Podcast
Questions and Answers
Why is the concept of 'units' so fundamental in physics?
Why is the concept of 'units' so fundamental in physics?
- Units allow for qualitative descriptions of physical phenomena.
- Units are arbitrary labels assigned to physical quantities for ease of memorization.
- Units provide a standardized way to communicate measurements, ensuring clarity & consistency in data and calculations. (correct)
- Units are only relevant in theoretical physics but not in experimental work.
How are derived units related to base units?
How are derived units related to base units?
- Derived units are more fundamental than base units and cannot be expressed in terms of them.
- Derived units are used for historical reasons, but are not relevant in modern physics.
- Derived units are physical quantities that are measured independently of base units.
- Derived units are combinations of base units through multiplication or division. (correct)
Which of the following sets contains only base quantities as defined in the SI system?
Which of the following sets contains only base quantities as defined in the SI system?
- Force, energy, power
- Length, mass, time (correct)
- Area, volume, density
- Velocity acceleration, force
What is the purpose of dimensional analysis in physics?
What is the purpose of dimensional analysis in physics?
If an equation contains the term $v^2$, where $v$ represents velocity ($[L][T]^{-1}$), what is the dimension of this term?
If an equation contains the term $v^2$, where $v$ represents velocity ($[L][T]^{-1}$), what is the dimension of this term?
If a newton (N) is defined as $kg \cdot m/s^2$, what are the dimensions of pressure, typically measured in pascals (Pa), in terms of mass ([M]), length ([L]), and time ([T])?
If a newton (N) is defined as $kg \cdot m/s^2$, what are the dimensions of pressure, typically measured in pascals (Pa), in terms of mass ([M]), length ([L]), and time ([T])?
Which of the following equations is dimensionally consistent, where $v$ is velocity, $a$ is acceleration, $t$ is time, and x is distance?
Which of the following equations is dimensionally consistent, where $v$ is velocity, $a$ is acceleration, $t$ is time, and x is distance?
Consider an equation where energy (E) is expressed as $E = k \cdot m \cdot c^3$ where $m$ is mass and $c$ is the speed of light. What must be the dimensions of $k$ for the equation to be dimensionally consistent?
Consider an equation where energy (E) is expressed as $E = k \cdot m \cdot c^3$ where $m$ is mass and $c$ is the speed of light. What must be the dimensions of $k$ for the equation to be dimensionally consistent?
Why is scientific notation essential in physics?
Why is scientific notation essential in physics?
Which of the following numbers is correctly expressed in scientific notation, suitable for physics calculations?
Which of the following numbers is correctly expressed in scientific notation, suitable for physics calculations?
Convert 0.0000000000067 meters to scientific notation with two decimal places.
Convert 0.0000000000067 meters to scientific notation with two decimal places.
Express $4.2 \times 10^{-7}$ kilograms in micrograms (g).
Express $4.2 \times 10^{-7}$ kilograms in micrograms (g).
What is the purpose of using prefixes (e.g., kilo, mega, micro) with SI units?
What is the purpose of using prefixes (e.g., kilo, mega, micro) with SI units?
Convert 50 kilometers per hour (km/h) into meters per second (m/s).
Convert 50 kilometers per hour (km/h) into meters per second (m/s).
Convert a density of 13.6 g/cm (grams per cubic centimeter) to kg/m (kilograms per cubic meter).
Convert a density of 13.6 g/cm (grams per cubic centimeter) to kg/m (kilograms per cubic meter).
A rectangular block has dimensions of 2.0 cm x 3.0 cm x 4.0 cm. If its mass is 48 g, calculate its density in kg/m.
A rectangular block has dimensions of 2.0 cm x 3.0 cm x 4.0 cm. If its mass is 48 g, calculate its density in kg/m.
What is the key difference between scalar and vector quantities?
What is the key difference between scalar and vector quantities?
Which of the following quantities is a scalar: displacement, velocity, force, or speed?
Which of the following quantities is a scalar: displacement, velocity, force, or speed?
