Unit 7: Work, Power, and Mechanical Energy

I. Work Depends on: Force Displacement the force is applied for Question: If we apply a force to an object and it doesn’t move, how much work has been done? None, the force did not cause displacement 2

I. Work By doing work on an object, you transfer __________ from one object to another. energy Equation: W = Fd Units – N*m = Joule (J) scalar no direction Work is a ______ quantity(____________) 3

I. Work Example: A 50 kg crate is pulled 40 m across a horizontal surface in 120 s by a force of 150 N. Find the work done. 4

A. Work Done Against Gravity Use the ___________________ (weight) of an object that is being moved to find the amount of work done in lifting the object force due to gravity 5

A. Work Done Against Gravity How much work is done lifting a 3 kg backpack a distance of 1.25 m? How many Calories did you burn? (1 kilocalorie = 4184 J) (kcal vs. J article) 0.00880 Calories : ( 6

B. Work and the Direction of the Force Work is done when a force is applied New modified Formula parallel ________to the motion W = Fcos(θ)d 7

B. Work and the Direction of the Force Example: A 2.3 kg block rests on a horizontal surface. A force of 5 N is applied to the block at an angle of 30 degrees to the horizontal. Determine the work done in moving the block a distance of 2 m. 8

C. Finding Work from a Force vs. Distance Graph Area Under Line= 9

II. Power rate Definition: _________ of doing ________ (how quickly work is done) Power is _________ quantity work scalar Equations (see Reference Tables): Units: 10

II. Power Example: An electric motor lifts an elevator that weighs 1.20 x 10 4 N a distance of 9 m in 15 s. What is the power of the motor? 11

II. Power Example: A person applies a force of 25 N to a toy car and it moves at an average velocity of 10 m/s. What is the power developed by the car? 12

Work and Power Whiteboard Problems: If a 25 kg mass is dropped from a height of 5 m, find the following: A) Work done by gravity B) If the average velocity of the mass is 7 m/s, what power was developed by gravity? A constant force of 5 N acting at an angle of 25 degrees from the horizontal is applied to a box to move it at a constant speed. Determine how much power is dissipated in moving the box 5 m along the floor in 2 seconds. A 0.125 kg rubber hockey puck slows down from 20.0 m/s to 10.0 m/s as it slides along ice for 102 m. Calculate the following: A) Force of friction (hint: see ref. tabs). B) Average Velocity C) Power developed by friction D) Work done by friction A) 1,226 J B) 1,717 W 11.3 W A) 0.184 N, B) 15.0 m/s, C) 2.76 W, D) 18.8 J 13

III. Kinetic Energy Definition: “Energy of __________” motion Equation (see ref. tabs.) KE = ½ mv2 KE Units: Joule (J) v 14

III. Kinetic Energy Example: A 75 kg skydiver is falling through the air at 60 m/s. What is the kinetic energy of the skydiver?

A. Gravitational Potential Energy (GPE) IV. Types of Potential Energy Definition: ______energy (based on _______) stored position A. Gravitational Potential Energy (GPE) Definition: _______energy due to ________in a gravitational field stored height 16

A. Gravitational Potential Energy (GPE) Equation (see ref. tabs.) PE = mgh PE (J) Slope = mg (weight) Units: Joule (J) h (m) Reference Point: Position where gravitational energy equals _________ zero 17

A. Gravitational Potential Energy (GPE) Example: What is the gravitational PE of a 100 kg skydiver that is in a plane 1000 m above the ground? 18

B. Elastic Potential Energy Restoring Force: force required to return spring to ___________ position its original Spring Constant: (k) (Phet Sim) “stiffness” of spring Larger the spring constant, larger the _________ force 19

B. Elastic Potential Energy Hooke’s Law (see ref. tabs) Fs = k x Slope = k Fs (N) x = displacement (m) k = spring constant (N/m) x (m) 20

B. Elastic Potential Energy Why does this happen? 21

B. Elastic Potential Energy Factors that affect how much elastic PE an object has: 1) Displacement of spring 2) Spring constant 22

