Further Mechanics + Thermal Physics

Question 1

The Newtonian mechanics of pressure of an ideal gas.
Explain why doing this, causes a change in pressure.
6 marks

Answer 1

P= F/A
-Constant cross-sectional area

P=mv
Changing volume, decreases pressure
Increasing temperature, p and v increase

Question 2

Pressure law; at constant temperature

At constant volume

Answer 2

• p directly proportional to T
  1) Higher temperature - higher kinetic energy - greater higher velocity -F= change in p/ change in time (between collisions)
  Pressure increases - greater force from wall on particle
  Greater force from particle on wall, thus pressure is greater as force increases.

Question 3

Charles’ law; Newtonian laws

Constant pressure

Answer 3

1) volume is directly proportional to temp
2) Increase in temp - higher kinetic energy - higher velocity - increase in pressure
3) since, F= change is pressure/ change in time
Collisions happen less frequently. Force will reduce
- Increasing distance between two walls + time between collisions increase

Question 4

Boyle’s law; Newtonian

Constant temperature

Answer 4

1) pressure is INVERSELY proportional to volume p=1/v
2) Reduce distance between walls- we need to reduce time between collisions f=p/t
3) Thus, force increases, pressure increases

Question 5

Doing work on a gas; manipulating p,v +t

Answer 5

If a gas is “squashed” its temperature increases.
If a gas expands its temperature decreases.
How much energy/ work to squash the gas?
Work done = force x distance (against force)
P=F/A. F=PA
W= p x A x distance
(Volume)
Work done; (to heat up) or work done (expanding cylinder)
W= p x vol
Heat - expands
Heat - contract

Question 6

A small quantity of fine sand is placed onto the surface of the plate. Initially the sand grains stay in contact with the plate as it vibrates. The amplitude of vibrating surface ram is constant, over full frequency range of signal generator. Above a particular frequency the sand grains loose contact with the surface.
Explain how this happens

Answer 6

1) When vibrating surface accelerates down with (a) less than (a) of free fall the sand stays in contact
2) Above a particular frequency, (a) is greater than g
3) there is no contact force on the sand
4) Sand no longer in contact downwards (a) of plate is greater than (a) of sand due to gravity.

Question 7

Resonance
Effect of Applied frequency on amplitude;
(4-6 marker)

Answer 7

Applied frequency;

1) < resonant frequency (or natural frequency)
2) At resonant frequency (applied frequency = natural frequency)
3) > Resonant frequency (or > natural natural frequency

Amplitude + phase difference;

1) Forced vibrations, Amplitude is small, vibrations (almost) in phase with driver.
2) Resonates at natural frequency, Amplitude gets very large, phase difference is (pi/2) out of phase.
3) Forced vibration, decreases more + more, Increases from (pi/2) towards (pi radians) pout of phase.

Question 8

Examples of oscillating motion;

Answer 8

• object on a spring moving up + down repeatedly
• A pendulum moving to and fro
• A ball-bearing rolling from side to side
• Small boat rocking from side to side

Question 9

Define free vibration

Answer 9

The amplitude is constant + no frictional forces are present

Question 10

Their phase difference in radians

Answer 10

2(pi)x(change in t)/ time period

Question 11

Brownian motion

Answer 11

Nutrients

Question 12

What is the definition of SHM?

Answer 12

Any object oscillating with a constant time period (even if changing amplitude) is considered to be moving with SHM.

Question 13

Explain significance of (-) sign in equation for acceleration

Answer 13

-Acceleration + displacement are in opposite directions;

Question 14

1) Free vibration

2) forced vibration

Answer 14

1) When a system is displaced + left to oscillate

2) oscillation due to periodic driving force

Question 15

Question when asked what will be the result on the car

Answer 15

• see if time= period
• if so resonance occurs
• Large amplitude oscillations

Question 16

MAXIMUM velocity equations

Answer 16

1) wA

2) 2(pi)fA

Question 17

Define frequency

Define period of oscillations

Answer 17

• The frequency of oscillation is the number of complete cycles per second
• The period of oscillations is the time taken to complete a cycle.

Question 18

To find force

Answer 18

F= k x displacement

Question 19

Give three examples of situations in which centripetal forces arise, detailing precisely which forces [3] contribute to the centripetal force.

Answer 19

Solution: Anything valid e.g. vehicles on banked turns (reaction/friction force), satellites in orbit (gravity), yoyos being whirled (tension)

Question 20

Outline a simple experiment you could perform to explore circular motion. As well as describing [3] the experimental setup, explain how you would calculate the centripetal force for different radii,
speeds and masses

Answer 20

Solution:
Two masses, M and m are attached to either end of a piece of string. This passes through a tube. Attached to the string on the side of the larger mass, M, is a paperclip. Holding the tube, mass m is swung in circles. The cetripetal force here is the weight of mass M.
F = Mg = mv2
r
Manipulating this equation allows us to evaluate the required quantities.

Question 21

The reaction of the surface and the frictional force both act on the cyclist, but at a distance from [3] the centre of mass. They therefore provide a torque. Qualitatively, explain why a cyclist leaning
inwards when cycling around bends helps to prevent these torques destabilising the bike.

Answer 21

Solution: 3 forces acting on the bike: weight, friction and reaction of the surface. The first acts through the COM and therefore doesn’t provide a torque. The other two act from the same point. Given that their magnitudes can’t be changed, the only way to balance them is to change the angle between the direction of the force and the line intersecting the COM and the point through which they act

Question 22

Express the tension in the string in terms of the mass, the mass’s velocity and the radius of the [2] circle in which it moves.

Answer 22

mv^2 / r= T sin θ

Question 23

Velocity

Answer 23

Arc length/ time

Question 24

What is damping?

Answer 24

• Caused by resistive forces (eg: air resistance)
• Causes amplitude of oscillations to decrease with time
• Energy is lost to surroundings (eg: as work is done against frictional forces.)

Question 25

Resonance?

Answer 25

• occurs for forced vibrations when DF=RF
• produces maximum amplitude of vibration
• Gives maximum rate of energy transfer from driver to system