Base & Derived Quantities Quiz

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Questions and Answers

How do you determine the resultant of two vectors that are not at a right angle?

To find the resultant, draw the two vectors, complete a parallelogram, and measure the diagonal from the origin to the opposite corner.

What is the relationship between mass and weight, and how is weight calculated?

Mass is the amount of matter in an object, while weight is the force exerted on that mass by gravity, calculated using the formula $w = mg$.

If an astronaut has a mass of 70 kilograms on the moon, what is her weight given the moon's gravitational field strength of 1.6 N/kg?

Her weight on the moon is $112$ newtons, calculated as $70 imes 1.6$.

Define the center of gravity and its relevance in the stability of an object.

The center of gravity is the point where the weight of an object acts and affects its balance; a lower center of gravity with a wide base indicates higher stability. Signup and view all the answers

What characterizes unstable equilibrium in terms of center of gravity and base width?

Unstable equilibrium occurs when the center of gravity is high and the base is narrow, making the object prone to tipping over. Signup and view all the answers

What defines a fundamental quantity in physics?

A fundamental quantity is one that cannot be expressed as a combination of other quantities. Signup and view all the answers

Provide an example of a derived quantity and explain its components.

Speed is a derived quantity, which is calculated as distance per unit time. Signup and view all the answers

List the five base quantities that must be known at this level and their units.

Length (meters), mass (kilograms), time (seconds), current (amperes), and temperature (kelvin). Signup and view all the answers

What does the prefix 'milli' represent in the metric system?

Milli represents a factor of $10^{-3}$, meaning one thousandth. Signup and view all the answers

How would you convert 5600 milliseconds to seconds?

5600 milliseconds is equal to 5.6 seconds, calculated by dividing by 1000. Signup and view all the answers

What distinguishes a scalar quantity from a vector quantity?

A scalar has magnitude only, while a vector has both magnitude and direction. Signup and view all the answers

What is the resultant of two vectors in the same direction, each measuring 5 newtons?

The resultant is 10 newtons, obtained by summing the two vectors. Signup and view all the answers

How is the net force calculated when two forces are acting in opposite directions?

The net force is the difference between the two forces. Signup and view all the answers

Explain how to resolve two perpendicular vectors using Pythagoras' theorem.

Use the equation $a^2 + b^2 = c^2$ where a and b are the magnitudes of the vectors. Signup and view all the answers

If one vector measures 3 units and another measures 4 units, what is the magnitude of the resultant?

The magnitude of the resultant is 5 units, calculated as $c = \sqrt{9 + 16}$. Signup and view all the answers

Study Notes

Base and Derived Quantities

A base quantity cannot be defined in terms of other quantities, examples are length, time, and mass.
A derived quantity is defined in terms of base quantities, example is speed, which is a combination of distance and time.
Five base quantities you need to know: length (meter), mass (kilogram), time (second), current (ampere), and temperature (kelvin).
Derived quantities with their units:
- Area (meter squared)
- Volume (meter cubed)
- Pressure (pascals, newton per meter squared)
- Force (newtons, kilogram meter per second squared)
- Charge (coulomb, ampere second)

Prefixes

Five prefixes you need to know:
- Micro (µ, 10^-6, divide by a million)
- Milli (m, 10^-3, divide by a thousand)
- Centi (c, 10^-2, divide by a hundred)
- Kilo (k, 10^3, multiply by a thousand)
- Mega (M, 10^6, multiply by a million)

Vectors

Scalar quantities have magnitude but no direction (examples: distance, speed, area, volume, density).
Vector quantities have both magnitude and direction (examples: displacement, velocity, acceleration, force, momentum).
Vectors in the same direction: add magnitudes for the resultant.
Vectors in opposite directions: subtract magnitudes for the resultant.
Vectors at right angles: use the Pythagorean theorem to find the resultant.
Vectors not at right angles: complete a parallelogram and use the diagonal as the resultant.

Mass vs. Weight

Mass is a measure of the amount of matter in an object (measured in kg).
Weight is the force exerted on an object by gravity (measured in newtons).
Weight can be calculated using the formula: w = mg (where w = weight, m = mass, and g = acceleration due to gravity).

Center of Gravity

Center of gravity is the point where an object's weight acts.
Stable equilibrium: Center of gravity is low and the base is wide.
Unstable equilibrium: Center of gravity is high and the base is narrow.
Neutral equilibrium: Center of gravity doesn't change when the object is moved.

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Description

Test your knowledge on base and derived quantities, including their definitions and units. This quiz also covers important prefixes and the distinction between scalars and vectors. Perfect for students learning the fundamentals of physics.