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