Physics

Datum

"ground" or the zero potential energy position

2 most common conservative forces

1. Electrostatic 2. Gravitational (Elastic can also be included in this but sometimes they will not ignore the frictional forces that will cause a dissipation of energy so they will be nonconservative in that case)

Right hand rule for direction of cross product resultant vector C = A x B

1. Point thumb in direction of Vector A 2. Extend fingers in direction of B 3. Your palm establishes plane between two vectors. The direction your palm points is direction of C

elastic potential energy equation

1/2kx^2 x = magnitude of displacement from equilibrium

Josh, who has a mass of 80 kg, and Sarah, who has a mass of 50 kg, jump off a 20 m tall building and land on a fire net. The net compresses, and they bounce back up at the same time. Which of the following statements is NOT true? A. Sarah will bounce higher than Josh. B. For Josh, the change in speed from the start of the jump to contacting the net is 20m/s C. Josh will experience a greater force upon impact than Sarah. D. The energy in this event is converted from potential to kinetic to elastic to kinetic.

A Sarah will not bounce higher than Josh. (you start with a potential energy and will end with that same energy, so that same height if all mechanical energy is conserved). Assuming that mechanical energy is conserved, Sarah and Josh will start with a given amount of potential energy, which is converted into kinetic energy, then elastic potential energy, then kinetic energy again with no loss of energy from the system, eliminating choice (D).

Cross product

A x B = |A| |B| sin(θ) Then, we use right-hand rule to determine direction

Dot product

A · B = |A| |B| cos(θ)

When multiplying vector to generate a vector we use ____ product

Cross product

In a cross product, what is the angle of the resultant vector?

Always perpendicular to the plane created by the 2 vectors

Instantaneous velocity vector in uniform circular motion is

Always tangent to the circular path

base unit vs derived unit

Base = standard unit (i.e. kg) Derived= formed from associating base units (i.e 1 N = 1 kg*m/s^2)

Centripetal force generates

Centripetal acceleration

What keeps object in a circular path from breaking out and moving in a linear direction along the tangent?

Centripetal force pointing inward

First law of thermodynamics

Conservation of mechanical energy - energy is never created nor destroyed, merely transferred from one form to another

What is acceleration if no net force on object?

Constant velocity (not experiencing acceleration because F=0)

A consumer is comparing two new cars. Car A exerts 250 horsepower, while Car B exerts 300 horsepower. The consumer is most concerned about the peak velocity that the car can reach. Which of the following statements would best inform the consumer's decision? (Note: 1 horsepower = 745.7 W) A. Car A and Car B both have unlimited velocities, ignoring nonconservative forces. B. Car A will reach its peak velocity more quickly than Car B. C. Car A will dissipate less energy to the surroundings than Car B. D. Car A will have a lower peak velocity than Car B.

Correct Answer: A Explanation: Horsepower is a unit of power, as evidenced by the name and the conversion factor given in the question stem. Power is a rate of energy expenditure over time. Given unlimited time, both cars are capable of unlimited increases in (kinetic) energy, meaning that they have unlimited maximum velocities. The fact that Car B has a higher power rating means that it will reach any given velocity faster than Car A, eliminating choice (B). There is not enough information to make any judgments on the efficiency of the cars, eliminating choice (C). While it may take longer for Car A to reach a given velocity, both cars have unlimited maximum velocities according to the information given in the stem, eliminating choice (D).

During uniform circular motion, which of the following relationships is necessarily true? A. No work is done. B. The centripetal force does work. C. The velocity does work. D. Potential energy depends on position of the object around the circle.

Correct Answer: A Explanation: In uniform circular motion, the displacement vector and force vector are always perpendicular; therefore, no work is done. Potential energy is constant for an object in uniform circular motion, whether it is the gravitational potential energy of a satellite orbiting the Earth or the electrical potential energy of an electron orbiting the nucleus of an atom. In both cases, potential energy does not change and does not depend on the position of the object around the circle, eliminating choice (D).

A parachutist jumps from a plane. Beginning at the point when she reaches terminal velocity, which of the following is/are true? I. The jumper is in translational equilibrium. II. The jumper is not being acted upon by any forces. III. There is an equal amount of work being done by gravity and air resistance. A. I only B. I and III only C. II and III only D. I, II, and III

Correct Answer: B Explanation: At terminal velocity, the force of gravity and force of air resistance are equal in magnitude, leading to translational equilibrium. Thus, statement I is true. If these forces have the same magnitude and act over the same displacement, then the work performed is the same as well, making statement III true. Even though the net force is equal to zero, there are still forces acting on the parachutist, making statement II false.

