Further Mechanics

Question 1

What is angular displacement?

Answer 1

The angle swept at the centre of the circular path

Question 2

What is angular displacement measured in ?

Answer 2

Radians

Question 3

How can you work out the angular displacement?

Answer 3

S(arc length ) / radius

Question 4

How can you convert radians into degrees ?

Answer 4

180/ pi

Question 5

What is the angular speed?

Answer 5

The angle that the object rotates per unit time

Question 6

What is angular speed measured in ?

Answer 6

Rad/s

Question 7

How would you work out the angular speed ?

Answer 7

The angle swept at the centre / time = @s/ r

Question 8

How would you convert revolutions per minute (rpm) into rad/s ?

Answer 8

2pi / 60

Question 9

How would you convert revolutions per second (rps ) into rad/s ?

Answer 9

Multiply by 2pi

Question 10

What is the relationship between linear speed and angular speed ?

Answer 10

V = rw ( r@ /t )

Question 11

What is uniform circular motion ?

Answer 11

The motion of an object along a circle at a constant speed

Question 12

Describe the velocity when an object is travelling in a uniform circular motion ?

Answer 12

The velocity keeps changing as the direction is constantly changing

Question 13

Describe the acceleration when an object is travelling in a uniform circular motion ?

Answer 13

The object can be said to accelerate as the velocity keeps changing due to the direction changing .

The acceleration is directed at the centre of the circle

Question 14

How would you calculate the centripetal acceleration?

Answer 14

a = v^2 / r = w^2 r

Question 15

Explain why there is a centripetal force acting on an object travelling in a uniform circular motion ?

Answer 15

As there is a change in velocity the object is said to be accelerating, which is towards the centre.

• 1st law - there must be a resultant force acting upon the body
• 2nd law - the force must be acting in the direction of the acceleration ( towards the centre )

Question 16

How would you work out the centripetal force ?

Answer 16

F= ma = mw^2r = mv^2 / r

Question 17

Why does the tension vary when an object is travelling in a vertical circle at a constant speed ?

Answer 17

The tension varies as the weight of the object provides a part in the centripetal force as it goes round

Question 18

What is the tension when an object is at the top of the vertical circle ?

Answer 18

• as the centripetal force = mg + T
• T = F - mg = mv^2 / r - mg

Question 19

What is the tension at the bottom of a vertical circle ?

Answer 19

As the centripetal force is equal to the tension - mg

• T = F + mg = mv^2 / r + mg

Question 20

When is the tension the greatest when an object is moving in a vertical circle at a constant speed ?

Answer 20

At the bottom as it is greater than the centripetal force

mv^2/r +mg = T

Question 21

What is the minimum tension when an object is travelling in a vertical circle at a constant speed ?

Answer 21

At the top

T = mv^2/r -mg

Question 22

Why doesn’t the weight contribute to the centripetal force when an object is travelling at in a horizontal circle at a constant speed ?

Answer 22

The weight is at a right angle to the centripetal force so there is no impact from the weight

Question 23

Describe the tension when an object is travelling in a horizontal circle at a constant speed

Answer 23

The tension is the same at any point

• T =mv^2 / r

Question 24

What is the frequency of an object completes n rotations per second ?

Answer 24

n - cycles per second

Question 25

Why wouldn’t the string not be horizontal in practice ?

Answer 25

The weight of the object would be supported by the vertical component of the tension - so the string wouldn’t be horizontal. And the only component that provides the centripetal force would be the horizontal component. If not there wouldn’t be any support for the weight - not practical

Question 26

What is the phase difference between the displacement and velocity ?

Answer 26

Pi/2 = 90degrees

Question 27

What is the phase difference between the displacement and the acceleration?

Answer 27

Pi = 180 degrees out of phase

Question 28

When is the kinetic energy at a maximum when an object is in simple harmonic motion ?

Answer 28

Kinetic energy is at maximum at the equilibrium position

Question 29

When is the potential energy a maximum when an object is moving in a simple harmonic motion ?

