Unit 7: Work and Energy

Section A: Work Corresponding Book Sections: PA Assessment Anchors: 7.1 PA Assessment Anchors: S11.C.3.1

What is “Work” ? Work occurs when three conditions are met: A force is applied to an object The object moves At least some of the force being applied is in the direction of the motion of the object

General Equation for Work W = Fd Unit: Joule (J)

Practice Problem Find the work necessary to accomplish what is shown in the picture. m = 98 kg

Am I doing work? Let’s say I go shopping at Weis: Picking out items from the shelf Placing the groceries on the belt Holding the bag of groceries Carrying the bag of groceries to my car

Work, version 2.0 What happens in this situation? Does our equation for work “work” ?

The best equation for Work W = Fd cos θ

Practice Problem Find the work done by gravity in this situation: mass = 4970 kg distance = 5 m

Positive, Negative, Zero Work Work is positive if the force has a component in the direction of motion Work is zero if the force has no component in the direction of motion Work is negative if the force has a component opposite the direction of motion

Finding Total Work Work can be added together, just like forces: Wtotal = W1 + W2 + W3 + … = ∑W Wtotal = Ftotald cos θ Sum of the Work

Practice Problem Find the work done in this situation:

Section B: Work & Energy Corresponding Book Sections: 7.2 PA Assessment Anchors: S11.C.3.1

Work-Energy Theorem The total work done on an object is equal to the change in its kinetic energy. Wtotal = ΔK =

Practice Problem A truck moving at 15 m/s has a kinetic energy of 140,000 J. What is the mass of the truck?

Practice Problem #2 How much work is required for a 74 kg sprinkler to accelerate from rest to 2.2m/s ?

Pratice Problem #3 A boy pulls a sled as shown. Find the work done by the boy and the final speed of the sled after it moves 2 m, assuming initial speed of 0.5 m/s.

Let’s take another look at PP#3 Could we solve this using the kinematics equations and Newton’s 2nd Law? The answer is YES. Should we try?

Work on a Spring “k” is referred to a the spring constant Remember…from the last unit…

Practice Problem In the chase scene from Toy Story the Slinky Dog is stretched 1m, which requires 2J of work. Find the spring constant.

Practice Problem, Part 2 How much work is required to stretch the dog from 1m to 2m?

Power A measure of how quickly work is done Units: Joule / second: J/s Watt: W (preferred unit)

Typical values of power

Practice Problem #1 Calculate the power needed to accelerate from 13.4 m/s to 17.9 m/s in 3.00 s if your car has a mass of 1,300 kg.

Practice Problem #2 What is the average power needed to accelerate a 950 kg car from 0 m/s to 26.8 m/s (60 mph) in 6 s. Ignore friction.

Section C: Energy Corresponding Book Sections: PA Assessment Anchors: 8.1, 8.2, 8.3 PA Assessment Anchors: S11.C.3.1

Two main types of energy Kinetic Energy Energy an object has while it’s in motion Potential Energy Energy an object has while it’s not moving

Kinetic Energy Energy an object has while in motion Unit: Joule (J)

Practice Problem #1 A truck moving at 15 m/s has KE of 14,000 J. Find the mass.

Potential Energy Energy available to be converted to kinetic energy (energy of non-motion) Unit: Joule (J)

Gravitational Potential Energy Your book uses “U” to represent Potential Energy -- I’ll use “PE”

Two types of forces: Conservative The work done by a conservative force is stored as energy that can be released later Example: Lifting a box from the floor As you lift the box, you exert force and do work If you let go of the box, gravity exerts a force and does work

Two types of forces: Nonconservative The work done by a nonconservative force cannot be recovered later as KE Example: Sliding box across floor The work done to slide the box can’t be restored as KE Instead, the energy changes forms into heat

Examples of Conservative & Nonconservative Forces Springs Gravity Nonconservative Friction Tension

Sections D & E: Momentum Corresponding Book Sections: 9.1, 9.2, 9.3 PA Assessment Anchors: S11.C.3.1

What is momentum? Linear momentum Units: kg m/s The product of an object’s mass and velocity Units: kg m/s

So, this means… If mass increases, momentum increases If speed increases, momentum increases Vice-versa if speed or mass decrease

Sample Problem #1 A 1180 kg car drives along a street at 13.4 m/s. Find the momentum.

Sample Problem #2 A major league pitcher can throw a 0.142 kg baseball at 45.1 m/s. Find the momentum.

Change in Momentum Just like the change in speed, distance, etc. Final - initial Equation:

Adding momentum Since momentum is a vector quantity, it will add like vectors add We’ll keep it simple and say that:

Practice Problem #1 Two 4.00 kg ducks and 9.00 kg goose swim toward some bread that was thrown in the pond. The ducks each have a speed of 1.10 m/s while the goose has a speed of 1.30 m/s. Find the total momentum.

Momentum and Newton’s 2nd Law Remember that Newton’s 2nd Law is ƩF=ma We can relate this to momentum:

Impulse Relationship between applied force and time

What is impulse? Vector quantity Units: kg m/s Points in same direction as average force

Another way to represent Impulse: If: Then: And if:

Practice Problem #1 A 0.144 kg baseball is moving toward home plate at 43.0 m/s when it is hit. The bat exerts a force of 6,500 N for 0.0013s. Find the final speed of the ball.

Practice Problem #2 After winning a prize on a game show, a 72 kg contestant jumps for joy with a speed of 2.1 m/s. Find the impulse experienced.

Rain vs. Hail As you’re holding an umbrella, does it require more force, less force, or the same force to hold up the umbrella if the raindrops turn to hail?

Conservation of momentum If the net force acting on an object is zero, its momentum is conserved In other words, the momentum before a collision is the same as the momentum after a collision pf = pi

Practice Problem #1 A honeybee with a mass of 0.150g lands on a 4.75g popsicle stick. The bee runs toward the opposite end of the stick. The stick moves with a speed of 0.120 cm/s relative to the water. Find the speed of the bee.

Elastic vs. Inelastic Collsions Momentum is conserved Kinetic energy is conserved In other words: Objects bounce off each other Inelastic Momentum is conserved Kinetic Energy is NOT conserved In other words: Objects either stick or stop