5 m3 of a gas are brought from an initial pressure of 1 kPa to a pressure of 3 kPa through an isochoric process. During this process, the work performed by the gas is: A. -10 kJ B. -10 J C. 0 J D. +10 kJ

Correct Answer: C Explanation: An isochoric process, by definition, is one in which the gas system undergoes no change in volume. If the gas neither expands nor is compressed, then no work is performed. Remember that work in a thermodynamic system is the area under a P-V curve; if the change in volume is 0, then the area under the curve is also 0.

A rock (m = 2 kg) is shot up vertically at the same time that a ball (m = 0.5 kg) is projected horizontally. If both start from the same height: A. the rock and ball will reach the ground at the same time. B. the rock will reach the ground first. C. the ball will reach the ground first. D. the rock and ball will collide in the air before reaching the ground.

Correct Answer: C Explanation: We only need to analyze the motion in the vertical dimension to answer this question. If both the rock and ball began with no vertical velocity, they would reach the ground at the same time. However, because the rock begins with an upward component of velocity, it will take time to reach a maximum height before falling back toward the ground. Functionally, the rock's free fall thus starts higher and later than the ball's (free fall starts at the top of the parabola where the ball's free fall starts at the lower level). The rock will necessarily hit the ground after the ball.

work done by nonconservative forces only equation

Exactly equal to amount of energy lost from the system -W means energy is being dissipated from the system

Centripetal force formula

Fc = mv^2/r

Newton's second law: equation and explain

Fnet = ma An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector

Newton's first law: equation and explain

Fnet = ma = 0 Law of inertia: A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it. This law is a special case of his second law

Magnitude of gravitational force equation

G = 6.67E-11 Nm^2/kg^2 This equation is commonly tested in the context of proportionalities

Higher force normal means

Higher friction

DIstance

How far an object moves - considers the pathway taken and is a scalar quantity

Simple machines

Inclined Plane Lever Pulley Wedge Screw Wheel and Axle

kinetic energy formula

KE=1/2mv^2 v= speed NOT velocity; object has same kinetic energy regardless of direction of velocity vector

What are the magnitudes and directions fo the resultant vectors from the following cross products: C = AxB and D = BxA A: x = -3N; Y=0 B: x=0; Y=+4m

Magnitude for both: A x B = |A| |B| sin(θ) = 3 x 4 x sin90 = 12 Nm Direction for AxB = 12 Nm into the page Direction for BxA = 12 Nm out of the page ORDER MATTERS FOR CROSS PRODUCTS!

Is instantaneous velocity = instantaneous speed?

Magnitude is equal

Mechanical advantage meaning

Measure of the increase in force accomplished by using a tool (simple machine)

Weight can be given in

Newtons

Is average velocity = average speed?

No

Is mass dependent on gravity?

No

When calculating the sum of vectors A+B, we put the tail of B at the tip of A. what would be the effect of reversing this order (B+A)?

No effect - vector addition, unlike vector multiplication is a commutative function

Is work energy?

No, work is a measure of energy transfer. The other form is heat

What accounts for the difference between work input and work output in a system that operates at less than 100% efficiency?

Nonconservative forces

At a place where g is 9.8 m/s2, an object is thrown vertically downward with a speed of 10 m/2 while a different object is thrown vertically upward with a speed of 20 m/2. What object undergoes a greater change in speed in a time of 2 seconds.

Note = both objects expereince an acceleration of 10m/s2 which means that each object's velocity changes by 9.8 m/s each second. Therefore, both objects experience the same change in velocity over the 2 second period. However, this questions asks for change in SPEED. For the downward path, we will use the equation v final = v i + at.vf = -5 - (10)*2 = -25 m/s. Therefore the change in speed will be v final - v initial = 25 - 5 = 20 m/s. For the upward path, we will do the same thing: vf = 10 m/s + (-10)*2s = -10 m/s. change in speed (just magnitude of change) = 0 m/s - 10 m/s = 10 m/s Scenario A experiences greater change in speed

Clockwise rotation is what sign

Positive (counterclockwise is negative)

Power

Rate at which energy is transferred from one system to another (energy/time)

second condition of equilibrium

Rotational equilibrium exists only when the vector sum of all the torques acting on an object is zero

distance, speed, energy, pressure, mass are vectors or scalars?

