Science 10 Unit B Physics Review Notes

Science 10 Unit B Physics Review

Significant Digits

• The number 10.060 contains 4 significant digits.
• The value of 1275 written correctly as two significant digits would be 1.3 \times 10^3.

Delta Symbol

• The symbol \Delta (delta) means change in.
• \Delta = change in
• \Delta means subtract to find the difference between two values.

Scalar Quantity

• A scalar quantity has only magnitude.
• Speed is a scalar quantity.

Vector Quantity

• A vector quantity has both magnitude and direction.
• Velocity is a vector quantity.

Distance and Displacement

• Distance depends on the path taken between two points.
• Displacement is sometimes equal to the magnitude of the displacement.
• Distance is always greater than or equal to the magnitude of displacement.

Galileo Spacecraft Example

• Galileo spacecraft reached Jupiter in 1995.
• It used gravitational forces between Venus and Earth to accelerate to a speed of 39 km/s.

Numerical Response 1

• The distance Galileo traveled in one minute at a speed of 39 km/s, expressed in scientific notation, is a.bc x 10^d m.
• Convert 1 minute to 60 seconds.
• Convert 39 km/s to 39000 m/s.
• Using the formula: v = \frac{\Delta d}{\Delta t}, rearrange to solve for \Delta d .
• \Delta d = v \cdot \Delta t = 39000 \cdot 60 = 2.34 \times 10^6 m
• The value of a.bc is 2.34 and d = 6.

Motion Graphs

Velocity vs. Time Graph

• From t=1 s until t=2 s, the motion of the car is traveling at uniform speed.

Distance Calculation from Velocity-Time Graph

• The distance traveled can be found by calculating the area under the velocity-time graph.
• From t=0 s to 1 s (Area A): \frac{1}{2} \cdot b \cdot h = \frac{1}{2} \cdot (1) \cdot (10) = 5.0 m
• From t=1 s to 2 s (Area B): l \times w = 1 \cdot (10) = 10.0 m
• The distances traveled from t=0 s to 1 s and from t=1 s to 2 s are 5.0 m and 10.0 m, respectively.

Numerical Response 2

• Wayne Gretzky shoots the puck at a speed of 90 km/h from 15 m away from the net.
• Convert 90 km/h to m/s: 90 \frac{km}{h} \times \frac{1000 m}{1 km} \times \frac{1 h}{3600 s} = 25 m/s
• Using the formula: v = \frac{\Delta d}{\Delta t}, rearrange to solve for \Delta t .
• \Delta t = \frac{\Delta d}{v} = \frac{15 m}{25 m/s} = 0.60 s

Displacement-Time Graph

• On a displacement-time graph, a straight line indicates uniform motion.

Velocity-Time Graph and Displacement-Time Graph Correspondence

• The object could be moving in a negative direction.

Position vs. Time Graph

• A horizontal line indicates the object was standing still.
• A downward slope of a straight line indicates that the object was slowing down
• An upward slope of a straight line indicates that the object was moving at a constant velocity.
• An upward curving line (a changing slope) indicates that the object was accelerating.

Sun Spider Example

• Sun spiders can move up to 16 km/h.
• Convert 16 km/h to m/s: 16 \frac{km}{h} \times \frac{1000 m}{1 km} \times \frac{1 h}{3600 s} = 4.44 m/s
• The distance between two fig trees is 3.6 m.
• Using the formula: v = \frac{d}{t}, rearrange to solve for t.
• t = \frac{d}{v} = \frac{3.6 m}{4.44 m/s} = 0.81 s

Lifting a Bag of Sugar

• The mass of the bag of sugar is 4.54 kg.
• The acceleration due to gravity is 9.81 m/s^2.
• Using the formula: F = m \cdot a = 4.54 kg \times 9.81 m/s^2 = 44.5 N

Weight of an Object

• The weight of an object is the force of gravity acting on its mass.

Numerical Response 3 - Work Calculation

• Carrying a box of books weighing 67.8 N up a flight of stairs.
• Each step is 15.0 cm high, and there are 22.0 steps.
• Total vertical distance: 22 \times 0.15 m = 3.3 m
• Work done: W = F \cdot d = 67.8 N \times 3.3 m = 223.74 J \approx 224 J

Kinetic Energy Units

• According to the formula for kinetic energy, J = kg \cdot \frac{m^2}{s^2}.

Ball Thrown in the Air

• When you throw a ball into the air and it reaches its maximum height, the ball would contain all potential energy.

Soccer Goalie Catches a Ball

• The kinetic energy is transformed into heat.

Increasing Kinetic Energy on a Swing

• Push in the same direction as the swing is moving.

