2.2.2 Mechanics - Kinetics

Question 1

What are the equations for

s = distance travelled around an arc of a circle

v = angular velocity

a = angular acceleration

Answer 1

R = radius

theta = angle of arc in radians

Note: These equations always result in radians

Also note: angular part eg angular velocity acceleration is on far right and needs manipulation

Question 2

Answer 2

1/6 rad/s , 5(pi) rev/min

Question 3

Answer 3

1/160(pi) rev/s^2

Question 4

Answer 4

89,000 ft

Question 5

What is the formula for the period T of a pendulum

Answer 5

Question 6

What is the formula for Time Period T and consequently for f frequency?

Answer 6

Question 7

What is simple harmonic motion (shm)?

Answer 7

If we consider only the horizontal motion of the mass and neglect its vertical motion as it swings (an assumption which can be made if the string is long compared to the amplitude of swing), then the periodic motion is said to be simple harmonic motion

Question 8

In terms of a pendulum;

If the displacement of the mass is plotted as a function of time, it will trace out a pure _____ wave

Answer 8

sine

Question 9

Frequency is measured in:

Answer 9

The number of cycles per second, f in hertz

formula: f = 1 /T where T is the time period

Question 10

In terms of a pendulum:

When its velocity is zero, its acceleration is a _______and when its acceleration is zero, its velocity is _______

Answer 10

In terms of a pendulum:

When its velocity is zero, its acceleration is a maximum and when its acceleration is zero, its velocity is maximum

Question 11

Answer 11

0.6 Hz, 16.8 seconds

also recall: frequency f = 1/T

Question 12

What is the formula for Work

Answer 12

Work = (Force)(Distance)

Question 13

Because of the constant presence of friction, the _____ work is always greater than the _____ work.

Some of the input work is not useful work but serves to produce sound energy (a squeek), light energy ( a spark) or heat energy

Answer 13

Because of the constant presence of friction, the input work is always greater than the output work.

Some of the input work is not useful work but serves to produce sound energy (a squeek), light energy ( a spark) or heat energy

Question 14

The type of lever shown in the picture is a First/Second/Third class lever?

Answer 14

First class lever: The fulcrum is between the load and the applied force.

Question 15

The type of lever shown in the picture is a First/Second/Third class lever?

Answer 15

Second class: The load is between the fulcrum and the applied force.

(remember: second class citizens are scum and load their bags on the plane not caring)

Question 16

The type of lever shown in the picture is a First/Second/Third class lever?

Answer 16

Third class: The applied force is between the load and the fulcrum.

(Remember: 3rd world countries put a lot of effort in but are still poor despite their efforts)

Question 17

In a system of pulleys, how would you find the mechanical advantage?

Answer 17

Count the number of ropes excluding the force bit of the rope and that is your mechanical advantage of that system.

Question 18

What is the Ideal Mechanical Advantage formula for a wheel and axle

Answer 18

where r is the radius of the axle

and R is the radius of the wheel

Question 19

What is the Ideal Mechanical Advantage formula of an inclined plane?

Answer 19

where theta = angle of inclined plane

Question 20

The screw jack is a development of the _____________

What is the formula for the Ideal Mechanical Advantage of a screw jack?

Answer 20

inclined plane

where p is the pitch of the screw (distance between adjacent threads)

and r is the radius of the turn

Question 21

Answer 21

3

Question 22

Answer 22

3

Question 23

Answer 23

71%

Efficiency = AMA / IMA

Question 24

Answer 24

80%

Efficiency = W_o / W_i

(Efficiency also = AMA / IMA)

Question 25

Answer 25

33.3 lbs Recall that: Wheel and axle IMA = R/r (R=radius of wheel and r= radius of axle) Efficiency = AMA /IMA AMA = F_o / F_i

Question 26

Answer 26

375 lbs Recall: Hydraulic jack ima = R² / r² (where R is radius of large piston and r is radius of small piston) However question gives area already so really Hydraulic jack ima = large area/small area Efficiency = AMA/IMA (also = W_o / W_i ) AMA = F_o / F_i

Question 27

Answer 27

90.9% IMA of a pulley system = number of strands efficiency = AMA / IMA (= W_o / W_i ) AMA = F_o /F_i

Question 28

Does the idler gear alter the velocity ratio?

Answer 28

The idler gear does not alter the overall Velocity Ratio

Question 29

Velocity Ratio is (in terms of teeth on a gear)

Answer 29

Question 30

What is the gear ratio?

Answer 30

Gear ratio = Product of number of teeth in driven gears / Product of number of teeth in driver gears

Question 31

What is meant by concurrent forces?

Answer 31

Concurrent forces means that the forces all act at a single point

Question 32

What is meant by non concurrent forces?

Answer 32

Non-concurrent means the forces do not act at a single point.

Question 33

What is meant by Non concurrent coplanar

Answer 33

Non-concurrent coplanar means that the forces act in different lines but only on one plane, in other words two dimensions only. There will be a resultant force and a resultant moment of force but only in the plane of the paper