Lecture 13 Physics I
Chapter 9
Work and Kinetic Energy
Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
IN THIS CHAPTER, you will learn how to solve problems using two new concepts: work and kinetic energy instead of forces. .
Today we are going to discuss: Chapter 9:
Work done by a force: Section 9.2; 9.3 Kinetic Energy: Section 9.2 Scalar (Dot) product of two vectors: Section 9.3 Work-Kinetic Energy theorem: Section 9.2
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Exam II Results Problems: MCQ problem 2 problem 3 problem 4 Total
Average: 17.8 11.9 14.7 11.9 56.3 points Max 90 points
Average 62.5%
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Since the N. 2nd law is a foundation of our mechanics, we have to “dance” from the N. 2nd law if we want to introduce something new.
So, Let’s get work and energy from N. 2nd law What is so special about solving problems using energies? Why do we have to go there? N. 2nd law with forces is great and any problem can be solved. But forces are vectors and it is more difficult to deal with vectors than with scalar quantities. And energy is a scalar quantity. So, let’s try to make life easier
Read this derivation only if you want PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Work-Kinetic Energy Principle vf vi F
s We started from the N. 2nd law
and got this
xf
1 1 2 2 mv f mvi F ( x)dx 2 2 xi Let’s give “nice names” to new quantities
Kinetic energy
xf
1 2 K mv 2
So, after renaming we have this:
Work done by F
F ( x)dx xi
Work-Kinetic Energy Principle
K f K i K Wnet
The work done by the force is equal to the change in the kinetic energy.
•
Work and energy have units of Nm, or Joules (J), and are scalars !!
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Translational Kinetic Energy Kinetic energy (K) is the energy of motion Translational kinetic energy is the energy of motion in a line or trajectory
1 2 Kinetic energy K mv 2 Kinetic energy is the energy possessed by an object because of its motion PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Example Net Work required to accelerate a 1000kg car from
vi (a) from 20 m/s to 40 m/s?
vf Work-Kinetic Energy Principle
K f K i K Wnet
m 2 2 1000 W K [v f vi ] [40 2 20 2 ] 600,000 J 600kJ 2 2 (b) from 40 m/s to zero? m 2 1000 2 W K [v f vi ] [0 40 2 ] 800,000 J 800kJ 2 2 If the net work is positive, the kinetic energy increases. If the net work is negative, the kinetic energy decreases. PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Let’s look at work “deeper”
As you noticed, I like to simplify, let’s do it again: assume a constant
if F ( x) const Work done by F
W Fs
xf
xf
xi
xi
force
W F ( x)dx F dx F ( x f xi ) Fs
This is true when a force acts along a line of motion, but What if a force makes an angle with a line of motion (more general case)
Work
done by F
cos
s
Work done on an object by a force If a constant force F moves object by a displacement s, work done by force is given by W = Fss, where Fs is the component of the force along s PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
ConcepTest. To Work or Not to Work A) yes
Is it possible to do work on an
B) no
object that remains at rest?
Work done by F
Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done. The amount of work you actually do may have little relationship to the amount of effort you apply. For example, if you push on a car stuck in a snow drift, you may exert a lot of force (and effort) but if the car does not budge, you have not done any work! In order for work to be done on an object, the object must move some distance as a result of the force you apply.
Example A force of 5 N, applied in the direction shown, moves a donkey across a horizontal distance of 10 m. How much work does the force do on the stubborn creature?
F 5N
By definition
5 ∙ 10
60
60° = 25J
s 10m Work done by a force can be positive/negative/zero:
F
s
F
W0 PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
W0
s
F 90
W 0
s
ConcepTest A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?
Friction and Work I A) friction does no work at all B) friction does negative work C) friction does positive work
Friction acts in the opposite
N Displacement
direction to the displacement, so the work is negative. Or using the
Pull
f
definition of work (W = F s cos ), because = 180º, then W < 0.
mg
Example
Work on a backpack
(a) Determine the work a hiker must do on a 15.0-kg backpack to carry it up a hill of height h = 10.0 m, as shown. Determine also (b) the work done by gravity on the backpack, and (c) the net work done on the backpack. For simplicity, assume the motion is smooth and at constant velocity (i.e., acceleration is zero).
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Example Work on a backpack FH θ
d
180‐θ
J
mg
It is not an accident that the net work is zero.
Wherever, the net force acting on an object is zero, the net work will be zero as well PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
End of class
ConcepTest A box is being pulled up a rough
Force and Work A) one force
incline by a rope connected to a
B) two forces
pulley. How many forces are
C) three forces
doing work on the box?
D) four forces E) no forces are doing work
Any force not perpendicular to the motion will do work: N does no work
N
T
T does positive work ffr
ffr does negative work mg does negative work mg
Let’s digress from work for a few slides and then, we will get “back to work”
In order to simplify the work expression, let’s introduce very useful
Dot Product of Vectors or
Scalar product
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
Scalar(Dot) Product of Two Vectors The scalar product of two vectors is:
A
In a magnitude/angle form:
In a component form:
B
A Ax iˆ Ay ˆj Az kˆ B Bx iˆ B y ˆj Bz kˆ
A B Ax Bx Ay B y Az Bz Work done by F
Therefore, we can say that work is a scalar product of force and displacement
Work done by F
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
∙
Example A constant force F acts on an rabbit as it moves from position r1 to r2. What is the work done by this Force? Work done by F
∙
F 4iˆ 5 ˆj 2kˆ r1 2iˆ 4 ˆj 3kˆ
r2 5iˆ 3 ˆj 6kˆ
s r r2 r1 3iˆ 7 ˆj 9kˆ W F s (4)(3) (5)(7) (2)(9) 29 J PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
r1
F
s r2
ConcepTest
Play Ball!
In a baseball game, the catcher
A) catcher has done positive work
stops a 90-mph pitch. What can
B) catcher has done negative work
you say about the work done by
C) catcher has done zero work
the catcher on the ball?
s
W 0
F
The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F s cos ), because = 180º, then W < 0. Note that because the work done on the ball is negative, its speed decreases.
ConcepTest A ball tied to a string is being whirled around in a circle. What can you say about the work
Tension and Work
A) tension does no work at all B) tension does negative work C) tension does positive work
done by tension?
No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F s cos ), because = 90º, then W = 0. Follow-up: Does the Earth do work on the Moon?
T v
Thank you See you on Wednesday
PHYS.1410 Lecture 13 Danylov
Department of Physics and Applied Physics
ConcepTest Work and KE A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child?
1) positive work was done 2) negative work was done 3) zero work was done
The kinetic energy of the child increased because her speed increased. This increase in KE was the result of positive work being done.
Follow-up: What does it mean for negative work to be done on the child?
