Forces, Motion, And Models

A car coasts after you stop pressing the gas pedal. Another car brakes hard and comes to rest. A third car turns a corner without changing speed. Physics treats each as the same kind of question. What causes the velocity of an object to change.

Motion means change of position. The key quantity is velocity $v$, which is how fast and in what direction position changes. Its SI unit is metres per second $(\text{m/s})$. Velocity can change in three ways. It can grow in size, shrink in size, or change direction.

A change in velocity is acceleration $a$. Acceleration tells you how quickly velocity changes per second, and it points in the direction the velocity is being pushed. Its SI unit is metres per second squared $(\text{m/s}^2)$. When you brake in a straight line, the velocity points forward while the acceleration points backward. When you turn at steady speed, the speed stays the same but the velocity changes direction, so there is still an acceleration pointing toward the inside of the turn.

Use the annotated situation to connect the arrows to a real braking event and to separate forces from the resulting motion.

A force is not the same thing as motion. Forces are proposed causes. Motion is the outcome you can measure.

Forces as pushes and pulls

A force is an interaction that can change an object’s velocity or deform it. Force is a vector, so it has both a size and a direction. The standard symbol is $F$. The SI unit is the newton $(\text{N})$.

When you describe a force in physics, you must say three things. You must name the agent applying it, the object receiving it, and the direction you choose as positive. For example, a road can push upward on a car, and brakes can push backward on the car through friction at the tyres.

Forces you will meet early in this course include these.

• Weight acts on a mass because of gravity and points toward the centre of the planet.
• A normal force is a contact push perpendicular to a surface.
• Friction is a contact force parallel to a surface that opposes relative sliding or the tendency to slide.
• Tension is a pulling force transmitted by a taut rope or cable.

Common mistake: treating a force as something an object has, like a stored ingredient. A force is something that happens between objects. No interaction, no force.

Mass and weight are different quantities

Mass $m$ measures how much inertia an object has, meaning how strongly it resists changes in velocity. Its SI unit is the kilogram $(\text{kg})$. A shopping cart with more mass is harder to speed up, slow down, or turn because changing its velocity requires more interaction.

Weight $W$ is a force. It is the gravitational pull on an object, and it points downward near Earth’s surface. Its SI unit is the newton $(\text{N})$. Weight depends on the local gravitational field strength $g$, which near Earth is about $9.8\ \text{m/s}^2$.

The physical situation is an object near a planet where gravity is approximately uniform over the object’s size. The model assumptions are that the object is small compared with the planet, and $g$ is roughly constant in the region of motion. Under those conditions, weight relates to mass by

$$W = mg$$

Here $W$ is weight in newtons, $m$ is mass in kilograms, and $g$ is gravitational field strength in metres per second squared. Limiting case check. If $m=0$, then $W=0$, which matches the idea that no mass means nothing for gravity to pull on.

Compare Earth and Moon scale readings to separate what changes, the gravitational force, from what stays the same, the object’s inertia.