Further Mechanics

Question 1

What kind of force is required to keep and object moving in a circle at constant speed?

Answer 1

A constant centripetal force

Question 2

An object moving in a circle at a constant speed is accelerating. True or False, and why?

Answer 2

True - direction is constantly changing so velocity is constantly changing so it is accelerating

Question 3

What equations can you use to calculate angular speed, w?

Answer 3

w = v / r
w = 2 x π x f

Question 4

What is angular acceleration in terms of angular velocity in the form of an equation?

Answer 4

Ac = w^2 x r

Question 5

What is angular acceleration in terms of velocity in the form of an equation?

Answer 5

Ac = v^2 / r

Question 6

What are the equations for centripetal force?

Answer 6

Fc = m x r x w^2
Fc = (m x v^2) / r

Question 7

What is a radian?

Answer 7

The angle of a circle sector such that the radius, r, is equal to the arc length, and are normally written in terms of pi. 2π = 360º

Question 8

What are the conditions for simple harmonic motion?

Answer 8

• Acceleration (a) must be proportional to its displacement (-x) from the equilibrium point
• It must act towards the equilibrium point

Question 9

What is the constant of proportionality linking acceleration and x in SHM?

Answer 9

• Angular velocity squared (w^2)
  or
• -k/m

Question 10

What is x as a trig function of t and w in SHM?

Answer 10

x = Acos(wt)
or
x = Asin(wt)

Question 11

How can you calculate the maximum speed using w and A?

Answer 11

Max speed = w x A

Question 12

How can you calculate the maximum acceleration using w and A?

Answer 12

Max acceleration = w^2 x A

Question 13

What is the equation for the time period of a mass - spring simple harmonic system?

Answer 13

T = 2π √(m/k)

Question 14

What is the equation for the time period of a simple harmonic pendulum?

Answer 14

T = 2π√(l/g)

Question 15

What is the small angle approximation for sinx?

Answer 15

sinx = x

Valid in radians

Question 16

What is the small angle approximation for cosx?

Answer 16

cosx = 1 - (x^2/2)

Valid in radians

Question 17

Describe the graph for potential energy and kinetic energy against displacement, for a SHM system?

Answer 17

• At the mean position, the total energy in simple harmonic motion is purely kinetic and at the extreme position, the total energy in SHM is purely potential energy
• At other positions, kinetic and potential energies are interconvertible and their sum is equal to 1/2 x k x a^2
• The graph is parabolic in nature

Question 18

Define simple harmonic motion.

Answer 18

The motion of a body which is acted upon by a resultant force whose magnitude is proportional to the distance of the body from a fixed point and whose direction is always towards that point

Question 19

Define free vibrations.

Answer 19

The frequency a system tends to vibrate at in a free vibration is called the natural frequency

Question 20

Define forced vibrations.

Answer 20

A driving force causes the system to vibrate at a different frequency. For higher driving frequencies, the phase difference between the driver and the oscillations rises to π radians. For lower frequencies, the oscillations are in phase with the driving force.

Question 21

What is resonance in a SHM system?

Answer 21

When vibrations caused by a driving force most efficiently transfers energy to the system, the phase difference will be π/2 radians

Question 22

Define dampened harmonic motion.

Answer 22

When amplitude diminishes with time as a consequence of a small damping force impeding the motion

Question 23

Define damping.

Answer 23

Occurs when an opposing force dissipates energy to the surroundings

Question 24

Explain what is critical damping.

Answer 24

Reduces the amplitude to zero in the quickest time

Question 25

Explain what is overdamping.

Answer 25

When the damping force is too strong and it returns to equilibrium slowly without oscillation

Question 26

Explain what is underdamping.

Answer 26

When the damping force is too weak and it oscillated with exponentially decreasing amplitude

Question 27

What happens to a vibration with greater damping?

Answer 27

The amplitude is lower at all frequencies due to greater energy losses from the system. The resonant peak is also broader

Question 28

What are some of the implications of resonance in real life?

Answer 28

• Soldiers must break stop when crossing bridges

- Vehicles designed for no unwanted vibrations