  product  of the potential 

  and kinetic energy on the system. 
________________  5. Conservative  forces  generate  work  that  depends  on  the 
  path taken by the object. 

C. Find  the  potential and kinetic energy of the 50-kg cart on the system 

on each point identified in the figure below (10 points). 

 
Total mechanical energy: _______________________ 
Mass of the cart: 50 kg 
Acceleration due to gravity: 9.81 m/s2 
 

  A   B   C   D  E 

(h = 10 m)  (h = 5 m)  (h = 0 m)  (h = 2.5 m)  (h = 10 m) 

Potential           
Energy (J) 

Kinetic           
Energy (J) 

 
 
 

 
 
7.3. Conservative and Nonconservative Forces  13 
 
  
Unit 7: Work, Power, and Energy 
 

  Challenge Yourself 
 

A. Solve and answer the following questions.  

1. An  egg  falls  from  a  nest  at  a  height  of  3  m.  What  is  the  velocity  of  the  egg  before  it 
hits the ground? Disregard air resistance. 
2. How  much  work  is  done  when  lifting  a  100-g  cup  of  coffee  1-meter-high  from  the 
ground then moving it down by 0.5 m?  
 

B. Analyze and explain your answer.  

1. What  will  happen  on  a  roller  coaster  on  a  frictionless  track  reaching  a  loop  that  is 
higher than its launching point? 
2. How do conservative forces differ to nonconservative forces? 
 

C. Create  a  possible  computation  for  the  total  mechanical  energy  on  a 

pendulum of your design. 
 
 
 

  Bibliography 
Kirkpatrick,  L.D.,  &  Francis, G. E. Kirkpatrick’s Physics. 6th ed. California: Thomson Brooks/Cole, 
2007 
 
Serway,  R.  A.  Physics  for  Scientists  and  Engineers  with  Modern  Physics  6th  Ed.  Singapore: 
Thomson Learning Asia, 2004. 
 
Young,  H.  D.  &  Freedman,  R.  A.  University  Physics  9th  Edition.  Boston,  USA:  Addison-Wesley 
Publishing Company Inc., 2004. 
 

 
7.3. Conservative and Nonconservative Forces  14 
 
  
Unit 7: Work, Power, and Energy 
 
Giambattista, A. et al. College Physics 2nd ed. Boston: McGraw-Hill Co., Inc., 2007. 
 
Hecht,  E.  &  Bueche,  F.  Schaum’s  Outline  of  College  Physics.  10th  ed.  Boston:  McGraw-Hill  Co., 
Inc., 2006. 
 
 

  Key to Try It! 

1. 58 860 J 
2. 58 669 J 
3. 19.81 m/s 
 

 
7.3. Conservative and Nonconservative Forces  15