Physics CH1
Vectors and Scalars
*VECTORS* - physical quantities that have both magnitude & direction - displacement, velocity, acceleration, and force, among others. *SCALARS* - quantities w/out direction - the magnitude of vectors, like speed, or may be dimensionless, like coefficients of friction. Vector *ADDITION* may be accomplished using the tip-to-tail method or by breaking a vector into its components and using the Pythagorean theorem. Vector *SUBTRACTION* is accomplished by changing the direction of the subtracted vector and then following the procedures for vector addition. *MULTIPLYING* a vector by a scalar changes the magnitude and may reverse the direction. Multiplying *TWO* vectors using the *dot product* results in a scalar quantity. The dot product is the product of the vectors' magnitudes and the cosine of the angle between them. Multiplying *TWO* vectors using the *cross product* results in a vector quantity. The cross product is the product of the vectors' magnitudes and the sine of the angle between them. The right-hand rule is used to determine the resultant vector's direction.
Inclined Planes Forces
-When the parallel component of gravity is stronger than the force of friction, the object slides down the plane. -You can remember mgSin(angle) because the mass Slides down the incline. mgSin()=the net force down any inclined plane due to gravity and the normal force -mg cosS is always the normal force
Velocity and Acceleration Relationship
1.) Any change in velocity is acceleration, whether it is a change in magnitude, direction, or both. Thus a particle must accelerate in order to change the direction of its motion. An object traveling at 10 m/s north one moment and 10 m/s east the next moment has accelerated, even though its speed has not changed. A particle moving at constant velocity has no acceleration; that is, an acceleration equal to zero. 2.)velocity and acceleration do NOT have to be in the same direction. A particle can be moving to the left while accelerating to the right, or moving up while accelerating down. If velocity and acceleration are in opposite directions, the object is slowing down. For instance, a ball thrown upwards is accelerating downwards due to the force of gravity even though it is moving upwards. This is why the ball slows down and eventually starts to fall. The ball is even accelerating the moment it reaches its maximum height, where its velocity is zero, because it is changing direction to start moving downwards.
Pythagorean Triangles
3-4-5 5-12-13
Projectile Motion
Acceleration in the vertical direction is constant and equal to gravitational acceleration, 10 m/ s2. There is no acceleration in the horizontal direction. In the absence of air resistance, horizontal velocity remains constant throughout the object's flight, since acceleration is required for any change in motion. In projectile motion, the component with acceleration - the vertical component - determines the time for both con1ponents. Without the force of gravity pulling the projectile towards the earth, the projectile would travel indefinitely in the horizontal direction.
Hooke's Law
Compressing or stretching an object creates another type of force, which follows Hooke's law. Solids that have been deformed tend to 'remember' their shape and re-form to it. Hooke's law describes the force that most objects apply against a deforming force. If Hooke's law comes up on the MCAT®, it will probably be in a problem concerning springs. 'k' is often referred to as the 'spring constant.' The negative sign in the formula can usually be ignored. force F is the tension in the spring and x is the change from the spring's position at rest. Rearranging Hooke's Law shows that the spring has a spring constant k = mg/x. The object's force is directly proportional to the amount of deformation or, more precisely, the change in position (x). k is a constant unique to a given object negative sign indicates that the force is in the opposite direction of the displacement Yield Point- All solids violate Hooke's law at some limit of displacement, unique to each object. The point of violation is called the yield point. When an object is deformed beyond its yield point, it loses the ability to regain its original shape. At some greater displacement, the object will reach the fracture poin.t and break.
Displacement and Velocity
Displacement is the vector representation of a change in position. It is path independent and is equivalent to the straight line distance between the start and end locations. Distance is a scalar quantity that reflects the path traveled. Velocity is the vector representation of the change in displacement with respect to time. Average velocity is the total displacement divided by the total time. Average speed is the total distance traveled divided by the total time. Instantaneous velocity is limit of the change in displacement over time as the change in time approaches zero. Instantaneous speed is the magnitude of the instantaneous velocity vector.
Newton's 2nd Law
F=ma equation shows that for a given force, the smaller the mass experiencing the force, the greater the acceleration
If the newton is the product of kilograms and meters/second^2, what units comprise the pound?
Force will obey the same relationship with mass and acceleration, regardless of the unit system. Force is always the product of mass and acceleration, so one pound (lb) must be equal to one slug.ft/s^2
gravitational force
G = gravitational constant G = 6.67E-11 N.m^2/kg^2 m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass magnitude of the gravitational force is inversely related to the square of the distance (that is, if r is halved, then Fg will quadruple) magnitude of the gravitational force is also directly related to the masses of the objects (that is, if m1 is tripled, then Fg will triple)
Law of Universal Gravitation
Gravitational force is the attractive force that every mass in the universe exerts on every other mass in the universe. Each mass pulls on the other; not only does the Earth pull on a person, but a person pulls on the Earth. The magnitude of gravitational force is directly proportional to both of the masses, m1 and m2 , and inversely proportional to the square of the distance r between their centers of mass. Note that r represents the distance from the center of one mass to the center of the other, not the distance between their surfaces. G is equal to 6.67 x 10- 11 m3 kg-1 s-2
What is the relationship between instantaneous velocity and instantaneous speed? Between average velocity and average speed?
