Topic 1 Flashcards
Motion, Force, and Energy
What are scalar quantities?
Scalar quantities have only a magnitude.
What is an example of a scalar quantity?
Mass is an example of a scalar quantity because it has magnitude without direction.
What are other examples of scalar quantities?
Energy and volume are also examples of scalar quantities.
What are vector quantities?
Vector quantities have both magnitude and direction.
What is an example of a vector quantity?
Weight is an example of a vector quantity because it is a force and therefore has both magnitude and direction.
What are other examples of vector quantities?
Acceleration and momentum are also examples of vector quantities.
What is distance?
Distance is a measure of how far an object has travelled, regardless of direction.
What does distance measure?
Distance is the total length of the path taken.
What type of quantity is distance?
Distance has a magnitude but no direction, so it is a scalar quantity.
What is displacement?
Displacement is a measure of how far it is between two points in space, including the direction.
How is displacement defined?
Displacement is the length and direction of a straight line drawn from the starting point to the finishing point.
What type of quantity is displacement?
Displacement has a magnitude and a direction, so it is a vector quantity.
What is the difference between distance and displacement?
Displacement is a vector quantity, while distance is a scalar quantity.
How does distance differ from displacement in a student’s travel to school?
The overall distance includes the total lengths of all the roads, while the overall displacement is a straight line between their home and school.
What is speed?
Speed is a measure of the distance travelled by an object per unit time, regardless of the direction.
What type of quantity is speed?
Speed has magnitude but no direction, so it is a scalar quantity.
What is velocity?
Velocity is a measure of the displacement of an object per unit time, including the direction.
What type of quantity is velocity?
Velocity has magnitude and direction, so it is a vector quantity.
What is the relationship between speed and velocity?
An object can have a constant speed but a changing velocity if the object is changing direction.
What are some common examples of scalar and vector quantities?
Scalar: distance, speed, mass, energy, volume, temperature.
Vector: displacement, velocity, weight, force, acceleration, momentum.
How should an instructor explain the difference between mass and weight?
Step 1: Scalars have only magnitude; Vectors have both magnitude and direction.
Step 2: Mass is a scalar quantity.
Step 3: Weight is a vector quantity.
How does mass change with location?
The instructor might explain that their mass will not change as their location in the Universe changes.
How does weight change with location?
The instructor might explain that their weight varies depending on their location, such as being less on the Moon than on Earth.
How are vectors represented?
Vectors are represented by an arrow.
What does the length of the arrow in a vector represent?
The length of the arrow represents the magnitude.
What does the direction of the arrow in a vector indicate?
The direction of the arrow indicates the direction.
How should the scale of arrows in vector diagrams be?
The scale of the arrows should be proportional to the relative magnitudes of the forces.
How long should an arrow for a 4 N force be compared to a 2 N force?
An arrow for a 4 N force should be twice as long as an arrow for a 2 N force.
What do vector diagrams of two forces show?
The length of the arrows are proportional to the magnitude of the forces and show the direction that forces act in.
How can vector diagrams be used?
Vector diagrams can be used to combine vectors.
What can be said about vectors at right angles to one another?
Vectors at right angles to one another can be combined into one resultant vector.
What does the resultant vector represent?
The resultant vector will have the combined effect of the two original vectors.
How are component vectors sometimes drawn?
Component vectors are sometimes drawn with a dotted line and a subscript indicating horizontal or vertical.
What does F subscript V represent?
F subscript V is the vertical component of the force F.
What does F subscript H represent?
F subscript H is the horizontal component of force F.
What does calculating vectors graphically involve?
Calculating vectors graphically means carefully producing a scale drawing with all lengths and angles correct.
What tools are needed for accurate vector calculations?
This should be done using a sharp pencil, ruler, and protractor.
What is the first step to carry out calculations with vectors on graphs?
Choose a scale which fits the page.
What is an example scale for vector diagrams?
For example, use 1 cm = 10 m or 1 cm = 1 N, so that the diagram is around 10 cm high.
What is the next step after choosing a scale?
Draw the vectors at right angles to one another.
What should be done after drawing the vectors?
Complete the rectangle.
How is the resultant vector drawn?
Draw the resultant vector diagonally from the origin.
How do you measure the length of the resultant vector?
Carefully measure the length of the resultant vector.
What should be done with the scale factor?
Use the scale factor to calculate the magnitude.
How do you measure the angle of the resultant vector?
Use the protractor to measure the angle.
Can vectors be measured or calculated graphically?
Vectors can be measured or calculated graphically using scaled vector diagrams.
What is a method for combining vectors by calculation?
In this method, a vector diagram is still essential but it does not need to be exactly to scale.
What form can the vector diagram take in calculations?
The vector diagram can take the form of a sketch, as long as the resultant side and component sides are clearly labelled.
What can be used when the magnitude of only one vector is known?
When the magnitude of only one vector is known, and the angle is known, then trigonometry can be used to find the magnitude of the missing vector.
What mnemonic helps remember trigonometric functions?
The mnemonic ‘soh-cah-toa’ can be used to remember the trigonometric functions.
When can Pythagoras’ theorem be used?
Pythagoras’ theorem can be used when the magnitudes of two of the three vectors are known.
What is the first step in the worked example of calculating resultant force?
Step 1: Draw a vector diagram.
What is the formula to calculate the magnitude of the resultant force?
F = √(60² + 100²)
F = √(13600) = 117 N
How do you calculate the direction of the resultant vector?
tan(θ) = opposite / adjacent
tan(θ) = 100 / 60; θ = tan⁻¹(100/60) = 59°
What is the final answer for the resultant force?
F = 117 N at 59° from the horizontal.
What should you do if the question specifies a calculation method?
If the question specifically asks you to use the calculation or graphical method, you must solve the problem as asked.
Which method is sometimes easier, graphical or calculation?
The graphical method sometimes feels easier than calculating, but calculating is quicker and more accurate once confident with trigonometry and Pythagoras.
