Jacksparrow MCAT C/P

What is a vector

A quantity with a number and a direction

What is a scalar?

A quantity with a magnitude only

Describe the tail to tip method?

The tail to tip method is a way of calculating the sums (or substractions) of vectors. Simply put the vectors tail to tip (flip the vector for negative)

How does one break a vector into components?

Choose two axes (vertical & horizontal or parallel & perpendicular) and use two vectors to represent the original vector.

Which component of a vector will cos(theta) give you? (horizontal/vertical and parallel/perpendicular)

Horizontal or Perpendicular

How does one calculate the magnitude of a vector from its components?

Square both component vector magnitudes, add them, and square root the sum.

How do the components of vectors add when two overall vectors are summed?

The components themselves simply sum.

What does multiplying a vector by a negative number do?

Change the magnitude and direction of the vector.

When multiplying vectors, what type of product should be used to create a scalar?

Dot product

What is a dot product?

The product of the magnitudes of two vectors and the cosine of the angle between them.

When multiplying vectors, what type of product should be used to create a new vector?

Cross Product

What is a cross product?

A cross product is the product of the magnitude of two vectors and the sin of the angle between them.

What is the purpose of the right hand rule?

To determine the direction of the resultant vector of a cross product.

How does one use the right hand rule?

for C = A x B 1. Point thumb in the direction of vector A 2. Point fingers in the direction of vector B 3. The direction your palm is facing is the direction of vector C

What is displacement?

Displacement is a vector quantity that describes an objects change in position in space. It is an arrow from initial position to final position.

What is distance?

Distance is a scalar quantity that describes the length that an object has traveled. It is a tallying of the total length an object has moved to get from its initial position to its final position.

What is velocity?

Velocity is a vector quantity that describes the change in displacement per unit of time.

What is speed?

Speed is a scalar quantity that tallies the length of distance travelled over time.

How does one calculate the average velocity of an object?

Take the change in (displacement) and divide it by the change in time.

Instantaneous velocity and instantaneous speed are [...] [Explanation]

Instantaneous velocity and instantaneous speed are equivalent This makes sense because it takes time to change the direction of a vector. In velocity, you're moving at some speed and you can change direction at some point. In speed, you're just moving at some speed not worrying about direction. In any given instant, you are only travelling in one direction. It takes time to turn and go into different directions, messing with displacement and therefore velocity. Therefore, with a timescale of 0 (instantaneous) velocity is only going in one direction and is therefore equivalent to instantaneous speed.

What is the formula for the magnititude of gravitational force?

What is the formula for static friction?

Where us is the coefficient of static friction and N is the magnititude of the normal force.

What is static friction?

The force that exists between a stationary object and the surface upon which it rests.

What is the normal force?

The normal force is a contact force that keeps objects from passing through one another. The normal force is perpendicular to the plane of contact between two surfaces.

What is the formula for kinetic friction?

where uk is the coefficient of kinetic friction and N is the normal force.

What is kinetic friction?

Kinetic friction is the force that acts between two objects sliding against each other.

How can there be a range of static frictions?

The magnititude of static friction depends on factors like the amount of surface area in contact (more = higher).

What are the 2 important differences between static friction and kinetic friction

1. Static friction takes a range of values. Kinetic friction, on the other hand, is constant and does not depend on contact area, velocity of sliding objects, etc. ***fact check 2. The coefficient of static friction is always higher than the coefficient of kinetic friction. This means accelerating a static object takes more force than accelerating an already moving object. Furthermore, the maximum static frictional force will always be larger than the kinetic frictional force.

How does one relate mass and weight?

Where Fg is the force of weight (gravity), m is mass, and g is acceleration due to gravity.

What is the value of acceleration due to gravity?

10m/s2

What is acceleration?

The rate of change of velocity m/s2

How does one calculate the average acceleration over time?

In what direction do frictional forces act?

Opposite that of the accelerating force.

What is Newton's First Law?

An object at rest or in motion with constant velocity will remain that way unless a force acts on it.