Scalars

acceleration on graph of velocity vs. time

Tangent to the graph at any time t = instantaneous acceleraton

How do the forces acting in free fall and projectile motion differ?

The only force acting in both free fall and projectile motion is gravity

Newton's third law: equation and explain

To every action, there is always an opposed but equal reaction (physical contact is not necessary for newton's third law - i.e. gravitational force)

Cross product is used to calculate (example)

Torque

Torque equation

Torque is greatest at 90 degrees (perpendicular) to lever arm

True/False: Total distance traveled can never be less than total displacement.

True

Gravitational potential energy equation

U=mgh

When multiplying vector to generate a scalar we use ____ product

Use dot prodcut

Acceleration is a vector or scalar

Vector

Force is a vector or scalar

Vector

Is velocity a vector or scalar?

Vector

Displacement

Vector quantity: - the change in position of an object (connects in a straight line, the objects initial and final position) - Does NOT account for pathway taken

displacement, velocity, acceleration, force are vectors or scalars?

Vectors

Vector vs. Scalar

Vectors have magnitude and direction Scalars solely have magnitude

Work equation

W = F · d W = Fdcos(theta) theta = angle between force and displacement vectors F= magnitude of applied force d = magnitude of displacement through which force is applied

Provide three methods for calculating the work done on or by a system

W = Fdcos(theta) * dot product of force and displacement vectors W = P(delta V) * Area under pressure volume curve Wnet = deltaKE * Work-energy theorem

SI unit for power

Watt (W) = J/s

work-energy theorem

Work = change in Kinetic energy = Kf -Ki the net work done by all the forces acting on an object is equal to the change in the object's kinetic energy - Allows us to calculate work without knowing magnitude of forces acting on an object or the displacement through which forces act

Efficiency formula

Work input = product of effort and effort distance Work output = product of load and load distance Load = weight of object Effort = force required to lift the object Load distance = to lift certain object in the air Effort distance = how much you have to pull through

Work in terms of effort

Work(in) = effort x effort distance

Dot product is used to calculate (example)

Work: W = F · d

magnitude of resultant vector

X^2 + Y^2 = V^2 or V = √(X^2 + Y^2)

Can a moving object be in equilibrium?

Yes (as long as velocity constant)

Are nonconservative forces path dependent?

Yes, the longer the distance traveled, the larger the amount of energy dissipated

What is the tangential force in uniform circular motion?

Zero - there is no change in speed of the object

Weight (Fg)

a measure of gravitational force on an object's mass

Deceleration

acceleration in the direction opposite to velocity; acceleration that results in a decrease in velocity

first condition of equilibrium

an object is in translational equilibrium when the sum of forces pushing it one direction is counterbalanced by the sum of forces acting in the opposite direction

kinetic friction equation

fk = μk*N

Relate Weight to Mass

g = 9.8 m/s2

Determining if a force is conservative

if the change in energy around any round-trip path is zero, or if the change in energy is equal despite taking any path between two points, then the force is conservative

Newton units

kg*m/s^2

Joule units

kgm^2/s^2

Watt units

kgm^2/s^3

Mass

measure of a body's inertia (the amount of matter in the object)

Inclined plane forces

parallel to the plane: mgsinθ perpendicular to the plane: mgcosθ

Conservative forces

path independent and do not dissipate the mechanical energy of a system

Velocity

rate of change of displacement/time

Is mass scalar or vector?

scalar

Is speed a vector or scalar?

scalar

2 types of friction

static and kinetic

center of mass/gravity

the point in an object that moves as if all the object's mass were concentrated at that point (the center of mass for a uniform object is at the geometric center of the object)

Total Mechanical Energy

the sum of kinetic and potential energy E = U + K

instantaneous velocity equation

v= lim as t→0 ∆x/∆t

Magnitude of static friction

μ = coefficient of static friction (unitless quantity dependent on two materials in contact) N = magnitude of normal force (component of force between 2 objects in contact that is perpendicular to the plane of contact)

Is μk or μs larger?

μs is always larger

distance vs displacement on a circular path

Distance = positive Displacement = 0

what is the cost of reducing the force needed to accomplish a given amount of work?

Distance through which smaller force must be applied must be increased - but since displacement is pathway independent, the actual distance traveled from the initial to final position does not matter, assuming all forces are conservative - if no nonconservative forces, Win = Wout (just force input will be lower, with correspondingly longer distance)

Speed

Distance travelled per unit time