B. Elastic Potential Energy Equation (see ref. tables) PEs = ½ k x2 PEs (J) Units: Joules (J) x (m) 23

B. Elastic Potential Energy Example: A 0.0500 kg mass is hung from a spring causing it to stretch 0.150 m. What is the spring constant? B) What is the PE stored in the spring? 24

1630 kg 91.8 N/m 2670 N/m A) 2.08 x 10 5 J, B) 9.81 x 10 4 J _____ Types of Energy Whiteboard Problems: 1. A car has a kinetic energy of 4.32 X 10 5 J when traveling at a speed of 23 m/s. What is its mass?   2. A spring is 1.5 meters long and is stretched to a length of 4.3 meters, producing 360 joules of elastic potential energy. What is the spring constant? 3. A force of 32 N is required to pull a horizontal spring 0.012 m from its equilibrium position. What is the spring’s k? 4. A 50 kg shell is shot from a cannon at Earth’s surface to a height of 425 m. A) What is the GPE of the shell when it is at this height? B) What is the change in the GPE when the shell falls to a height of 225 m? 5. A ball is thrown upward from the Earth’s surface. While the ball is rising, its GPE is increases/decreases/remains the same. 1630 kg 91.8 N/m 2670 N/m A) 2.08 x 10 5 J, B) 9.81 x 10 4 J _____ 25

V. Conservation of Energy created Energy cannot be _______nor _________. It is transferred from one from to another. Therefore, total energy before = ___________________ destroyed total energy after Equation: MEbefore = MEafter (Mechanical E = KE + PE) KEi + PEi = KEf + PEf Larger Pendulum Version Video 26

V. Conservation of Energy More conservation of Energy Animations 27

Example: A B C 40 m 10 m If the cart starts from rest, has a mass of 100 kg and assuming no friction, find the following: A) The amount of KE and speed at position B. B) The speed at position C. 28

A) The amount of KE and speed at position B. Example: If the cart has a mass of 100 kg and assuming no friction, find the following: A) The amount of KE and speed at position B. 29

B) The speed at position C. Example: If the cart has a mass of 100 kg and assuming no friction, find the following: B) The speed at position C. 30

Conservation of Energy Whiteboard Problems: A 40.0 kg test rocket is fired vertically on a level surface. Its fuel gives it a kinetic energy of 3.00 x103 J before it leaves the pad. What is the maximum height the rocket will reach? A 20.0 kg object is dropped off of a 30.0 m cliff. How fast is the object going when it hits the ground? A 150. kg roller coaster is released from rest at the top of a 50.0 m hill. How fast will it be going if the second hill is 10 m high? A 0.300 kg toy has a spring attached to it so it can be shot straight up into the air. The spring is compressed 0.0500 m and has a spring constant of 300. N/m. A) Find the KE of the object when it is shot into the air. B) Find the maximum height of the toy (relative to the end of the barrel). 7.65 m 24.3 m/s 28.0 m/s A) 0.375 J, B) 0.128 m 31

VI. Conservation of Energy and the Motion of a Pendulum A. What does the work on a pendulum? Gravity ________(does not take away from total ME) Mechanical Energy is conserved (neglecting friction) 32

NEGLECTING FRICTION h = max h = max PE = max PE = max v = 0 h h v = 0 KE = 0 KE = 0 ME = PE v = max h = 0 ME = PE KE = max PE = 0 ME = KE 33

Energy vs. Horizontal Position Graph for a Frictionless Pendulum 34

VII. Work-Energy Theorem Definition: When work is done in a system, mechanical energy can be __________or __________ in the system added removed Equation (see ref. tabs.) W = Fd = ΔET 35

VII. Work-Energy Theorem Example: A 1000 kg car traveling 40 m/s slows to 20 m/s. What is the initial KE? B) What is the final KE? C) How much work is done on the car in slowing it down? 36

VII. Work-Energy Theorem Even though work is a _________ quantity, it can be positive or negative. SCALAR If work is applied in the same direction of motion it is ________ because it is adding mechanical energy to the object. POSITIVE If work is applied in the opposite direction of motion it is ________ because it is taking away mechanical energy from the object. NEGATIVE Friction applies _________ amount of work to objects. NEGATIVE 37

