Forces & Motion Lecture Notes

Flashcards covering concepts, definitions, formulas, and worked calculation examples from the Forces and Motion lecture notes.

What is a force, and what three characteristics of an object can forces change?

A force is a push or pull acting on an object. Forces can change an object's size (like squeezing a stress ball), shape, and motion.

What unit is force measured in?

Newtons ($N$).

What is gravity?

Gravity is a force of attraction between objects where the atoms of one object pull on the atoms together.

What are two examples of non-contact forces and two examples of contact forces?

Two non-contact forces are gravity and magnetic force. Two contact forces are friction and normal force.

What is the key difference between mass and weight?

Mass is the amount of matter in an object and is measured in milligrams ($mg$), grams ($g$), and kilograms ($kg$). Weight is the measure of the force of gravity acting on an object's mass and is expressed in Newtons ($N$).

What formula is used to calculate weight, and what is the gravitational pull on Earth?

$Weight = mass \times gravitational\,pull\,(acceleration)$ ($W = m \times g$). On Earth, the gravitational pull is $9.8\,m/s^2$, meaning an object with a mass of $1\,kg$ has a weight of $9.8\,N$.

A stack of books has a mass of $7.4\,kg$. What is its weight on Earth?

$W = m \times g = 7.4\,kg \times 9.8\,m/s^2 = 72.52\,N$.

A dog has a weight of $215.6\,N$. What is her mass on Earth?

$Mass = \frac{Weight}{Gravity} = \frac{215.6\,N}{9.8\,m/s^2} = 22\,kg$.

An object has a mass of $59\,kg$. Given $g = 9.81\,m/s^2$, what is its weight?

$W = 59\,kg \times 9.81\,m/s^2 = 578.79\,N$.

What happens when balanced forces act on a stationary object versus a moving object?

A stationary object with balanced forces remains at rest. A moving object maintains its state of motion, continuing to move at a constant speed in a straight line.

What happens when an unbalanced force acts on a stationary object versus a moving object?

A stationary object will start to move, accelerating in the direction of the net force. A moving object's state of motion changes, causing it to accelerate, decelerate, or change direction.

What is a resultant force, and how do opposite versus same-direction forces combine?

A resultant force is the overall combined effect of forces acting on an object. When forces act in opposite directions, they subtract; when they act in the same direction, they add together.

What is air resistance, and what does it do to moving objects?

Air resistance (also known as drag) is the force exerted by air on moving objects. It opposes the motion of objects through the air.

What is terminal velocity and when does it occur?

Terminal velocity is the maximum speed attainable by an object as it falls through a fluid (like air). It occurs when the upward force of fluid resistance (drag) equals the downward force of gravity, making the net (resultant) force on the object zero.

How is speed defined and calculated?

Speed is the rate at which an object covers distance, measuring how fast an object moves regardless of direction. It is calculated as $Speed = \frac{distance}{time}$ ($S = \frac{d}{t}$), with units in $m/s$ or $km/h$.

How do you convert between $m/s$ and $km/h$?

Multiply by $3.6$ to convert from $m/s$ to $km/h$, and divide by $3.6$ to convert from $km/h$ to $m/s$.

A car covers $60\,km$ in $60$ minutes. What is the car's speed in $km/h$?

$Time = \frac{60\,mins}{60\,min/h} = 1\,hour$. $Speed = \frac{60\,km}{1\,hour} = 60\,km/h$.

Usain Bolt runs $100\,m$ in $10$ seconds. What is his speed?

$Speed = \frac{100\,m}{10\,s} = 10\,m/s$.

Florence Griffith Joyner holds the female world record for the $100\,m$ at $10.49$ seconds. What is her speed in $m/s$?

$Speed = \frac{100\,m}{10.49\,s} \approx 9.5\,m/s$.

Kimi Antonelli drives for $10\,km$ at a constant speed of $300\,km/h$. How long does the drive take in hours, minutes, and seconds?

$t = \frac{d}{v} = \frac{10\,km}{300\,km/h} = \frac{1}{30}\,hours = \frac{1}{30} \times 60\,min = 2\,mins = 2 \times 60\,seconds = 120\,seconds$.

What is the difference between instantaneous speed and constant speed?

