WORK ENERGY POWER Types and changes of Energy

How does energy change take place? • An outside force is needed!

4 ways to approach a mechanics problem 1) Kinematics 2) Newton’s 3 Laws 3)

If released from rest, car would accelerate Can’t use kinematics because the track is

Energy • • Energy: The ability to do work Energy is a scalar value

Kinetic Energy • Energy of Motion • Translational Kinetic energy exists when an object’s

Potential Energy • Stored energy • Gravitational Potential Energy is energy stored due to

More Vocab • Mechanical Energy: Sum of kinetic and potential energy

Work • Its units are Joules • That’s the same as energy!! • (That’s

Work • Can be defined as – A change in energy W = ΔE

Power • Whether you walk up a mountain or drive up it, the same

Example • A 10 kg pumpkin is moved horizontally 5 m at a constant

Example A 3 kg pineapple is held 1. 2 m above the floor for

Example A 50 kg banana box is pulled 11 m along a level surface

Example • A 1385 kg car traveling at 16. 9 m/s is brought to

Example • A 60 kg student is running at a uniform speed of 5.

Example • The kinetic energy of 2. 1 kg rotten tomato is 1000 J.

Example A 15 kg textbook is sitting on a 1. 2 m tall table.

Example An archer pulls on a bow string with an average force of 240

Example An experiment was conducted on a 1. 1 kg cart. The force to

Example It takes 1000 J of work to compress a spring 0. 1 m.

Example • A spring with force constant 250 N/m is initially at its equilibrium

Example • Lover’s Leap is a 122 m vertical climb. The record time of

Example • A 1000 kg car accelerates from rest to a velocity of 15

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WORK, ENERGY, POWER

Types (and changes) of Energy

How does energy change take place? • An outside force is needed!

4 ways to approach a mechanics problem 1) Kinematics 2) Newton’s 3 Laws 3) Energy 4) Momentum

If released from rest, car would accelerate Can’t use kinematics because the track is curved Acceleration changes, so kinematics equations are not valid Must use energy concepts instead

Energy • • Energy: The ability to do work Energy is a scalar value Measured in Joules A joule is a Nm or kg m 2/s 2

Kinetic Energy • Energy of Motion • Translational Kinetic energy exists when an object’s center of mass is moving • K = ½ mv 2 • Rotational Kinetic energy exists when an object rotates (more about this in another unit)

Potential Energy • Stored energy • Gravitational Potential Energy is energy stored due to an object’s height • Ug = mgΔh • Elastic Potential Energy is energy stored by a spring • Us = ½ kx 2 • k is the spring constant, x is distance stretched

More Vocab • Mechanical Energy: Sum of kinetic and potential energy

Work • Its units are Joules • That’s the same as energy!! • (That’s because energy is the ability to do work!)

Work • Can be defined as – A change in energy W = ΔE – OR – The product of force and distance W = Fd

Power • Whether you walk up a mountain or drive up it, the same amount of work is done on you. You weigh a certain number of newtons and you move a certain distance. But clearly there is a difference in walking up over the course of several hours and driving up over several minutes. That difference is power! Power = energy/time • Rate of doing work • Units are Watts. A watt is a Joule/sec • P = W/t = ΔE/t

Example • A 10 kg pumpkin is moved horizontally 5 m at a constant velocity across a level floor using a horizontal force of 3 N. How much work is done in moving the pumpkin? • Note: Use applied force, not net force

Example A 3 kg pineapple is held 1. 2 m above the floor for 15 s. How much work is done on the pineapple? Note: No distance means no work

Example A 50 kg banana box is pulled 11 m along a level surface by a rope that makes an angle of 35 o with the floor. The tension in the rope is 90 N. How much work is done on the box? • Note: Use the component of the force that is in the direction of displacement

Example • A 1385 kg car traveling at 16. 9 m/s is brought to a stop while skidding 42 m. What is the work done on the car by friction? • Note: Work can be negative if the force doing the work acts in a negative direction

Example • A 60 kg student is running at a uniform speed of 5. 7 m/s. What is the kinetic energy of the student?

Example • The kinetic energy of 2. 1 kg rotten tomato is 1000 J. How fast is it moving?

Example A 15 kg textbook is sitting on a 1. 2 m tall table. If the book is lifted 0. 8 m above the table, how much gravitational potential energy does it have: a) with respect to the table? • b) with respect to the floor? • Note: Ug is always measured relative to a reference point

Example An archer pulls on a bow string with an average force of 240 N while drawing the arrow back a distance of 0. 2 m. Calculate the potential energy of the bow-arrow system.

Example An experiment was conducted on a 1. 1 kg cart. The force to pull it up a. 26 m ramp and the height of the ramp were measured for 3 trials and the data is shown here. Calculate the work done and the Ug at the top of the ramp for each trial. Trial 1 Trial 2 Trial 3 Force 3. 3 N 5. 0 N 6. 2 N Height 0. 08 m 0. 12 m 0. 15 m How does the work done on the cart compare to its gain in potential energy?

Example It takes 1000 J of work to compress a spring 0. 1 m. What is the spring constant? To compress the spring an additional 0. 1 m, does it take 1000 J, more than 1000 J, or less than 1000 J. Verify your answer.

Example • A spring with force constant 250 N/m is initially at its equilibrium length. How much work must you do to stretch the spring 0. 05 m?

Example • Lover’s Leap is a 122 m vertical climb. The record time of 4 min 25 s was achieved by Dan Osman (65 kg). What was his average power output during the climb?

Example • A 1000 kg car accelerates from rest to a velocity of 15 m/s in 4 s. Calculate the power output of the car. Ignore friction.