Further Mechanics

Question 1

What is a radian?

Answer 1

Uts the ratio of the arc length to the radius

Question 2

What is 1 radian equal to in degrees?

Answer 2

57.3

Question 3

What is angular velocity?

Answer 3

The velocity of a particle that travels through an angle

Used in circular motion as particles closer to the centre have different tangential velocity than the outermost particles - But they travel through the same angle so angular velocity used instead

Question 4

What is tangential velocity?

Answer 4

The velocity of a particle at a tangent to its direction of travel

Question 5

What is the equation that links tangential and angular velocity?

Answer 5

V=WR

Velocity = angular velocity x radius

Question 6

Equations for angular velocity?

Answer 6

w=(2 x pi)/time period

w=2 x pi x frequency

Question 7

Equation for tangential velocity?

Answer 7

v=1/frequency

Question 8

Examples of angular velocity?

Answer 8

Clock

Engine revolutions

Question 9

What is centripetal force?

Answer 9

The resultant force that causes an object to move in a circular path

Question 10

Equation for centripetal acceleration?

Answer 10

a=(v^2)/r

a=(w^2) x r

Question 11

Equation for centripetal force?

Answer 11

F=(m(v^2))/r

F=m x (w^2) x r

Question 12

Examples of centripetal force?

Answer 12

Car as it corners - friction

Earth - Gravity

Atoms - Electrostatic

Question 13

How would you find the centripetal force on an object at an angle? e.g. a car on a banked corner.

Answer 13

1. W=mg
2. W = Ncos(x) (weight same as vert comp of normal force)
3. mg=Ncos(x)
4. N =(mg)/Cos(x) (Rearrange for N)
5. F=(m(v^2))/r
6. Nsin(x) = (m(v^2))/r (Centripetal same as horiz comp of normal)
7. mg/cos(x) x sin(x) = (m(v^2))/r (Sub N in)
8. tan(x) x g = (v^2)/r
9. tan(x) = (v^2)/g x r

Question 14

How would you find the centripetal force of an object cornering on the flat. (e.g. a car)

Answer 14

Friction would be the resultant force towards the centre

So F=(m(v^2))/r would be the friction and the centripetal force

Question 15

How would you find the speed limit for and object to successfully corner

Answer 15

Increase the values of V until the friction supplied by the tires can no longer fulfill the centripetal force required for the car to corner

Fr > F

Question 16

Explain what happens for an object in a vertical loop in terms of the forces at 1 = the bottom of the loop 2 & 4 the sides and 3 the top of the loop

Answer 16

1 = The object will ‘feel’ the most force. As the weight of the object is working downward in the opposite direction to the centripetal force required. So the reactionary force has to overcome the weight and fulfill the centripetal force required. Hence the feeling of ‘being heavier’

2 & 4 = The objects weight is perpendicular to the reaction force and centripetal force so the objects centripetal force can be fulfilled just by the reaction force.

3 = The object has weight and the normal reaction force working in the same direction as the centripetal force required. As weight is constant and contributing towards the centripetal force, the reaction force will lessen hence a feeling of ‘weightlessness’

Question 17

What 2 requirements are there for an object to be in Simple Harmonic Motion (SHM)

Answer 17

acceleration is directly proportional to displacement from equilibrium

accelerates in the opposite direction to it’s displacement

Question 18

What effect does increasing the amplitude have on time period and velocity?

Answer 18

Time period remains the same

Velocity must increase as it has to travel further in the same time period

Question 19

Equation for acceleration in SHM

Answer 19

acceleration = -(angular velocity)^2 x displacement

a= -(w)^2 * x

Question 20

Equation for displacement in SHM

Answer 20

displacement = Amplitude x cos(angular velocity x time)

x= A x cos(wt)

Question 21

Equation for velocity in SHM

Answer 21

velocity = + or -(w)sqroot((Amplitude)^2 - (displacement)^2)

Question 22

Equation for max velocity in SHM

Answer 22

velocity max = angular velocity x amplitude

Vmax = w x A

Question 23

Equation for max acceleration

Answer 23

acceleration max = (angular velocity)^2 x amplitude

Amax = (W)^2 x A

Question 24

Time period in SHM for a mass spring system

Answer 24

time period = 2 x Pi x sqroot(mass/spring constant)

T = 2 x Pi x sqroot(m/k)

Question 25

Time period in SHM for a simple pendulum

Answer 25

time period = 2 x Pi x sqroot(length/gravity)

T = 2 x Pi x sqroot(l/g)

Question 26

How would you find the value of gravity or the spring constant by using time period of SHM

Answer 26

You would use a graph and plot T squared against either
L (if your trying to find g)

or M (if your trying to find the spring constant).

Then find the gradient of the graph.

As your using T squared, square the whole time period of SHM equation then rearrange and solve for g or k

Question 27

Describe the correlation between velocity and displacement

Answer 27

90 degrees out of phase

Question 28

Describe the correlation between velocity and acceleration

Answer 28

90 degrees out of phase

Question 29

Describe the correlation between acceleration and displacement

Answer 29

180 degrees out of phase

Question 30

Correlation between potential energy and displacement?

Answer 30

PE directly proportional to Displacement

Question 31

Corellation between Kinetic energy and velocity?

Answer 31

KE directly proportional to (velocity)^2

Question 32

When will SHM be damped?

Answer 32

When there are resistive forces present in the system

Question 33

What does dampening cause in SHM?

Answer 33

It causes the amplitude of the oscillations to decrease with time