Two vectors are considered equal if and only if:
Two vectors are considered equal if and only if:
If Vector A has a magnitude of 10 units pointing east, what is the negative of Vector A?
If Vector A has a magnitude of 10 units pointing east, what is the negative of Vector A?
Two co-linear forces, 50 N and 80 N, act on an object. If they act in opposite directions, what is the magnitude of the resultant force?
Two co-linear forces, 50 N and 80 N, act on an object. If they act in opposite directions, what is the magnitude of the resultant force?
If $A_x = 4$ and $A_y = 3$ for a vector A, what is the magnitude of A?
If $A_x = 4$ and $A_y = 3$ for a vector A, what is the magnitude of A?
A vector has components $A_x = -5$ and $A_y = 5$. What is the direction of the vector with respect to the positive x-axis?
A vector has components $A_x = -5$ and $A_y = 5$. What is the direction of the vector with respect to the positive x-axis?
What is the primary principle behind the parallelogram method of vector addition?
What is the primary principle behind the parallelogram method of vector addition?
Two forces, 30 N and 40 N, act on an object at a 90 angle to each other. What is the magnitude of the resultant force?
Two forces, 30 N and 40 N, act on an object at a 90 angle to each other. What is the magnitude of the resultant force?
Two forces of equal magnitude F are applied to an object. If the angle between these forces is 120, what is the magnitude of the resultant force?
Two forces of equal magnitude F are applied to an object. If the angle between these forces is 120, what is the magnitude of the resultant force?
In a scenario where multiple forces act on an object resulting in a net force of zero, what is this condition called?
In a scenario where multiple forces act on an object resulting in a net force of zero, what is this condition called?
If the x-component of a force is positive and the y-component is negative, in which quadrant does the force vector lie?
If the x-component of a force is positive and the y-component is negative, in which quadrant does the force vector lie?
A force vector is given by $\vec{F} = 3\hat{i} + 4\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along the x and y axes, respectively. Determine the angle this force vector makes with the x-axis.
A force vector is given by $\vec{F} = 3\hat{i} + 4\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along the x and y axes, respectively. Determine the angle this force vector makes with the x-axis.
A boat is being pulled by two tugboats. Each tugboat exerts a force of 5000N, and the angle between the two ropes is 30 degrees. What is the resultant force on the boat?
A boat is being pulled by two tugboats. Each tugboat exerts a force of 5000N, and the angle between the two ropes is 30 degrees. What is the resultant force on the boat?
A car weighing 15,000 N is parked on a hill with a 10-degree slope from the horizontal. What is the component of the car's weight that is parallel to the road?
A car weighing 15,000 N is parked on a hill with a 10-degree slope from the horizontal. What is the component of the car's weight that is parallel to the road?
A traffic light is suspended between two poles by two cables which each make an angle of 15 degrees with the horizontal poles. If each cable has a tension of 1000 N, what is the weight of the traffic light? (Assume the system is in equilibrium)
A traffic light is suspended between two poles by two cables which each make an angle of 15 degrees with the horizontal poles. If each cable has a tension of 1000 N, what is the weight of the traffic light? (Assume the system is in equilibrium)
An athlete runs 50 m due east, then turns and runs 30 m due north. Determine the magnitude of the resultant displacement.
An athlete runs 50 m due east, then turns and runs 30 m due north. Determine the magnitude of the resultant displacement.
A hiker walks 5 km in a direction 30 degrees east of north, then 4 km in a direction 60 degrees west of north. What is the hiker's total displacement from the starting point?
A hiker walks 5 km in a direction 30 degrees east of north, then 4 km in a direction 60 degrees west of north. What is the hiker's total displacement from the starting point?
A projectile is launched with an initial velocity of 30 m/s at an angle of 60 degrees above the horizontal. Find the x and y components of the initial velocity.
A projectile is launched with an initial velocity of 30 m/s at an angle of 60 degrees above the horizontal. Find the x and y components of the initial velocity.
