Section 7 - Further Mechanics Flashcards

1
Q

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

A

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

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2
Q

Is an object moving in a circle at a cosntant speed accelerating and why?

A

Yes - the direction is always changing hence the velocity is always changing, and acceleration is defined as the rate of change in velocity

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3
Q

What is a radian?

A

The angle of a circle sector such that the radius is equal to the arc length - written in terms of π

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4
Q

What are the conditions for SHM?

A
  • Acceleration must be proportional to its displacement from the equilibrium point
  • It must act towards the equilibrium point
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5
Q

What is the small angle approximation for sinx?

A

sinx≈x

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6
Q

What is the small angle approximation for cosx?

A

cosx≈1-x^2/2

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7
Q

What does the graph for potential energy and kinetic energy against displacement for a SHM system look like?

A
  • Potential energy - x^2 graph
  • Kinetic energy - -x^2 graph
  • Where the peak and trough line up
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8
Q

What is the definition for free vibrations?

A

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

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9
Q

What is the definition for forced vibrations?

A
  • A driving force causes the system to vibrate at a different frequency
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10
Q

Define damping and explain the different types

A

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

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11
Q

What happens to a vibration with greater damping?

A
  • 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
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12
Q

What are some implications of resonance in real life?

A
  • Soldiers must break stop when crossing bridges
  • Vehicles must be designed so there are no unwanted vibrations
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13
Q

What is the defintion of angular speed?

A

The angle an object has rotated through per unit time - rads^-1

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14
Q

What is the frequency of circular motion?

A

The number of complete revolutions per second (revs^-1 or Hz)

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15
Q

What is the time period of circular motion?

A

The time taken for a complete revolution

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16
Q

What is the restoring force in SHM?

A
  • The force pulling or pushing the object back towards the midpoint
17
Q

When does resonance happen?

A

When the driving frequency = the resonant frequency

18
Q

What does the displacement time graph look like in SHM?

A

x, varies as a cosine with a maximum value, A (the amplitude)

19
Q

What does a velocity time graph look like in SHM?

A

Reflection of sin graph in x

20
Q

What does an acceleration-time graph look like in SHM?

A

Reflection of the cos graph in x

21
Q

Discuss the consequences for the forces acting on a pole when one of the 2 swinging object’s mass is increased?

A
  1. Mass of the object has increased so weight has increased and therefor tension in rope
  2. Centripetal force would be greater for the more massive object
  3. The pole would bend towards the more massive object