2. Work and Energy EQUATIONS

Question 1

(2) (Equation) What is the equation for kinetic energy?

Answer 1

K= Kinetic energy (in Joule)
Joule= (kg×m^2)/s^2
m= mass (in kilograms!)
v= speed in meters per second

Question 2

(2) (Equation) What is the equation for gravitational potential energy?

Answer 2

U=mgh

U= potential energy(in Joule)
Joule= (kg×m^2)/s^2 

    m= mass in kilograms
g= acceleration due to gravity (9.8 m/s)
h= height of the object above the datum.

Question 3

(2) (Equation) What is the equation for elastic potential energy?

Answer 3

U= potential energy
k= spring constant (a measure of the stiffness of the spring)
x= the magnitude of displacement from equilibrium

Question 4

(2) (Equation) What is the equation for work? (like pushing or pulling something)

Answer 4

Work is a function of force and displacement

W= F *d = Fd cos Ө

W= work
F= magnitude of the applied force
d= distance of displacement
Ө= the angle between the applied force vector and the displacement vector

Question 5

(2) (Equation) What is the equation for work? Like a piston?

Answer 5

W= P ∆V

W= work
P= pressure
∆V= volume

Key Concept: When work is done by a system (the gas expands), the work is said to be positive. When the work is done on a system (the gas compresses), the work is said to be negative. The MCAT will not expect you to calculate the integral of a P-V graph using calculus, but you are expected to be able to calculate the area under a straight line graph if necessary.

Question 6

(2) (Equation) What is the equation for power?

In terms of work?

Answer 6

P= power
SI unit for power is Watt, which is equal to J/s
W= work (which is equal to ∆E, the change in energy)
t= time

Question 7

(2) (Equation) What is the work-energy theorem, what what does it mean?

Answer 7

The work-energy theorem states that when net work is done on or by a system, the system’s kinetic energy will change by the same amount. In more general applications, the work done on or by a system can be transferred to other forms of energy as well.

W_net= ∆K = K_f- K_i

W_net= total energy completed
∆K= change in kinetic energy
K_f= final kinetic energy
K_i= initial kinetic energy

Question 8

(2) (Equation): What is the equation for mechanical advantage?

Answer 8

Mechanical Advantage = F_out/F_in

F_out= force exerted on an object by a simple machine
F_in = force actually applied on the simple machine

Mechanical advantage is a ratio of the output force generated given a particular input force.
Efficiency is a ratio of the useful work performed by a system compared to the work performed on the system.

Question 9

(2) (Equation) In mechanical advantage, what is the equation for efficiency?

Answer 9

Efficiency
W_out= load or load distance
W_in= effort or effort distance

Another way to think of this is efficiency= (Force x distance for the load being lifted or the object) / (Force x distance for the person pulling the object).

In this case, the distance is going to be less for the object, and more for the person pulling. However the force will be less for the person pulling, and more for the object.

Mechanical advantage is a ratio of the output force generated given a particular input force.
Efficiency is a ratio of the useful work performed by a system compared to the work performed on the system.