Section 7 - 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

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

Answer 2

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

Question 3

What is a radian?

Answer 3

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

Question 4

What are the conditions for SHM?

Answer 4

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

Question 5

What is the small angle approximation for sinx?

Answer 5

sinx≈x

Question 6

What is the small angle approximation for cosx?

Answer 6

cosx≈1-x^2/2

Question 7

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

Answer 7

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

Question 8

What is the definition for free vibrations?

Answer 8

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

Question 9

What is the definition for forced vibrations?

Answer 9

• A driving force causes the system to vibrate at a different frequency
• For higher drivign frequencies, the phase difference between the driver and 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 10

Define damping and explain the different types

Answer 10

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 oscialltion
* Underdamping - when the damping force is too weak and it oscillates with exponentiallu decreasing amplitude

Question 11

What happens to a vibration with greater damping?

Answer 11

• The amplitude is lower at all frequencies due to greater energy losses from the system
• The resonant peak is also broader because od the damping

Question 12

What are some implications of resonance in real life?

Answer 12

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

Question 13

What is the defintion of angular speed?

Answer 13

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

Question 14

What is the frequency of circular motion?

Answer 14

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

Question 15

What is the time period of circular motion?

Answer 15

The time taken for a complete revolution

Question 16

What is the restoring force in SHM?

Answer 16

• The force pulling or pushing the object back towards the midpoint
• The size is directly proportional to the displacement - as the restoring force causes acceleration towards the midpoint, the acceleration is proportional to the displacement

Question 17

When does resonance happen?

Answer 17

When the driving frequency = the resonant frequency

Question 18

What does the displacement time graph look like in SHM?

Answer 18

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

Question 19

What does a velocity time graph look like in SHM?

Answer 19

• v, is the gradient of the displacement-time graph. It has a maximum value of ωA (where v, is the gradient of the displacement-time graph.
• It has a maximum value of ωA (where ω is the angular frequency of the oscillation), and is a quarter of a cycle in front of the displacement
• Reflection of the sin graph in x

Question 20

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

Answer 20

• a, is the gradient of the velocity-time graph
• It has a maximum value of ω^2A, and is in antiphase with the displacement
• Reflection of the cos graph in x