VII. Work-Energy Theorem 38

VII. Work-Energy Theorem Example: A 15 N block rests at the bottom of an incline that is 0.2 m high. If it takes 4 J of work to push the block up an incline, how much work was done against friction? 39

VII. Work-Energy Theorem Whiteboard: A 0.500 kg baseball bat strikes a 0.125 kg ball at rest on a tee with an average force of 2.00 x 10 4 N. If the bat stays in contact with the ball for a distance of 5.00 x 10 - 3 m, A) what kinetic energy will the ball acquire from the bat? B) What will be the ball’s speed after contact? 40

VIII. Conservation of Energy when Work is Done Problem: A 0.1 kg apple falls from the tree at a height 2 m and compresses the spring 0.3 m. What is the spring constant of the spring (ignore air resistance) 41

VIII. Conservation of Energy when Work is Done When work is done by a non-conservative force (friction, outside push), mechanical energy can be added or taken away from the initial mechanical energy of the object Conservation of Energy when Work is done Equation: KEi + PEi + W = KEf + PEf + W = energy added - W = energy lost Total Energy (ET) = PE + KE + Q Q = Internal Energy (energy of molecules/particles – excluding KE + PE) 42

VIII. Conservation of Energy when Work is Done If mechanical energy (KE and PE) is lost, it can go into __________ energy. For example, if an object slides across a rough level floor and comes to a stop, it loses ____________ energy (specifically, _____________ energy). Friction generates __________ energy (molecules rub against each other and increase the temperature of the object). INTERNAL MECHANICAL KINETIC INTERNAL 43

VIII. Conservation of Energy when Work is Done 44

VIII. Conservation of Energy when Work is Done Example: A 30.4 N force is used to slide a 40.0 N crate a distance of 6.00 m at a constant speed along a 30.0 degree incline to a vertical height of 3.00 m A) Determine the total work done by the 30.4 N force. 45

VIII. Conservation of Energy when Work is Done Example: A 30.4 N force is used to slide a 40.0 N crate a distance of 6.00 m at a constant speed along a 30.0 degree incline to a vertical height of 3.00 m B) Calculate the total increase in gravitational potential energy of the crate after it has slid 6.00 m along the incline. 46

VIII. Conservation of Energy when Work is Done Example: A 30.4 N force is used to slide a 40.0 N crate a distance of 6.00 m at a constant speed along a 30.0 degree incline to a vertical height of 3.00 m C) State what happened to the kinetic energy, potential energy, mechanical energy, and internal energy of the crate as it slides along the incline.   Kinetic: ___________ Potential: ____________ Mechanical: ____________ Internal: _____________ Constant Increased Increased Increased 47

VIII. Conservation of Energy when Work is Done Example: A 100 kg sled is located at top of an incline that is 20 m long and 5 m high. The force of friction between the sled and the incline is 45 N. What is the speed of the sled at the bottom of the incline, if the sled starts down the incline at 5 m/s? 48

A) 392 J, B) 8.85 m/s, C) 8.51 m/s (8.27 m/s) 0.0612 m/s 283,000 J Conservation of Energy When Work is Done Whiteboard Problems: A 10.0 kg block rests at the top of an incline that is 4.00 m high and 5.00 m long. A) Find the potential energy of the block when it is at the top of the incline. B) What is the speed of the block at the bottom of the incline, if it is frictionless? C) If the incline is not frictionless, and the block experiences a constant 10.0 N force of friction as it moves down the incline, find the speed of the block at the bottom. A 10.0 kg block is pushed against a horizontal spring that has a spring constant of 15.0 N/m. If the spring is displaced 0.0500 m, find the speed of the block after it is released from the spring. A 100. kg skier starts at the top of a 300. m double-black diamond slope. How much energy was lost to friction if his velocity at the bottom of the hill is 15.0 m/s? A 5.00 kg ball is dropped from a height of 10.0 m and 10.0 J of energy are lost due to air resistance. (a) What is the ball’s kinetic energy as it strikes the ground? (b) What is the final velocity as the ball strikes the ground? A) 392 J, B) 8.85 m/s, C) 8.51 m/s (8.27 m/s) 0.0612 m/s 283,000 J A) 481 J, B) 13.9 m/s 49