Work/Energy Flashcards
Energy & corresponding units
Our system’s ability to do work; (kg*m^2)/s^2
Units for work
SI unit: J
Other unit: 1 Pa * m^3
Relationship between kinetic energy and speed
v^2 so if v doubles, kinetic energy quadruples
What is potential energy
Energy associated with a given object’s position in space
what is gravitational potential energy
Stored energy between the object and Earth
What is thermal energy ∆Eth?
Energy associated with friction
∆Eth = - Wfriction
kinetic energy
Energy associated with motion/acceleration
K = 1/2mv^2
Calculating gravitational potential energy:
U = mg∆y
Calculating elastic potential energy of a spring
∆Usp = (1/2)k(x^2)
*k is the spring constant
*x is the magnitude of displacement of the spring from equilibrium
∆Usp = - Wspring
Relationship between spring potential energy and displacement
There is a square relationship.
If the spring is stretched/compressed double than before, the Usp is quadrupled.
∆x increases by 4
Usp increases by 16 and so on…
Conservation of energy equation when given a problem of one type of energy being converted into another
Einitial = Efinal
Example question using the equation shown in picture: Spring potential energy –> kinetic energy
Calculating Fsp (spring force)
Fsp = k∆x
∆x is how much extra distance is covered when the spring stretches from equilibrium
Fsp is the force of the spring required to go back to its equilibrium position (the recoil)
The larger the spring constant, the (more elastic/more stiff) the spring.
More stiff
In a diagram of a person pushing a spring in, what direction is the displacement and what direction is the spring force? What is the relationship between them?
Displacement is always going the opposite direction of spring force (Fsp).
As Fsp increases, the displacement increases by the same ratio.
Fsp always points towards the equilibrium point (the position at which the spring originally started)
Spring force vs. displacement graph
Linear relationship, slope = k (spring constant)
Springs in parallel:
∆x decreases by 1/2
k (spring constant) increases by 2
Springs in a series
∆x increases by 2
k (spring constant) decreases by 1/2
If two springs are put in parallel, the springs become (more soft/more stiff).
More stiff, because the spring constant k increases
Equation for work
W = |F||d|cosθ
θ is the angle between the applied force vector & the displacement vector
*Note sometimes the force and displacement vectors go in the same direction and are parallel, so in that case θ is 0
Equation for power
P = Work/∆t or ∆E/t or Fvelocity
Units: Watts, J/s, (kgm2)/s3, (ft*lb)/s
Work-energy theorem
W = ∆K = 1/2m((Vfinal)^2 - (Vinitial)^2)
∆K is the change in kinetic energy
If the displacement vector and force vector are at a 90° angle from each other, the work will always be _____.
Zero; cos90° is 0 so that makes the work for that particular force to be 0.
Can work be negative?
Yes it can, in particular when the angle between the displacement and force vector is greater than 90°, work is NEGATIVE.
Give 2 examples of when work is 0.
- If d=0, object isn’t moving –> work is 0.
- If the angle between the force & displacement of the object is 90°. For example, a person carrying a suitcase with their hand across a straight surface.
If a person is traveling down a slope at a constant speed, what is their kinetic energy? What energy transformation takes place?
- Kinetic energy = 0
*anytime it says constant speed assume that it is 0 - Ug (potentialE) –> Eth (thermal/friction)
*The person is sliding which produces frictional energy
Tip: If anything is rising or gaining distance in the upward direction, potential energy always increases.
What is the work done by gravity when a person pushes a 2kg file cabinet 10m up a ramp which is 10° tilted off the ground.
W = mgdcos100
W = 2010cos100
cos is 100 because when drawing the gravity vector in relation to displacement vector, the 10° has to be included in addition to the 90°
How does velocity affect gravitational potential energy?
It doesn’t affect ∆Ug. It doesn’t matter whether it is moving up or down, the object with the highest ∆Ug is the one with the highest height.
Equation for conservation of energy problems:
∆E = ∆K + ∆Ug + ∆Us + ∆Eth + ∆Echem
∆K = Kf - Ki
∆Ug = mgyfinal - mgyinitial
∆Eth = - Wfriction
∆Usp = Uspfinal - Uspinitial
What is torque
It is a rotational force that makes an object spin about a pivot point
Cardiac output formula
CO = Stroke volume * Heart rate
CO is vol of blood pumped by the heart in 1 min
Stroke volume = vol of blood pumped out in a single heartbeat
When do you use the conservation of energy formulas?
-When you/object are going from a motionless position to moving
-In general, when you see one form of energy is changing to another
Potential –> kinetic
Chemical –> kinetic
Digestion is an example of what type of energy change?
Chemical energy –> thermal energy
2 ways to calculate work
- W = Fdcostheta
- Pressure * volume on a PV diagram
Work done by a potential field is path independent. Work done for conservative forces is independent on path. Name some conservative forces:
Gravitational force, elastic spring force, electrostatic, force, buoyancy force