Instantaneous speed is the speed something is going in a snapshot of time (e.g., looking at a car's speedometer) and can change from moment to moment. Constant speed is the measure of the same speed over a period of time where the speed does not speed up or slow down (e.g., a conveyor belt moving at $5\,km/h$).

What is velocity, and how does it differ from speed?

Velocity is the rate of change of displacement with time ($velocity = \frac{\text{displacement}}{\text{time}}$). While speed only measures how fast an object moves, velocity tells both how fast something moves and in what direction.

What is acceleration, and what is its formula?

Acceleration is the rate at which velocity (speed or direction) changes with time. Its formula is $a = \frac{\Delta v}{t}$ ($acceleration = \frac{\text{change in velocity}}{\text{time}}$).

How do you calculate average speed on a distance-time graph?

$Average\,speed = \frac{Total\,distance}{Total\,time}$.

What does Newton's Second Law of Motion state?

It states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass ($F = m \times a$). A greater net force causes higher acceleration, while a higher mass results in lower acceleration for the same force.

A cheetah with a mass of $22\,kg$ accelerates at $15\,m/s^2$. How much force does it require?

$Force = mass \times acceleration = 22\,kg \times 15\,m/s^2 = 330\,N$.

A car with a mass of $1{,}000\,kg$ needs $3{,}250\,N$ of force to move. What is its acceleration?

$Acceleration = \frac{Force}{Mass} = \frac{3250\,N}{1000\,kg} = 3.25\,m/s^2$.

A skateboarder with a mass of $50\,kg$ accelerates at $0.8\,m/s^2$. What force is required?

$Force = mass \times acceleration = 50\,kg \times 0.8\,m/s^2 = 40\,N$.

On a distance-time graph, what do the gradient, a flat section, and a negative gradient indicate?

The gradient equals speed (steeper graph = greater speed). A flat section means stopped (speed = 0). A negative gradient means returning to the start point.

On a speed-time or velocity-time graph, what do the gradient, a flat section, and the area under the line represent?

The gradient represents acceleration (a negative gradient represents deceleration). A flat section means constant velocity (not stopped). The area under the graph represents distance travelled.

How do you calculate distance travelled from the area under a velocity-time graph?

For a constant speed section (rectangle/square): $\text{base} \times \text{height}$. For an acceleration or deceleration section (triangle): $\frac{1}{2} \times \text{base} \times \text{height}$.

What is the formula to calculate the slope (acceleration) of a line on a speed-time graph?

$Slope = \frac{rise}{run} = \frac{Speed}{time} = \frac{y_2 - y_1}{x_2 - x_1} = acceleration$.

What do the four speed-time curves shown in this figure describe about an object's motion?

From top to bottom: 1) Constant deceleration (acceleration is at constant rate/speed decrease), 2) Deceleration decreases, 3) Deceleration increases, 4) No acceleration (constant speed).

A speed-time graph starts at $(0\,min, 0\,m/min)$ and reaches $(15\,min, 2400\,m/min)$. What is the acceleration?

$Acceleration = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2400\,m/min - 0\,m/min}{15\,min - 0\,min} = \frac{2400}{15} = 160\,m/min^2$.

A lawn mower has a mass of $36\,kg$, a forward force of $20\,N$, and a friction force of $2\,N$. What is the net horizontal force, the downward gravitational force, and the acceleration?

Net horizontal force = $20\,N - 2\,N = 18\,N$ (accelerates in direction of $20\,N$ force). Downward force of gravity = $36\,kg \times 9.8\,m/s^2 = 352.8\,N$. Acceleration = $\frac{18\,N}{36\,kg} = 0.5\,m/s^2$.

George's Porsche has a mass of $2{,}000\,kg$ and accelerates from $0$ to $100\,km/h$ in $5.55\,seconds$. What is its speed in $m/s$, its acceleration, and the required force?

$Speed = \frac{100 \times 1000\,m}{3600\,s} = 27.78\,m/s$. $Acceleration = \frac{27.78\,m/s}{5.55\,s} \approx 5.005\,m/s^2$. $Force = 2000\,kg \times 5.005\,m/s^2 = 10010.01\,N$.

How do squared unit conversions proceed from $mm^2$ to $km^2$?

$mm^2 \xrightarrow{\div 100} cm^2 \xrightarrow{\div 10000} m^2 \xrightarrow{\div 1000000} km^2$.