What is Netwon's Second Law?

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

What is Newton's Third Law?

To every action(force), there is always an opposed but equal reaction.

What are the four assumptionless kinematics equations?

What is the vertical speed when an object reaches its maximum height?

0

What is air resistance?

The force of friction with the air. This force opposes movement and increases as speed increases, causing an object to reach a terminal velocity.

What is the uniform acceleration kinematics equation?

How does one approach a projectile motion problem?

Split all motion into x and y components.

How do you calculate the component of gravity parallel to the inclined plane?

What is uniform circular motion?

When an object's instantaneous velocity vector is tangent to the circular path but centripital force (which is pointed radially inward) keeps the motion circular.

What is the equation to calculate the centripital force and centripital acceleration on an object?

ac=v2/r

What is a free body diagram?

A visual accounting of all the forces on an object.

What is torque?

The rotational force that occurs when a force is applied to a lever arm on a fulcrum of some length.

How does one calculate torque?

How does one assign directionality to torques?

Torque that generates clockwise rotation is negative. Torque that generates counterclockwise rotation is positive.

How does one approach torque problems?

Identify all counterclockwise and clockwise torques and then identify all forces.

What is energy?

The capacity to do work

What is kinetic energy?

The energy an object has by virtue of its movement.

What is the formula to calculate an object's kinetic energy?

Where m is mass and v is speed

What are the base units of the Joule?

What is potential energy?

Energy of an object by virtue of its position in a system or some other intrinsic quality.

How does one calculate an object's gravitational potential energy?

Where should one assign the zero point when calculating gravitational potential energy?

Wherever is most convenient. We can pick a zero point wherever we want. Try to pick a zero point that eliminates variables.

What is the formula for elastic potential energy?

where k is the spring constant and x is the distance from the equilibrium position

What is an object's total mechanical energy?

The sum of the kinetic and potential energy (basically, the usable energy).

What is the first law of thermodynamics?

Energy is never created nor destroyed, only transferred from one form to another. In other words, the total energy at the beginning of a problem must equal the total energy at the end of a problem.

What are conservative forces?

Conservative forces are forces that do not dissipate energy e.g Gravity and Electrostatics PATH INDEPENDENT

What are non-conservative forces?

Non conservative forces dissipate energy into the form of heat/light/sound. e.g. Friction, air resistance, etc. PATH DEPENDENT

What should the change in total mechanical energy of an object be equal to when only dealing with conservative forces?

Zero

What should the change in total mechanical energy of an object be equal to when considering nonconservative forces?

The change in total mechanical energy will be equal to the work lost due to the nonconservative forces.

What is work?

Work is the mechanical transfer of energy from one object to another. Change in energy (can be potential or kinetic, think charge problem from class)

How does one calculate the amount of work done on an object?

Where F is the force, d is the distance over which the force was applied, and theta is the angle between the force and the displacement vector

How does one calculate the work done by gases?

Where P is pressure in pascals and V is volume in meters cubed.

How does one calculate the work done by a gas using a P-V graph?

Take the area within the curve

What is power? (No calculation, qualitative)

The rate at which energy is transferred from one system to another.

How does one calculate power in terms of work?

Where W is work, t is time, and E is total mechanical energy

What is the work energy theorem?

The work energy theorem says that the total change in energy (work) of an object can be calculated by determining the change in an object's kinetic energy. Work also equals negative change in potential energy for conservative forces

What are the three ways to calculate work done on or by a system?

What are the two types of energy transfer?

Heat(thermal) and Work(mechanical)

What is mechanical advantage?

Mechanical advantage is the ratio of magnitudes of the force exerted on an object by a simple machine to the force actually applied to the simple machine.

How does mechanical advantage work?

Mechanical advantage is when we use a machine of some sort to reduce the amount of force needed to achieve some outcome. This reduction in force is accomplished through an increase in distance through which the force has to be applied, thus conserving energy. (Work is the same both with and without pulley)

What is the formula to calculate efficiency?

load equals weight

What is the zeroth law of thermodynamics?

