Physics Midterms

motion in 2 dimensions

aka projectile motion

• form of motion experienced by an object or particle that’s thrown near the Earth’s surface and moves along a curved path under the action of GRAVITY ONLY

• the effects of air resistance and the Earth’s rotation are neglected

2 factors that affect projectile motion

initial velocity

projection angle

• at t=0, the projectile leaves the origin at its initial velocity. if the velocity vector makes an angle w/ the horizontal, that’s the projection angle

parabola

shape of the path of a projectile in Earth’s gravity field

trajectory

path followed by a projectile motion

range

distance between the launch pt and the pt where the projectile hits the ground

Take note

initial velocity (v₀) can’t be zero here bcs a projectile needs to be launched for projectile motion

all objects are launched at a certain angle

when an object is at max height, v_f and y component (not the x-component) is ZERO

MOST IMPORTANT EXPERIMENTAL FACT

horizontal and vertical motions are completely independent of each other (hence they have separate formulas)

motion in one direction has no effect on motion in the other direction

x doesn’t affect y and vice versa

horizontal motion

motion of a ball rolling freely along a level surface

no other force affects this (not gravity bcs vertical yun)

→ or ←

horizontal motion is ALWAYS CONSTANT, this its acceleration is 0

vertical motion

motion of a freely falling object

force due to gravity

vertical component of velocity changes w/ time due to gravity

factors that affect projectile motion

initial velocity (v₀)

projectile angle (theta₀)

• gravity doesn’t count bcs that is constant and alr a given

assume when t=0 the projectile leaves the origin at v₀. If the velocity vector makes an angle theta₀ w/ the horizontal, theta₀ is the projection angle

projection angle

higher angle = less range (distance travelled horizontally) but higher trajectory (distance travelled vertically)

lower angle = more range (distance travelled horizontally) but lower trajectory (distance travelled vertically)

force

commonly imagined as a push or a pull on some object

Contact Forces

Result from physical contact between two objects

Give solidity to our physical environment and everything in it

• normal, friction, and tension forces

Non-Contact Forces

Don’t involve direct physical contact

Newton used “action at a distance” concept of his law of gravity

• gravity, magnetic, electrostatic, and nuclear

Isaac Newton

1643-1727

proposed the Laws of Motion both to correct previous misconceptions about motion and to offer a systematic method of calculating an object’s motion due to forces exerted on it

First Law of Motion

Law of Inertia

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force

Inertia

Mass

Inertia

tendency of an object to continue in its original state of motion

Mass

measure of the object’s resistance to changes in its motion due to a force

greater mass = less acceleration under the action of a given applied force

Second Law of Motion

Law of Acceleration

The acceleration of an object (produced by a net force) is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

The constant of proportionality is equal to 1 (ex: mass doubles = acceleration halves)

gravitational force

gravitational force

mutual force of attraction between any two objects in the Universe

weight - magnitude of the gravitational force acting on an object of mass

Third Law of Motion

Law of Interaction

For every action, there is an equal and opposite reaction

there is a pair of forces acting on the two interacting objects

size of the forces on the first object = size of the force on the second object

direction of the force on the first object is opposite to the direction of the force on the second object

Forces always come in pairs - equal and opposite action-reaction force pairs

normal force

elastic force arising from the cohesion of matter

electromagnetic in origin

normal (a technical term from mathematics) means perpendicular in this context (bcs its always perpendicular to the surface)

balances the gravitational force acting on the objects

NORMAL FORCE ON A LEVEL SURFACE

normal force is equal to the weight of the object

NORMAL FORCE ON A SLOPE

In tilted coordinates, the gravity force splits into two components, one perpendicular to the slope and the other parallel to it

weight = hypotenuse

NORMAL FORCE ON A LEVEL SURFACE UNDER ACCELERATION

the magnitude of the normal force vector must equal the sum of the magnitudes of the gravitational force and the inertial quantity, ma

Friction Force

Friction is a contact force that derives from the microscopic interactions between a body and its environment

almost everywhere

• kinetic friction force

• static friction force

can never be a negative value (greater than or = to zero)

kinetic friction force

friction that arises during motion

static friction force

magnitude of the static friction force 𝑓𝑓𝑠𝑠 acting on an object at rest satisfies the inequality

• 0 ≤ 𝑓𝑠 ≤ 𝑓𝑠_max= µ_𝑠𝑛

Actual static friction force is always less than or equal to the maximum

max static force is when the object is ABOUT TO move and strong force is applied to it

kinetic vs static friction force

no relative motion → magnitude of f_s is less than or equal to f_smax

relative motion → magnitude of f_k

Tension Force

exerted by attaching a string or cable to an object and pulling it

acts along the direction of the cable and exerts a force both on object and on the person exerting force on the cable

Types of Forces

Applied Force- applied to an object by a person or another object (F_A)

Gravitational Force (W) - earth or other massively large object attracts another object towards itself. All objects upon earth experience a force of gravity that is directed downward towards the center of the earth. Caution: do not confuse weight with mass

Normal Force (n) - support force exerted upon an object that is in contact with another stable object. The force is always perpendicular

Friction Force - exerted by a surface as an object moves across it or makes an effort to move across it. It often opposes the motion of an object

Tension Force (T) - transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. It is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire

free-body diagram

most important step in solving a problem by means of Newton’s second law

Include only those forces that act directly on the object of interest