PHYS16 – Lecture 15 Work and Energy October 13, 2010
Feb 22, 2016
PHYS16 – Lecture 15
Work and Energy October 13, 2010
Agenda
• Administration– Homework for Week 5– Exam
• What have we learned so far? What do we still need to know?
• Energy• Mechanical Work
Description of Motion – What else do we need?
• We have:– Laws of Calculus – Displacement, Velocity and
Acceleration– Newton’s Laws – F=ma – Concept of Momentum
We need energy…
Definition of Energy• Energy– A quantity whose expenditure or transformation allows for
physical activity– An ability to drive motion– A capacity for action
• Scalar Quantity• Unit = Joule (J) = kg·m2/s2
• Comes in many forms– Thermal– Chemical– Mechanical!!!!!
Mechanical Energy• Kinetic Energy (K)– energy stored in the movement of an
object
• Potential Energy (U) – energy stored in the configuration of a system– Gravitational Potential Energy
– Spring Potential Energy
2
21 mvK
mghU
2
21 kxU
Energy can be transformed
• Wyle E. Coyote• http://www.youtube.com/watch?v=Jnj8mc04r9E&feature=related
Practice Question
• A 0.50 kg vase falls from 3.0 m. What is the kinetic energy of the vase just before it hits the ground?
A) 0 JB) 15 JC) 1.5 JD) 2.3 J
Practice Question
• A 0.50 kg vase falls from 3.0 m. What is the potential energy of the vase before it falls?
A) 0 JB) 15 JC) 1.5 JD) 2.3 J
We need work…
Definition of Work
• Mechanical Work (W) – energy transferred to an object due to the action of a force(+) transfer to object(-) transfer from object
xdFW
Aside on Dot Product
• Dot Product is one way to multiply two vectors– Basically just multiply components and add– Dot Product is a scalar
...
,...),(
,...),(
2211
21
21
BABABA
BBB
AAA
A
B
Aside on Dot Product
• Dot Product is one way to multiply two vectors– Basically just multiply components and add– Dot Product is a scalar
A
B181230
)2,5(
)6,6(
BA
B
A
Aside on Dot Product
• Dot Product is one way to multiply two vectors– Basically just multiply components and add– Dot Product is a scalar– Or multiply magnitudes and cosine angle between
the vectors
18)56cos(296)cos(
)2,5(
)6,6(
BABA
B
A
A
B
θ=56°
Work with a Constant Force
• Force = Constant, then can take force outside integral
cosxFW
xFW
Work with a Variable Force
• Force = Constant, then can take force outside integral
dxFW x
F x
x
Practice Question
• I pull a 4.0 kg sled a distance of 5.0 m. I pull the sled using a rope at a 30.0 degree angle with a force of 5.0 N. What is the work done by me?
A) 0 JB) 20 JC) 25 JD) 22 J
Practice Question
• A force is given by Fx = 3x2+2. What is the work done by the force for moving an object from x=0.0 m to x=4.0 m?
A) 72 JB) 50 JC) 0 JD) 200 J
Work – Energy Theorem
• Work = the transfer of Energy• Energy = the ability to do work
EW
Work done byExternal Force
Change in Energyto the system
Work and grav. potential energy• If I lift an object, how much work did I do on the object?• Use work-energy theorem to derive gravitational potential
energy
Uyymg
Udymg
UxdF
UEW
y
y
)(
)(
0
0
Force and displacementare both downward
Work and spring potential energy• If mass on a spring moves, how much work is done by spring?• Use work-energy theorem to derive spring potential energy
Uxxk
Udxkx
UxdF
UEW
x
x
)(21
)(
20
2
0
Work done by system is negative
Force and displacementare in opposite directions
Work and Kinetic energy• If an object speeds up, how much work is done on object?• Use work-energy theorem to derive kinetic energy
)(21 so...
1
)(21
)(21)(
20
2
20
2
20
2
vvmΔK
madtdvmv
vF
vvmdxdt
dtdF
vvmdxFdxd
KxdF
KEW
Assume K=mv2/2
and prove left side =right side
Just multiply and divideby dt since dt/dt=1
Now take derivative andremember to use chainrule