Three vectors act concurrently at a point: $\vec{A} = 5\hat{i} + 2\hat{j}$, $\vec{B} = -3\hat{i} - 5\hat{j}$, and $\vec{C} = \hat{i} + 3\hat{j}$. What is the resultant vector?
Three vectors act concurrently at a point: $\vec{A} = 5\hat{i} + 2\hat{j}$, $\vec{B} = -3\hat{i} - 5\hat{j}$, and $\vec{C} = \hat{i} + 3\hat{j}$. What is the resultant vector?
A rope is tied from a ceiling and used to suspend equal weights of 200 Newtons at the very bottom, so that the ropes forms an angle of 120 degrees. What is the magnitude of the tension in the ropes?
A rope is tied from a ceiling and used to suspend equal weights of 200 Newtons at the very bottom, so that the ropes forms an angle of 120 degrees. What is the magnitude of the tension in the ropes?
Flashcards
What is a unit?
What is a unit?
A standard used to express measurement of a physical quantity.
What are SI units?
What are SI units?
Internationally accepted system of units for measurements.
What are base quantities?
What are base quantities?
Seven fundamental quantities: length, mass, time, electric current, etc.
What are base units?
What are base units?
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What are derived quantities?
What are derived quantities?
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What are derived units?
What are derived units?
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What is dimensional analysis?
What is dimensional analysis?
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What is scientific notation?
What is scientific notation?
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Common prefixes?
Common prefixes?
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What is a scalar?
What is a scalar?
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What is a vector?
What is a vector?
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What are equal vectors?
What are equal vectors?
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What is a negative vector?
What is a negative vector?
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What is addition of Perpendicular Vectors?
What is addition of Perpendicular Vectors?
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What is Addition of Vectors - Parallelogram Method?
What is Addition of Vectors - Parallelogram Method?
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What is resolution of a vector?
What is resolution of a vector?
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What is equilibrium?
What is equilibrium?
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Study Notes
Units
- A unit is a standard that expresses the measurement of a particular physical quantity.
- Height can be shown in cm, mm, or m.
- SI (International Standard) Units are used.
- Base quantities are the seven fundamental quantities.
- The units of base quantities are called base units.
- Derived quantities are 7 base quantities which can be combined.
- Their units are called derived units.
Seven Base Quantities
- Length is measured in meters (m) and is represented by the symbol l.
- Mass is measured in kilograms (kg) and is represented by the symbol m.
- Time is measured in seconds (s) and is represented by the symbol t.
- Amount of substance is measured in moles (mol) and is represented by the symbol n.
- Electric current is measured in amperes (A) and is represented by the symbol I.
- Luminous intensity is measured in candelas (cd) and is represented by the symbol Iv.
- Temperature is measured in kelvin (K) and is represented by the symbol T.
Derived Quantities
- Speed is expressed as length/time and measured in meters/second (m/s or m·s⁻¹).
- Acceleration is expressed as length/(time)² and measured in meters/(second)² (m/s²).
- Volume is expressed as (length)³ and measured in (meter)³ (m³).
- Force = mass x acceleration = (mass)⋅(length)/(time)², and has units of kg⋅m⋅s⁻².
- 1N (newton) is defined as being equivalent to 1 kg⋅m⋅s⁻².
Dimensional Analysis
- Dimensions of mass: [M]
- Dimensions of length: [L]
- Dimensions of time: [T]
- Speed = Distance/Time = [L]/[T] = [L]⋅[T]⁻¹
- Force = mass x acceleration = [M]⋅[L]⋅[T]⁻²
- Dimensional analysis checks equations that describe the physical phenomena.
- This is done by checking that [Dimensions] LHS = [Dimensions] RHS
Dimensional Consistency
- The equation v = u + at² is dimensionally incorrect.
- Velocities v=u+at
- Distance S = ut + 1/2 at²
- Force F = T + ma
- Energy E = 1/2 mv²
Scientific Notation
- All numbers, both large and very small, must be expressed in scientific notation.
