phys16 – lecture 13
DESCRIPTION
PHYS16 – Lecture 13. Ch. 7 Work and Energy. Announcements. Test – Week of Feb. 28 during lab Formal reports and Notebooks due Tues. 5pm for M/T lab In-class Review on Friday – Ch. 1-6. Circular Motion Post-Questions. Circular Motion post-question. - PowerPoint PPT PresentationTRANSCRIPT
PHYS16 – Lecture 13
Ch. 7 Work and Energy
Announcements
• Test – Week of Feb. 28 during lab• Formal reports and Notebooks due Tues. 5pm
for M/T lab• In-class Review on Friday – Ch. 1-6
Circular Motion Post-Questions
Circular Motion post-question• A bicycle speedometer sensor is mounted on the bike at a
fixed location, usually the fork, and pulses when the spoke-mounted magnet passes by. If the speedometer sensor is mounted at a radius of 0.50 m and counts 320 pulses, how far has the cyclist traveled?
A) 0.50 kmB) 0.80 kmC) 1.0 kmD) 1.5 kmE) 1.8 km
sensor
magnet
Circular Motion post-question
• At the point P indicated in the figure the string suddenly breaks. What is the trajectory of the ball?
http://daed.be/paul/temp/review.php_files/fci7.jpg
Circular Motion post-question
• Tarzan is swinging across a lake on a vine that may not support his weight. What is the most likely point for the vine to break at?
A
CB
D
Circular Motion post-question
• An object is swung in uniform circular motion vertically. Where is the tangential acceleration the greatest?
A) At the top of the circleB) At the bottom of the circleC) At the point midway between top and bottomD) At both the top and bottom of the circleE) None of the above
Circular Motion post-question
• A pickup has a crate of apples in its bed. The pickup makes a right turn and the once stationary crate accelerates to the left with respect to the truck bed and hits the side of the pickup. In which direction is a force acting on the crate?
A) To the rightB) To the leftC) Not enough information
Description of Motion – What else do we need?
• We have:– Laws of Calculus – Displacement, Velocity and
Acceleration– Newton’s Laws – F=ma
We need energy…
• Mechanical Energy– Potential Energy– Kinetic Energy
• Work– Constant Force → Dot Product– Variable Force → Integral
• Work-Mechanical Energy theorem
Ch. 7 Work and Energy
Energy Pre-question
• A force F is used to raise a 4-kg mass from the ground to a height of 5 m, as shown in the diagram below. What is the work done by the force F? Ignore friction and assume the rope and pulleys are massless.
A) 50 JB) 100 JC) 174 JD) 200 JE) None of the above
F
θ = 60 degrees
mass
Demo – Name that Energy
http://undsci.berkeley.edu/images/us101/falling_objects.jpg
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
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
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(298)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
xdFW
Work with a Variable Force
• Force = Variable, then need to break into components and integrate
...dyFdxFW yx
F x
x
Practice Questions
• 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. The kinetic coefficient of friction is 0.1. What is the work done by me?
• 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?
22 J
200J
Conclusions
• Mechanical Energy– Potential Energy, Gravitational– Potential Energy, Spring– Kinetic Energy
• Work– Constant Force– Variable Force
cosxFW
...dyFdxFW yx
2
21 mvK
mghU 2
21 kxU