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 this car is released from rest, it would speed up toward the detector. It would be tempting to try to use the kinematics equations to determine the cart’s maximum speed. However, since the track is curved, the cart’s acceleration will be changing throughout its motion and therefore the kinematics equations we have learned are not valid. Therefore, we must use energy concepts we will learn in this unit.
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 KE = 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 GPE = mgΔh Elastic Potential Energy is energy stored by a spring SPE = ½ kx 2 k is the spring constant, x is distance stretched
More Vocab Internal Energy: Multi object systems can store energy based on how the objects are arranged in the system Mechanical Energy: Sum of kinetic and potential energy
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
Work Work is a scalar value Its units are Joules That’s the same as energy!!
Work Can be defined as –A change in energy W = ΔE –OR –The product of force and distance W = Fd
In physics, we talk about work being done ON an object If I hold a 30 kg weight at a height of 1.5m, I’m using energy, therefore…… I’m tired However, the work is NOT being done on the weight, it is being done on my muscles. Think of it like this: though I am exerting a force on the weight, its distance moved is zero, therefore NO work is done on it Another way to think about it is that the weight’s energy has not changed
Example If I were to lift the 30 kg weight up off the ground to a height of 1.5 m, how much work would be done on the weight?
When an object is lifted against gravity, the formula W = Fd becomes W = mgΔh m = mass g = acceleration due to gravity Δh= change in height
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: GPE 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. HINT: The work done to the bow is all being stored as potential energy. Note: We’ll discuss the work-energy relationship more later!
Example An experiment was conducted on a 1.1 kg cart. The force to pull it up a 2.6 ramp and the height of the ramp were measured for 3 trials and the data is shown here. Calculate the work done and the PE at the top of the ramp for each trial. How does the work done on the cart compare to its gain in potential energy? Trial 1Trial 2Trial 3 Force3.3N5.0N6.2N Height0.08 m0.12 m0.15 m
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 1000J, or less than 1000J. 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 0.05m?
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.