Bobsled Example

• Mass of the bobsled and riders: 250 kg
• Height of the run: 121 m

Potential Energy Calculation

• E_p = m \cdot g \cdot h = 250 kg \times 9.81 m/s^2 \times 121 m = 296752.5 J \approx 297 kJ

Velocity Calculation

• If all potential energy is converted into kinetic energy: Ep = Ek
• Ek = \frac{1}{2} m v^2 \implies v = \sqrt{\frac{2 Ek}{m}} = \sqrt{\frac{2(296752 J)}{250 kg}} = 48.7 m/s

Energy Conversion

• Some potential energy is lost through friction.

Race Car Example

• Distance: 100 m
• Average speed: 9.50 m/s
• Kinetic energy: 9.40 \times 10^3 J

Mass Calculation

• Ek = \frac{1}{2} m v^2 \implies m = \frac{2 Ek}{v^2} = \frac{2(9.40 \times 10^3 J)}{(9.50 m/s)^2} = 208 kg

Work and Kinetic Energy

• When a force does work on an object, the object might gain, lose, or have no change in its kinetic energy.

Pendulum Motion

• All the energy is gravitational potential energy at the top of the swing.
• All the energy is kinetic energy at the bottom of the swing.
• The energy is partly gravitational potential energy and partly kinetic energy between the top and bottom of the swing.

Useful Output Energy of a Motor

• Kinetic energy is the useful output energy of a motor.

Numerical Response 4 - Efficiency Calculation

• Energy from sunlight: 4.2 \times 10^4 kJ
• Useful energy converted by the plant: 4200 kJ
• Eff = \frac{output}{input} \times 100\% = \frac{4200 kJ}{4.2 \times 10^4 kJ} \times 100\% = 10\%

Motor Efficiency

• Electric motors are between 50% and 90% efficient.
• 73% efficient means 73% of the input energy is converted to kinetic energy.
• For every 100 J of input energy, 27 J of energy is wasted.

Total Energy

• TOTAL \ ENERGY = USEFUL + WASTED
• 100 J = 73 J + 27 J

Photosynthesis

• Photosynthesis results in an increase in potential energy.

Jackrabbit Acceleration

• Initial velocity: 0 m/s
• Final velocity: +18.5 m/s
• Time interval: 1.25 s
• a = \frac{\Delta v}{\Delta t} = \frac{vf - vi}{\Delta t} = \frac{18.5 m/s - 0 m/s}{1.25 s} = 14.8 m/s^2

Skier on a Chair Lift

• Mass: 54.8 kg
• Potential energy gained: 4.22 \times 10^5 J
• Ep = m \cdot g \cdot h \implies h = \frac{Ep}{m \cdot g} = \frac{4.22 \times 10^5 J}{54.8 kg \times 9.81 m/s^2} = 785 m

Ball and Spring Collision

• Mass of the ball: 92.4 g = 0.0924 kg
• Velocity: 4.28 m/s
• Elastic potential energy stored: 0.560 J
• E_k = \frac{1}{2} m v^2 = \frac{1}{2} (0.0924 kg) (4.28 m/s)^2 = 0.8463 J
• Eff = \frac{output}{input} \times 100\% = \frac{0.560 J}{0.8463 J} \times 100\% = 66.2 \%

Matching

• M represents any form of stored energy (Potential energy)
• X represents acceleration
• V describes size and direction (Vector)
• N describes size but not direction (Scalar)
• I represents the difference between two times (Interval)
• Q represents displacement in a unit time (Velocity)
• O represents distance traveled in a unit time (Speed)
• F represents Energy stored in a material that is bent, compressed, or stretched and will return to its original shape when released (Elastic potential energy)
• B represents Energy stored in the bonds which hold atoms, ions, and molecules together (Chemical potential energy)
• K represents Energy stored in the inner core of an atom (Nuclear potential energy)
• E represents the length of a path from one point to another (Distance)
• L represents location relative to a particular reference point (Position)
• J represents size or amount (Magnitude)
• H represents stored energy associated with the force of gravity between two objects (Gravitational potential energy).
• D represents straight line distance and direction from one point to another (Displacement)

Graph Analysis

• Distance vs. Time (uniform motion):

  • Sketch: A straight line with a positive slope.
  • Calculations: Slope of graph = velocity; speed = slope.

• Distance vs. Time (at rest):

  • Sketch: A horizontal line.
  • Calculations: Slope = speed = 0 m/s.

• Velocity vs. Time (uniform velocity):

  • Sketch: A horizontal line.
  • Calculations: Slope = acceleration = 0 m/s²; area under graph is the distance traveled.

• Velocity vs. Time (positive acceleration):

  • Sketch: A straight line with a positive slope.
  • Calculations: Slope = acceleration; area under the graph is the distance traveled.