MYP 4 Final Exam Physics: Forces, Motion, and Momentum Review

Preparation Guidelines and Required Calculation Methodology

The MYP 4 Physics curriculum focuses on key principles of mechanics, including forces, resultant force, mass, weight, Newton’s Second Law, and momentum. To ensure success in examinations, students must adhere to a rigorous 6-step method for all free-response calculation questions. This method includes: 1. State known quantities; 2. State the unknown quantity; 3. State the correct formula; 4. Substitute the values into the formula; 5. Complete the calculation; and 6. State the final answer with the appropriate units. General exam advice suggests that students should convert units to their standard forms before beginning a calculation, underline exactly what the question asks for, choose the correct formula based on known and unknown variables, and always verify that the final answer includes the correct unit (e.g., $N$ for force, $kg$ for mass, or $m/s^2$ for acceleration).

Types of Forces and Resultant Force

Forces are categorized into contact forces and non-contact forces. Contact forces require physical interaction between surfaces or objects and include friction, drag (air resistance), upthrust, tension, and reaction forces. Non-contact forces act at a distance and include gravity (weight) and magnetic forces. Force is measured in Newtons ($N$). The term resultant force refers to the total effect of all forces acting together on an object. The formula for finding the resultant force is the sum of forces in one direction minus the sum of forces in the opposite direction. For example, if a box is pulled to the right with a force of $14\,N$ and to the left with a force of $6\,N$, the resultant force is calculated as $14 - 6 = 8\,N$ to the right. If the forces on an object are equal and opposite, such as a tug-of-war where both sides pull with $250\,N$, the resultant force is $0\,N$.

Balanced forces occur when the resultant force on an object is exactly $0$. When forces are balanced, an object will either stay at rest or continue moving at a constant velocity without changing speed or direction. For instance, if the drag force equals the driving force on a moving car, the car will move at a constant speed. Conversely, if the resultant force is not zero, the forces are considered unbalanced, and the object will accelerate in the direction of the net force. Terminal velocity is a specific case where the weight of a falling object is balanced by air resistance, resulting in a constant falling speed. For a book resting on a table, the weight acting downward is balanced by the upward reaction force from the table.

Mass, Weight, and Gravitational Field Strength

Mass and weight are distinct physical quantities often confused in daily language. Mass is defined as the amount of matter in an object and is measured in kilograms ($kg$). It remains constant regardless of the object's location in the universe. Weight is the force of gravity acting on a mass and is measured in Newtons ($N$). Weight depends on the gravitational field strength ($g$) of the location. The formula linking these is $W = mg$, where $W$ is weight, $m$ is mass, and $g$ is the gravitational field strength. On Earth, $g$ is typically taken as $9.8\,N/kg$ or simplified to $10\,N/kg$ in school physics. To find mass from weight, the formula is rearranged to $m = \frac{W}{g}$.

Because weight depends on gravity, it changes based on location. An astronaut with a mass of $80\,kg$ will have the same mass on the Moon, but their weight will decrease significantly because $g$ on the Moon is only $1.6\,N/kg$, resulting in a weight of $128\,N$. In contrast, on Earth with $g = 9.8\,N/kg$, the same astronaut weighs $784\,N$. This explains why humans can lift heavier objects on the Moon. In deep space where gravity is very small, mass remains unchanged, but weight may become nearly zero. Specific examples of weight calculations include a $0.25\,kg$ apple on Earth ($W = 0.25 \times 10 = 2.5\,N$) and a $1500\,kg$ car on a planet with $g = 3.7\,N/kg$ ($W = 1500 \times 3.7 = 5550\,N$).

Newton’s Second Law and Acceleration

Newton’s Second Law of Motion describes the relationship between resultant force, mass, and acceleration. It is expressed by the formula $F = ma$, where $F$ is the resultant force in Newtons ($N$), $m$ is the mass in kilograms ($kg$), and $a$ is the acceleration in metres per second squared ($m/s^2$). To find acceleration, the formula is rearranged to $a = \frac{F}{m}$, and to find mass, it is rearranged to $m = \frac{F}{a}$. This law implies that if the resultant force increases and mass stays constant, acceleration will increase. If the mass increases while the force remains constant, acceleration will decrease.

Inertia is the property of mass that makes it resistant to changes in motion; therefore, a larger mass is harder to accelerate. When applying $F = ma$, the force ($F$) used must always be the resultant (net) force, not just any single force acting on the object. If a car accelerates forwards, the resultant force must act in the forward direction. A resultant force of zero means the acceleration is also zero ($0\,m/s^2$). For practical calculations, a $1200\,kg$ car accelerating at $2.5\,m/s^2$ requires a resultant force of $1200 \times 2.5 = 3000\,N$. Similarly, a $150\,N$ force producing an acceleration of $6\,m/s^2$ acts on a mass of $25\,kg$ ($m = \frac{150}{6}$). Students should ensure that the mass is in kilograms and the force is the net result of all vectors before substituting values.

Momentum and Vector Principles

Momentum is a vector quantity that represents the product of an object's mass and its velocity. It is calculated using the formula $p = mv$, where $p$ is momentum measured in kilogram metres per second ($kg\,m/s$), $m$ is mass in $kg$, and $v$ is velocity in $m/s$. As a vector, momentum has both magnitude and direction, meaning the direction of motion (e.g., North, East, West) must be included in the final answer. If an object is stationary, its velocity is $0$, and therefore its momentum is also zero. Momentum increases with both higher mass and higher velocity; thus, a slow-moving truck can have more momentum than a fast-moving bicycle because its significantly larger mass compensates for the lower speed.

The Principle of Conservation of Momentum states that in a closed system, the total momentum before an interaction is equal to the total momentum after the interaction. Practical calculations include finding the momentum of a $5\,kg$ object moving East at $4\,m/s$, which results in $20\,kg\,m/s$ East. If the velocity is required, the formula can be rearranged to $v = \frac{p}{m}$. For example, a $2000\,kg$ van with a momentum of $30000\,kg\,m/s$ has a speed of $15\,m/s$. When comparing two identical balls moving with equal speed but in opposite directions, they have the same magnitude of momentum but their momenta are different because the direction vectors are opposite.