Answer 29

At the maximum positive and negative amplitude

Question 30

Why is the total energy of an object in a simple harmonic motion constant ?

Answer 30

- we assume no energy has been transferred in the form of energy such as thermal … - only kinetic energy and potential energy is said to act in the object - sum of the potential and kinetic energy = constant

Question 31

What is the equation for the max velocity when an object is in simple harmonic motion ?

Answer 31

Vmax = wA - when x = 0 so sub in x as 0 into the equation

Question 32

What is the equation for max acceleration when an object is in simple harmonic motion ?

Answer 32

a max = w^2 A ( max displacement ) W can be replaced as 2pi f

Question 33

What factors affect the time period of a mass spring system ?

Answer 33

- the mass of the object - the spring constant of the spring

Question 34

What happens to the spring constant if two identical springs are attached in series ?

Answer 34

K/2 ( half ) As 1/kt = 1/k1 + 1/k1 = 2/k

Question 35

What happens to the spring constant if 2 identical springs in parallel ?

Answer 35

2k as Kt = k +K ( in parallel )

Question 36

What is the assumptions made when using the simple pendulum equation?

Answer 36

- amplified is small - less than 10 degrees - bob is a point mass - string is inextensible ( doesn’t change )

Question 37

How would you find the maximum speed of an object in a simple pendulum system using the Ep and the Ek equations ?

Answer 37

- equating the Ep and Ek equations together For Ep use the height as the change in height from the equilibrium position to the height at max Ep

Question 38

When is an object freely oscillating ?

Answer 38

When the only force acting on the object is the restoring force - no external forces This means the amplitude is kept constant as there is no energy dissipated into the surroundings Object is oscillating at its natural frequency

Question 39

Explain why the period of the trapeze changes when the acrobat lets go of the bar ?

Answer 39

- the length is a factor that affects the time period - length is from the point of suspension to the centre of mass- this decreases when the acrobat lets go as the centre of mass is higher . This means the time period will decrease as the effective length decreases

Question 40

What is meant by the natural frequency?

Answer 40

The frequency at which an object oscillated without the presence of a periodic external force

Question 41

What is a forced oscillations ?

Answer 41

- an external periodic force acts on the oscillating object resulting in the object to oscillate at the driving frequency

Question 42

What happens to the amplitude if there is no driving force present ?

Answer 42

Is there is no driving force present to sustain the oscillations , the amplitude will decrease until it eventually reaches zero and the object is at its equilibrium position as a result of resting forces which cause the energy of the system to decrease

Question 43

What is damping ?

Answer 43

Reduce forces that result in the total energy of the system to decrease

Question 44

What is meant by damped oscillation ?

Answer 44

The energy and amplitude of oscillations decreases over time due to resistive forces

Question 45

What remains constant of oscillations that are being damped ?

Answer 45

- time period - frequency

Question 46

What is light damping ?

Answer 46

When small amounts of energy is transferred to the surrounding with every oscillation - amplitude decrease gradually over time - decrease exponentially

Question 47

Why does the time period and frequency remain constant when an object is being damped ?

Answer 47

The time period and the frequency is independent of the amplitude

Question 48

What is critical damping ?

Answer 48

When the amplitude decreases to zero in the shortest possible time without oscillating

Question 49

What is over damping ?

Answer 49

When the amplitude decreases to zero without oscillating but takes longer to return to equilibrium than if it were critically damped

Question 50

What is resonance ?

Answer 50

When the driving frequency is equal to the natural frequency of the oscillator - producing the maximum amplitude

Question 51

What is the frequency at which resonance occurs ?

Answer 51

Resonant frequency

Question 52

What are the factors which allow the maximum energy to be transferred ?

Answer 52

The periodic force has to be in phase with the velocity of the system ( force and velocity in the same direction at the same time )

Question 53

Effects of damping in amplitude ?

Answer 53

- maximum amplitude decreases - frequency of the maximum amplitude shifts away from the natural frequency towards lower frequencies - resonant curve broadens