ch 9 Dot Product Test 2

Flashcards covering the concepts of the Dot Product, various forms of energy (Kinetic, Potential, Thermal), Power, Conservation of Energy, Work, simple machines, and mechanical advantage from the lecture notes.

When manipulating two or more vectors, what must be known?

The individual components of each variable.

How do you add or subtract two vectors?

Component by component.

What is the Dot Product?

A multiplicative operation for vectors in which the product of the two vectors is a scalar.

How is the Dot Product (C) calculated using vector components A⃗ = 〈Ax, Ay, Az〉 and B⃗⃗ = 〈Bx, By, Bz〉?

C = AxBx + AyBy + AzBz

What is an alternative method to calculate the Dot Product (C) using the magnitudes of vectors A⃗ and B⃗⃗ and the angle (θ) between them?

C = |A⃗||B⃗⃗| cos θ

What does the Dot Product tell you about two vectors?

How 'alike' those two vectors are.

If two vectors A⃗ and B⃗⃗ point in the same direction (θ = 0), what is the value of their Dot Product?

It reaches its maximum positive value.

If two vectors A⃗ and B⃗⃗ point in opposite directions (θ = 180°), what is the value of their Dot Product?

It reaches its maximum negative value.

If two vectors A⃗ and B⃗⃗ are perpendicular to each other (θ = 90°), what is the value of their Dot Product?

Zero.

In Physics, what is Energy (E)?

A quantity that describes a system’s capacity to exert forces over distances.

What are the units for Energy?

Joules (J), which are equivalent to N●m or kgm2/s2.

What is Kinetic Energy?

The Energy associated with an object's motion.

What is the formula for Kinetic Energy (K)?

K = 1/2 mv^2

What is Potential Energy?

The Energy associated with a system’s position and configuration, or stored energy.

Is a system's Potential Energy an absolute quantity?

No, it is always calculated in reference to the potential energy at another location.

What is the formula for Potential Energy from Gravity (V_Grav) near the surface of the Earth?

V_Grav = mgh (mass × gravitational acceleration × height above reference point)

What types of energy are considered mechanical in nature because they can freely swap between each form?

Kinetic and Potential Energy.

What is Thermal Energy (Q) a result of?

Friction.

What is Power (P) defined as?

The rate that Energy changes forms over time.

What is the formula for Power (P)?

P = ∆E/∆t

What are the units for Power?

Watts (W), which are Joules per second (J/s).

What is the principle of Conservation of Energy?

The Total Energy of a single system is constant; energy cannot be created or destroyed, only transferred from one form or system to another.

What is the formula for the Total Energy of a system in mechanics?

Total Energy = K + V + Q = Constant (Kinetic Energy + Potential Energy + Heat Loss due to friction).

What is Work (W)?

The Force exerted over a distance.

What is the formula for Work (W) using Force (F⃗), displacement (∆x⃗), and the angle (θ) between them?

W = F⃗ ∙ ∆x⃗ = Fd cos θ

How does the total Work done relate to an object's Kinetic Energy (K)?

The total Work done results in the change in Kinetic Energy for an object (W = ∆K).

How is the change in potential energy of a system related to the work done?

The change in potential energy is equal to the negative work done in moving the object from one location to another.

What are the six simple machines?

The incline plane, screw, wedge, lever, pulley, and wheel and axle.

What is Mechanical Advantage (MA)?

The ratio of Output Force to Input Force (MA = Output Force / Input Force).

In a real simple machine system, how is Work conserved?

Work In = Work Out + Heat Loss due to Friction.

What is the formula for the Actual Efficiency of a machine?

Actual Efficiency = Work Out / Work In

When might Newton's Laws be more advantageous to analyze a problem compared to energy?

If friction is present, because the force of friction can often be more easily determined analytically than the thermal energy.