Motion and forces Revision Notes

Ruler Drop Test Method

To measure reaction time using a ruler drop test, one person holds a 30 cm ruler vertically between the thumb and forefinger of another person, positioned so the zero mark is level with the top of their thumb. The holder drops the ruler without warning, and the other person catches it as quickly as possible. The distance the ruler falls before being caught is recorded. This process is repeated several times (e.g., 5-10 times), and an average distance is calculated. This average distance is then converted into a reaction time using a formula or a conversion chart. The formula relating distance (d) to time (t) under gravity (g) is approximately t = sqrt((2d)/g), where g is about 9.8 m/s².

Computer-Based Tests and Typical Results

Computer-based reaction time tests involve a visual or auditory stimulus appearing on a screen, and the participant must react by clicking a mouse or pressing a key. These tests typically record the time elapsed between the stimulus and the response in milliseconds. They offer higher precision and can easily track multiple trials. Typical human reaction times for simple tasks fall within the range of 0.2 to 0.5 seconds (200 to 500 milliseconds). However, individual results can vary based on factors such as age, sleep deprivation, practice, distraction, and the influence of caffeine or alcohol. Shorter reaction times indicate faster processing, which can be crucial in situations like driving or sports.

Newton's Third Law Overview

Newton’s third law: When two objects interact, the force object A exerts on object B is equal in size and opposite in direction to the force object B exerts on object A; these are always the same type of force and act on different bodies. Examples include contact, gravitational or electromagnetic forces. The third law does not imply the forces act on the same object or that they balance on one object.

Collisions and Conservation of Momentum

If no significant external forces act, when two objects collide, the action-reaction forces act for the same time, producing equal and opposite impulses. The resulting change in momentum for each object is equal and opposite. Thus, the total momentum of the system remains constant before and after the collision, consistent with conservation of momentum.

Defining Scalar Quantities

A scalar quantity is entirely defined by its magnitude, which means its size or numerical value. It has no specified direction. Think of quantities you can describe with just a number and a unit, like the amount of sugar in a recipe or the temperature of a room.

Examples of Scalar Quantities

Common examples include mass (e.g., 5 kg), time (e.g., 30 seconds), distance (e.g., 10 metres), speed (e.g., 20 m/s), temperature (e.g., 25 °C), and energy (e.g., 100 Joules). For these quantities, stating a direction would be meaningless or incorrect. For instance, '5 kg upwards' doesn't make sense for mass.

Calculations with Scalars

When performing calculations with scalar quantities, you use standard arithmetic operations (addition, subtraction, multiplication, division). For example, if you have two quantities of 5 kg and 3 kg, their sum is simply 8 kg. Direction does not influence how scalar quantities are combined.

Definition of Momentum

Momentum is a measure of the 'quantity of motion' an object has. It depends on an object's mass and its velocity. The greater the mass or the greater the velocity, the greater the momentum. It is a vector quantity, so direction is important.

Momentum Equation and Units

Momentum (p) is calculated by multiplying an object's mass (m) by its velocity (v). The equation is: p = m × v. The standard unit for mass is kilograms (kg), and for velocity is metres per second (m/s). Therefore, the unit for momentum is kilogram metre per second (kg m/s).

Calculating Momentum

To calculate momentum, ensure all values are in their standard SI units: mass in kg and velocity in m/s. If units are provided differently (e.g., mass in grams or velocity in km/h), they must first be converted before applying the formula p = m × v. For example, 1 kg = 1000 g, and 1 m/s = 3.6 km/h (or 1 km/h = 1000/3600 m/s).