- The formula is A=a.cdx10ʸ with the number correct to two decimal places.
- To express large numbers: 1788255397 =1.79×10⁹
- Express small numbers: 0.0000000369 = 3.69×10⁻⁸
- For every jump to the left, add 1 to the exponent.
- For every jump to the right, subtract 1 from the exponent.
Unit Conversions Prefixes
- giga (G) = 10⁹
- mega (M) = 10⁶
- kilo (K) = 10³
- deci (d) = 10⁻¹
- centi (c) = 10⁻²
- milli (m) = 10⁻³
- micro (µ) = 10⁻⁶
- nano (n) = 10⁻⁹
- pico (p) = 10⁻¹²
Length Conversions
- 1.78 m to cm = 178 cm = 1.78 x 10² cm
- 1239 mm to m = 1.24 m
- 125 cm to nm = 1.25 x 10⁹ nm
- 34889 µm to cm = 3.49 x 10² cm
Mass Conversions
- 108 kg to mg = 1.08 x 10¹¹ mg
- 76.98 mg to µg = 7.70 x 10⁴ µg
- 936.83 μg to kg = 9.37 x 10⁻⁷ kg
Time Conversions
- 100 s to ms = 10⁵ ms
- 1 year (365.25 days) to s = 3.16 x 10⁷ s
Volume Conversions
- 5 l to m³ = 5 x 10⁻³ m³
- 5 litres to ml = 5 x 10³ ml
- 2345 cm³ to dm³ = 2.34 x 10³ dm³
Mixed Conversions
- 3.478 g/cm³ to SI unit = 3.478 x 10³ kg⋅m⁻³
- 180 ml/min to SI unit = 3 x 10⁻⁶ m³/s
- 2758 kN/cm² to SI unit = 2.76 x 10¹⁰ N⋅m⁻²
Vectors and Scalars
- A SCALAR has only magnitude (e.g., time, mass, speed, length).
- A VECTOR possesses both magnitude and direction (e.g., velocity, acceleration, force, momentum).
Vector Properties
- Equality of Vectors: Vectors are equal if they have the same magnitude and direction.
- Negative Vectors: A negative vector (B) of A (i.e., B=-A) has the same Magnitude A and opposite direction.
- Addition/Subtraction of Co-linear Vectors: This involves adding or subtracting vectors that lie along the same line.
- Addition of Perpendicular Vectors: Vectors that are at right angles to each other are added.
- Magnitude: R = √(Ax² + Ay²)
- Direction: θ = tan⁻¹(+Ay / +Ax)
- Addition of Vectors - Parallelogram Method: The magnitude and direction of a vector sum or difference can be calculated by using the Parallelogram of Vectors.
- As an example using the cosine rule and wanting to finding the angle 0:
- AC² = AD² + CD² - 2 AD⋅CD⋅cos 133°
- Then using CD² = AD² + AC² - 2 AD-CD-cos 0
- As an example using the cosine rule and wanting to finding the angle 0:
Important Considerations of Vectors
- A non-zero resultant exists only when one or both of the components are NOT zero.
- A zero resultant occurs when BOTH the components are equal to zero with system in in equilibrium.
Resolution of a Vector into Components
- Equation: C = Ax x + Ay y + Bx x + By y = (Ax + Bx)x + (Ay + By)y
- Cx = Ax + Bx
- Cy = Ay + By
Example Forces and Components
- This is based on the diagram given with two forces displayed.
- F1: X-component = + 81.92 N, Y-component = + 57.36 N
- F2: X-component = - 51.42 N, Y-component = + 61.28 N
- R: X-component = 30.50 N, Y-component = 118.64 N
Solution for Magnitude
- Using forces and components:
- R = √Rx² + Ry² = √(30.50)² + (118.64)² = 122.50 N
Solution for Direction
- θ = tan⁻¹(+Ry / +Rx)
- = tan⁻¹(+118.64 / +30.50
- = 75.58°
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