# Nelson Grade 12: Kinematics and Forces

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• Published : March 4, 2013

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Unit 1 Forces and Motion: Dynamics
(Pages 2–3)

Knowledge and Understanding
1.

Scalar quantities include distance (metre, 5.0 m), time (second, 15 s), mass (kilogram, 65 kg), and frequency (hertz, 60 Hz). Vector quantities include velocity (metres per second, 15 m/s [E]), displacement (metre, 6.5 m [S]), acceleration (metres per second squared, 9.8 m/s2 [down]), and force (newton, 25 N [forward]). 2. (a) Both masses will hit the floor at the same time since the speed at which an object falls is independent of mass, and is related only to acceleration due to gravity (neglecting air resistance). (b)

(c) m = 20 g = 0.02 kg
Fg = ?
Fg = mg
= (0.02 kg)(9.8 N/kg [down])
Fg = 0.2 N [down]
The weight of the 20-g mass is 0.2 N [down].
(d) One example is the force of Earth pulling downward on the 20-g mass and the force of the 20-g mass pulling upward on Earth.
GM E mMoon
The magnitude of the force of gravity between Earth and the Moon depends linearly on the masses of 3. FG =
r2
Earth and the Moon, and depends inversely as the square of the distance between the centres of Earth and the Moon. 4. (a) Kinematics is the study of motion (e.g., analyzing motion with constant acceleration). Dynamics is the study of the causes of motion (e.g., analyzing forces by applying Newton’s three laws of motion). (b) Average speed is a scalar quantity, v

av

=

total distance
total time

. Average velocity is a vector quantity, vav =

change of position
time interval

.

(c) Static friction is a force that acts to prevent a stationary object from starting to move. Kinetic friction is a force that acts against a moving object. For a given situation, kinetic friction tends to be less than maximum static friction. (d) Helpful friction is needed in many cases (e.g., turning a doorknob, walking, and travelling around a corner on a highway). Unwanted friction usually increases the production of waste heat (e.g., friction in the moving parts of an engine).

(e) Frequency is the number of cycles of a vibration per unit time; it is measured in hertz (Hz) or s−1. Period is the time for one complete cycle of a vibration; it is measured in seconds (s). (f) Rotation is the spinning of an object on its own axis (e.g., Earth rotates daily). Revolution is the motion of one body around another (e.g., Earth revolves around the Sun once per year).

Inquiry and Communication

5. (a) The units of acceleration are m/s2, so the inspector could use a metre stick to measure the distance in metres (m), and a stopwatch to measure the time in seconds (s).
(b) The acceleration is the dependent variable, and the distance and time are the independent variables. (Students will discover in Chapter 3 that the distance is actually the radius of the circle and the time is the period of rotation of the ride.)

1

6.

Error analysis can be reviewed by referring to page 755 of the text. Note that possible error is also called uncertainty. (a) The possible error is ± half of the smallest division of the measurement, or ±0.05 m/s2. possible error

× 100%
(b) % possible error =
measurement
=

±0.05 m/s
9.4 m/s

2

2

× 100%

% possible error = ±0.5%
The percent possible error is ±0.5%.
measured value − accepted value
× 100%
(c) % error =
accepted value
2

=

9.4 m/s − 9.8 m/s
9.8 m/s

2

2

× 100%

% error = − 4.0%
The percentage error is –4.0%.
difference in values
(d) % difference =
× 100%
average of values
2

=

9.7 m/s − 9.4 m/s
1
2

7.

(9.7 m/s

2

2

+ 9.4 m/s

2

)

× 100%

% difference = 3.0%
The percentage difference is 3.0%.
A prediction is a stated outcome expected from an experiment. A hypotenuse is a tentative explanation of what is expected in an experiment.

Making Connections
8.

The rapid spinning in the centrifuge would cause the liquids to separate according to their densities, with the...