Energy conservation laws in mechanics

Impulse

$$p = m\cdot v$$

p - impulse
m - mass
v - speed (velocity)

Find It is known that:

Calculate 'p'

Mechanical work

$$A = F\cdot s$$

A - work
F - force
S - path

Find It is known that:

Calculate 'A'

Mechanical work and the angle

$$A = F\cdot s\cdot cos(a)$$

A - work
F - force
S - path
a - the angle between the directions of motion and force

Find It is known that:

Calculate 'A'

Power

$$N = \frac{A}{t}$$

N - power
A - work
t - time

Find It is known that:

Calculate 'N'

Power

$$N = F\cdot v$$

N - power
F - force
v - speed (velocity)

Find It is known that:

Calculate 'N'

Efficiency

$$\eta = \frac{A_{n}}{A}$$

η - efficiency
A_n - efficient (useful ) job
A - work

Find It is known that:

Calculate 'η'

Efficiency

$$\eta = \frac{P_{n}}{P}$$

η - efficiency
P_n - efficient (useful)power
P - power

Find It is known that:

Calculate 'η'

Mechanical energy

$$E = E_{k}+E_{p}$$

E - energy
E_k - kinetic energy
E_p - potential energy

Find It is known that:

Calculate 'E'

Kinetic energy

$$E_{k} = \frac{m\cdot v^{2}}{2}$$

E_k - kinetic energy
m - mass
v - speed (velocity)

Find It is known that:

Calculate 'E_k'

Kinetic energy and impulse

$$E_{k} = \frac{p^{2}}{2\cdot m}$$

E_k - kinetic energy
p - impulse
m - mass

Find It is known that:

Calculate 'E_k'

Potential energy

$$E_{p} = m\cdot g\cdot h$$

E_p - potential energy
m - mass
g - free fall acceleration
h - height

Find It is known that:

Calculate 'E_p'

Potential energy of the compressed (stretched) spring

$$E_{p} = \frac{k\cdot x^{2}}{2}$$

E_p - potential energy
k - stiffness (spring force constant)
x - elongation (shortening) of the spring

Find It is known that:

Calculate 'E_p'