Mechanics NAB

Question 0

Derive escape velocity

From Ek and Ep = 0 at infinity

Answer 0

Remember to use the specific Ep rather than the general one per unit mass

Question 1

Derive v = u + at

From a = dV/dT

Answer 1

-

Question 2

Derive Ek for SHM

Answer 2

Take v = +- w(A^2 - Y^2)

Substitute into 0.5mv^2

Question 3

Derive Ep for SHM

Answer 3

Total energy = Ek + Ep

At equilibrium Ep = 0

Find total energy

Substitute that into original formula for total energy with the formula for Ek and solve for Ep

Remember to use the new equation for Ek, not 0.5mv^2

Question 4

Conical Pendulum

What is the centripetal force equal to?

Answer 4

TsinO = mw^2r = mv^2/ r

Question 5

Conical Pendulum

What is the weight equal to?

Answer 5

TcosO = mg

Question 6

Conical pendulum

What is tanO =

Answer 6

tanO = (mw^2r)/mg = w^2r/g

    = (mv^2/r)/mg = (v^2)/rg

Question 7

Conical Pendulum

What else is sinO =

Answer 7

sinO = radius / length of string

Question 8

What does a graph of SHM kinetic and potential energy look like across displacement from the equilibrium?

Answer 8

Two semi circles.

Ep max at furthest displacement
Ek max at equilibrium

Question 9

What does a graph of SHM energies look like across time?

Answer 9

Two sine waves

Question 10

Describe the three parts to the Bohr model of the atom

Answer 10

Electrons only at allowed orbits

Circumference of electron orbit is an integer multiple of its de Broglie wavelength

The angular momentum of electrons is quantised as an integer multiple as well