When an object x is in thermal equilibrium with an object y, and that object y is in thermal equilibirum with another object z, x will be in thermal equilibrium with z.

What is temperature proportional to and founded upon?

The average kinetic energy of the particles that make up a substance.

In what direction(temperature wise) does heat flow?

From objects with high temperatures to objects with lower temperatures

The flow of heat from an object with a high temperature to an object with a low temperature is [...]

The flow of heat from an object with a high temperature to an object with a low temperature is spontaneous

What does it mean to be in thermal equilibrium?

No net heat is flowing between objects in thermal contact.

Do two objects need to be in physical contact to be in thermal contact.

No, it is possible for objects to be in thermal contact without touching one another, although, objects in thermal contact are usually in physical contact too.

What is the third law of thermodynamics?

The entropy of a perfectly organized crystal at absolute zero is zero. This really means that there can be no temperature lower than absolute zero.

What is body temperature in celsius and farenheit?

37, 98.6

What is thermal expansion?

The tendency of objects to increase in size with increases in temperature.

What is the equation for linear thermal expansion?

Mnemonic: When temperature changes, the length changes ALOT

What is the formula for volumetric expansion?

Beta is volumetric expansion coefficient

What is a system in the context of thermodynamics?

The portion of the universe we are interested in observing or manipulating. The rest of the universe is the surroundings.

What is an isolated system? Can internal energgy change?

An isolated system is a system that is incapable of exchanging energy or matter with its surroundings. It follows that the total change in internal energy in an isolated system will be equal to 0.

What is a closed system?

A closed system is one in which energy can be exchanged, but matter cannot. (ex. pistons)

What is an open system?

An open system is one in which both matter and energy can be exchanged with the surroundings. (ex. boiling pot of water, humans)

Which variable links the horizontal and vertical aspects of projectile motion?

Time. Once the ball hits the ground, the motion stops, both horizontal and vertical. Therefore, time is the one variable that you can solve for in one dimension and then use in another. This fact will often provide the necessary variables for solving certain kinematics problems.

What is a state function?

A state function is a thermodynamic property that is a function of only the current equilibrium state, not the path that was taken there.

Explain how something like pressure is a state function.

The pressure in a system is defined only by the current equilibirum state of the gas particles. Take for instance, 2 balloons with a pressure of 1 atm each. The pressures in these balloons are identical. It does not matter if the first balloon came to 1atm from 10atm and the second balloon came to 1 atm from .01atm. The fact of the matter is that, right now, their pressures are both 1atm.

What are the 9 state functions?

1. Pressure (P) 2. Density 3. Temperature 4. Volume 5. Enthalpy 6. Entropy 7. Potential Energy 8. Gibbs Free Energy 9. Internal Energy

What is a process function?

A process function is a thermodynamic property that is a function of the path taken to a certain state.

Explain how something like work is a process function

The work done by or on a system is defined by the path the work took. Work can be calculated using W = Fdcostheta where F is force and d is distance. Therefore, differing path lengths (d) are built into the equation and must be considered. For further elaboration, consider the following. Two weights are at a height of 10 meters. The first weight was brought from 0 meters to a height of 10 meters, which took some amount of work. The second weight, on the other hand, went up 10 m, left 5 meters, and then right 5 meters. Both weights are in the same final position, 10 meters above ground level, but the second case took more work.

What are the 2 process functions?

mechanical Work and Heat

What is the first law of thermodynamics in the context of Thermodynamics problems?

The change in the total internal energy of a system must be equal to the change in heat and work (because energy must be conserved). Q-W energy transfered in as heat minus work done by the system

When do we give heat positive or negative values?

When heat is entering or leaving the system, respectively.

When do we assign positive or negative values to work?

Neg. when work is being done on the system (compression) pos. when work is being done by the system (expansion). applies to Q-W version so if system compresses it becomes Q+W because neg times neg equals pos