Instantaneous speed is the magnitude of the instantaneous velocity vector. Average speed and average velocity may be unrelated because speed does not depend on displacement, but is rather the total distance traveled divided by time.
Newton's 1st Law
Law of Inertia = an object in a state of rest or in a state of motion will tend to remain in that state unless it is acted upon by a net force. Any change in motion requires acceleration, and where there is acceleration, there must be net force.
Units *Derived* Units:
SI *BASE* Units: Length-meter-*m* Mass (not weight)-kilogram-*kg* Time-second-*s* Current-ampère (coulomb/second)-*A* Amt of Substance-mole-*mol* Temperature-kelvin-*K* Luminous Intensity-candela-*cd* *Derived* Units: as name implies-> created by associating base units with each other. Ex: the Newton—a unit of force—is derived from kilograms, meters, and seconds: 1N = 1kg.m/s^2
Sin & Cos ∠ values
Sin ∠ Cos∠ 0° 0 1 30° .5 .9 45° .7 .7 60° .9 .5 90° 1 0
Graphs of linear motion: v vs. t
Slope at any point is the instantaneous acceleration at that time. An upward slope indicates positive acceleration, while a downward slope indicates negative acceleration. Negative acceleration is not necessarily slowing down. It is simply acceleration in what has been designated the reverse direction. Negative acceleration means slowing down if the velocity is in the positive direction, but speeding up if the velocity is in the negative direction. A straight line indicates constant slope and thus constant acceleration. A curved line has a changing slope, indicating a changing acceleration. The area beneath the curve can represent distance or displacement. If we label all of the area between the curve and zero velocity as positive, the total area represents distance. If we label the area below zero velocity as negative, the total area represents displacement. The linear motion equations can be used on any of the straight-line sections of a velocity vs. time graph because acceleration for those sections is constant.
True or False: Total distance traveled can never be less than the total displacement.
True. Displacement considers the most direct route between two points. Distance will always be equal or larger in magnitude than displacement.
Provide a definition for displacement or velocity in terms of the other variable.
Velocity is the rate of the change of the displacement of an object. Displacement is a function of velocity acting over a period of time.
Newton's 3rd Law
for every action, there exists an equal and opposite reaction. When object A applies a force to object B, object A experiences a force that is equal in magnitude but opposite in direction.
Friction
force that opposes *relative* motion caused by attractive molecular forces between surfaces that are in contact *unlikely to show up on the MCA"f®, but if it does, be sure to include it in free body diagrams.* Friction does NOT oppose motion; it opposes relative motion. Friction makes a car's movement possible by opposing relative motion between the tires and the road. Without friction, the tires would slide easily on the surface of the road, and the car would not move. Draw frictional force vectors to point in the direction that will prevent surfaces from sliding past each other. For instance, the frictional force on the front tires of an accelerating front wheel-drive car points in the direction of motion of the car because the force prevents the tires from sliding backwards on the road.
Type of Friction: Drag/Air Resistance
results from an object's collisions with air molecules usually considered to be negligible in problems involving projectile motion shape, surface area, and velocity of a projectile change the force of the air resistance that it experiences Air resistance is unlikely to appear on the MCAT® but if it does, you'll be ready. Air resistance brings together many physics topics, including fluids, collisions, projectiles, force, and acceleration. Remember, the force of air resistance depends on the number of collisions between an object and air molecules per unit time. The direction of air resistance is opposite to the direction of relative motion. More massive objects are less affected by air resistance than are less massive objects. When a golfball and a ping pong ball are thrown from the same height, the more massive golfball will be slowed down less than the ping pong ball.
Graphs of linear motion: d vs. t
slope at any point is the instantaneous velocity at that particular time. An upward slope indicates positive velocity, while a downward slope indicates negative velocity (i .e. velocity in the reverse direction). A straight line has a constant slope, indicating constant velocity. A straight horizontal line has a slope of zero, indicating that the particle is not moving. A curved line has a changing slope, indicating a changing velocity and thus acceleration. (Recall that acceleration is the rate of change in velocity). The area beneath the curve has no meaning in a displacement vs. time graph.
maximum height of projectile motion
v = √2gh g is positive 10m/s^2 When using it to find the maximum height of a projectile launched from the ground, v represents the initial vertical velocity, or Vosin(angle). This equation can also be used to find the final velocity v of a projectile that is dropped straight down from a height h. When the object begins to fall, the vertical velocity is zero, and is changing at a rate of g in the downward direction. This means that V0 is zero, and choosing the downward direction as positive gives g a positive value. Solving for v or h results in a positive value as well. Use the symmetry of projectile motion to help you solve problems. If we use only the second half of the trip, Example: vertical Vo is always equal to zero, making calculations easier
Uniformly Accelerated Motion and linear Motion
velocity - of a particle experiencing uniform acceleration changes at a constant rate. Recall that acceleration is a vector. Both the direction and magnitude of acceleration must remain constant for the acceleration to be considered constant.
Order the following units from smallest to largest: centimeter, angstrom, inch, mile, foot. __________<___________<___________<____________<____________
ångström < centimeter < inch < foot < mile
