Vector Mechanics & Force
What is a force, and how is it classified mathematically?
A push or a pull acting on an object. It is classified as a vector quantity because it possesses both magnitude (numerical strength) and direction.
According to Newton's First Law, what is the state of an object's motion if the net external force (Fnet) equals zero?
The object is in equilibrium, meaning its velocity is completely constant (either completely at rest or moving at a constant speed in a straight line with zero acceleration).
How does friction behave relative to the vector path of an object's intended motion?
It acts parallel to the contact surface and in the exact opposite direction of the relative motion.
What is the Law of Universal Gravitation?
A law stating that every mass in the universe attracts every other mass with a force that depends directly on their masses and inversely on the square of the distance between them.
What is Newton's First Law of Motion, and what physical variable solely determines its magnitude?
The Law of Inertia (an object resists changes to its state of motion). Its magnitude is solely determined by the object's mass.
What does the length and the orientation of a force vector arrow signify on a free-body diagram?
The length of the arrow represents the force's magnitude, and the orientation/arrowhead signifies its directional path.
What is a net force (Fnet)?
The vector sum (overall total) of all individual forces acting simultaneously on a single object.
What structural physical attribute dictates the basic strength of friction between two sliding solid objects?
The nature or roughness of the material surfaces (characterized by the coefficient of friction) and the force pressing them together (Normal Force).
What is the precise rate of acceleration due to gravity ($g$) near the surface of the Earth, ignoring air resistance?
9.8m/s^2 (or roughly 32.2ft/s^2).
State the algebraic formula representing Newton's Second Law of Motion, isolated to solve for acceleration.
Acceleration (a) = Net Force (Fnet) / Mass(m) or a = F/m.
What is a Newton, and what are its base metric units?
The SI unit of force; one Newton is equal to 1kg * m/s^2 (the force required to accelerate a 1-kilogram mass at a rate of 1 meter per second squared).
A heavy block is pulled concurrently to the right with 85 N and to the left with 45 N. What is the net force acting on the system?
40 Newtons to the right (85N - 45N).
Why does it require more initial force to start sliding a heavy box from rest than to keep it sliding once it is already in motion?
Because static friction (the force holding a still object in place) is mechanically stronger than kinetic friction (the force resisting an object already sliding).
If a capsule moves farther away from Earth until its distance from the planet's center doubles, what happens to the gravitational force acting on it?
It drops to one-quarter (1/4) of its original value (due to the Inverse-Square Law: 2^2 = 4).
According to Newton's Third Law, if a tennis racket strikes a ball with a forward force of 50 N, what force does the ball exert on the racket?
An equal and opposite force of 50 Newtons backward on the racket.
What is a field force, and what are three primary examples?
A non-contact force that alters motion across a distance via a force field. Examples include gravitational, magnetic, and electric fields.
An object experiences a downward gravitational pull of 15 N, an upward normal force of 15 N, and a forward mechanical push of 12 N. What is the net force?
12 Newtons forward (the vertical forces balance out to 0 N, leaving only the horizontal push).
What is fluid friction, and what variable changes its magnitude as an object speeds up?
The resistive force exerted by gas or liquid particles (like air resistance). Its magnitude increases dramatically as the object's velocity increases.
Differentiate mass and weight in terms of their physical properties and measurement units.
Mass is the quantity of matter measured in kilograms (invariant); weight is the gravitational force acting on that mass measured in Newtons (W=mg, variable by location).
If you apply a 120 N net force to a 12 kg shopping cart, at what rate will the cart accelerate?
10 m/s^2 (since a = F/m = 120N/12kg).
What is the normal force, and how does its direction relate to the contacting surface?
A perpendicular support force exerted by a surface against an object resting on it. Its vector is always exactly 90 degrees (perpendicular) to the plane of the surface.
If an object is moving at a constant speed along a curved track, are the forces acting on it balanced or unbalanced? Explain.
Unbalanced. Even though the speed is constant, the changing direction means the velocity is changing, which requires a non-zero net force causing acceleration (centripetal force).
In terms of surface contact and forces, why does a car slide more easily on wet ice than dry concrete?
Liquid water creates a thin barrier that fills the microscopic rough ridges of the surface, drastically lowering the coefficient of friction between the tire rubber and the ground.
Explain the forces acting on a skydiver when they reach terminal velocity.
The upward force of air resistance increases until its magnitude perfectly matches the downward force of gravity, resulting in a net force of zero and a constant downward velocity.
You apply the same net force to Object A and Object B. Object B has three times the mass of Object A. Compare their accelerations.
Object B will accelerate at one-third (1/3) the rate of Object A (acceleration is inversely proportional to mass).