6.1 Further Mechanics

Question 1

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

Answer 1

A constant centripetal force (A force applied always towards the centre of that circle).

Question 2

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

Answer 2

True.
The direction is always changing hence the velocity always changing, where acceleration is defined as the change in velocity over time.

Question 3

What equation(s) can you use to calculate the magnitude of angular speed (⍵)?

Answer 3

⍵=v/r or ⍵=2𝝅ƒ
⍵ - s^-1
v - ms^-1
r - m
f - Hz

Question 4

What is angular acceleration in terms of angular velocity?

Answer 4

A = ⍵²r
⍵ - s^-1
a - ms^-2
r - m

Question 5

What is angular acceleration in terms of velocity?

Answer 5

a = v² / r
a - ms^-2
v - ms^-1
r - m

Question 6

What are the equations for centripetal force?

Answer 6

F = mv²/r or F = m⍵²r
⍵ - s^-1
v - ms^-1
r - m
F - N
m - kg

Question 7

What is a radian?

Answer 7

The angle of a circle sector such that the radius is equal to the arc length.
Radians are usually written in terms of 𝝅
Ie 2𝝅 radians = 360 degrees

Question 8

What are the conditions for SHM?

Answer 8

● Acceleration must be proportional to its displacement from the equilibrium point.
● It must act towards the equilibrium point.
● a ∝ -x

Question 9

What is the constant of proportionality linking acceleration and 𝑥?

Answer 9

• ⍵² or - k/m

Question 10

What is 𝑥 as a trig function of t and ⍵?

Answer 10

𝑥=Acos(⍵t) or 𝑥=Asin(⍵t)
⍵ - s^-1
A - m
x - m
t - s

Question 11

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

Answer 11

Max speed = ⍵A
⍵ - s^-1
A - m

Question 12

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

Answer 12

Max acceleration = ⍵²A
⍵ - s^-1
A - m

Question 13

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

Answer 13

T = 2𝜋√(m/k)
m - kg
k - Nm-1
T - s

Question 14

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

Answer 14

T = 2𝜋√(l/g)
g - ms^-2
l - m
T - s

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 - 𝑥²/2

Valid in radians

Question 17

Define Free vibrations

Answer 17

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

Question 18

Define Forced vibrations

Answer 18

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. When resonance occurs, which is when it most efficiently transfers energy to the system, the phase difference will be π/2 radians.

Question 19

Define damping and explain what is critical damping, overdamping and underdamping

Answer 19

Damping - occurs when an opposing force dissipates energy to the surroundings.
Critical damping - reduces the amplitude to zero in the quickest time.
Overdamping - is when the damping force is too strong and it returns to equilibrium slowly without oscillation.
Underdamping - is when the damping force is too weak and it oscillates with exponentially decreasing amplitude.

Question 20

What happens to a vibration with greater damping?

Answer 20

For a vibration with greater damping, the amplitude is lower at all frequencies due to greater energy losses from the system.
The resonant peak is also broader because of the damping.

Question 21

What are some implications of resonance in real life?

Answer 21

Implications of resonance include that soldiers must break stop when crossing bridges and vehicles must be designed so there are no unwanted vibrations.

Question 22

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

Answer 22

Need diagram