Physics Class Test 1

Forces and Equilibrium

• When two forces act in the same direction, and a third force opposes them, equilibrium is maintained if the vector sum of the first two forces equals the magnitude and opposite direction of the third force.
• In a Newton balance experiment, forces must be balanced for equilibrium, indicating a stable system where the vector sum of forces equals zero.

Motion and Velocity

• Velocity is defined as the rate of change of displacement, calculated as displacement divided by time, and is a vector quantity expressed in meters per second (m/s).
• The slope of a displacement-time graph indicates the velocity of an object.
• In a velocity-time graph, the area under the curve represents the total distance traveled during a specified time interval.
• Speed is the distance covered per unit time, distinguishing it from the vector quantity of velocity which includes direction.

Displacement vs. Distance

• Distance measures the total path length traveled without considering direction; displacement is the shortest straight-line distance between two points, incorporating direction.
• Characteristics of vector quantities include both magnitude and direction, while scalar quantities have only magnitude.

Vector Addition and Calculation

• The resultant vector is obtained through vector addition, which can be visualized using graphical methods like the parallelogram law.
• Resultant vectors in opposite directions are found by subtracting the smaller vector from the larger one.
• 'Tip to tail' method arranges vectors for visual addition, allowing for an easy determination of the resultant vector's direction.

Experiment Procedures and Materials

• Oiling trolley wheels reduces friction, resulting in smoother motion and increased measurement accuracy.
• Vernier callipers and micrometres are tools used for measuring small distances accurately.

Acceleration and Motion Analysis

• The calculation for the distance an athlete travels before jumping in pole vaulting is derived from the area under the velocity-time graph.
• Acceleration can be calculated using the formula ( a = \frac{v - u}{t} ), demonstrating the rate at which velocity changes over time.
• Displacement during uniform acceleration is calculated using the formula ( s = ut + \frac{1}{2}at^2 ).

Ticker Tape and Experimental Accuracy

• Evenly spaced dots on ticker tape indicate constant velocity, helping reduce measurement errors.
• Necessary conditions for constant acceleration in experiments include appropriate runway slope, absence of external forces, and minimized friction.

Trigonometry in Vector Resolution

• Resolution of a vector involves breaking it into horizontal and vertical components using trigonometric functions: ( \text{adjacent} = \text{hypotenuse} \cdot \cos(\theta) ) and ( \text{opposite} = \text{hypotenuse} \cdot \sin(\theta) ).
• SOHCAHTOA is a mnemonic for remembering how to calculate sine, cosine, and tangent in right triangles, essential for resolving vectors.

Relationship Between Motion Variables

• The relationship between initial (( u )) and final velocity (( v )) under constant acceleration is expressed as ( v = u + at ).
• In methods of vector addition, Pythagoras' theorem aids in calculating the resultant when vectors are orthogonal, leading to accurate vector magnitudes.

This quiz covers key concepts in physics, such as force equilibrium and velocity in linear motion. It's designed to test your understanding of fundamental principles and their mathematical representations. Prepare to apply your knowledge of Newton's laws and motion concepts.