Question

crash course physics #9
available at http://youtu.be/w4cfjbpq8vo or just youtube/google \crash course physics 9\

1. work is what happens when you apply a force over

a certain ______ to a system.
a. what is referred to by the word \system\?
b. work is expressed in units known as ______.
c. how would you calculate the part of the force thats
parallel to the floor (pulling the box forward)?
i. we typically designate an angle in a system as ______.
d. one way physicists often write the equation for work is theyll set it equal to
____ times __ times the ____.
e. to find the work done by a varying force, you just have to ______
that force relative to the ______ the object moved.
f. joules are often used as the units for something else: ______.
g. energy is the ability to ______.
i. how does kinetic energy differ from potential energy?

1. how would you calculate gravitational

potential energy?
ii. some systems can lose energy. these are known as
______.
h. average power is used to measure how much energy is
______ from type to another over time.
i. power is the ______ applied to something
with a particular ______.

Explanation:

Part 1 (Main Question)

Step1: Recall the definition of work

Work in physics is defined as the product of a force applied to an object and the distance the object moves in the direction of the force. So the first blank is "force" and the second is "distance".

Step2: Analyze sub - questions

a. "System" in physics context

In physics, a "system" refers to the object (or group of objects) on which we are focusing our analysis, such as the box being pulled in the diagram.

b. Unit of work

The SI unit of work is the joule (J).

c. Calculating parallel force component

If we have a force \( F \) applied at an angle \( \theta \) to the horizontal, the component of the force parallel to the floor (horizontal direction) is calculated using the cosine of the angle. The formula is \( F_{\parallel}=F\cos\theta \).

i. Designating the angle

We typically designate the angle between the force vector and the displacement vector (or the horizontal/vertical as appropriate) as \( \theta \) (theta).

d. Equation for work

The equation for work when a force is applied at an angle \( \theta \) to the displacement \( d \) is \( W = Fd\cos\theta \), so it is equal to "force" times "distance" times the "cosine of the angle between them".

e. Work done by a varying force

To find the work done by a varying force, we need to integrate (or find the area under the curve of) the force relative to the "distance" the object moved. Mathematically, \( W=\int F(x)dx \) where \( x \) is the distance.

f. Other use of joules

Joules are also used as the unit of energy (since work and energy are related by the work - energy theorem).

g. Definition of energy

Energy is the ability to "do work".

i. Difference between kinetic and potential energy

Kinetic energy (\( KE=\frac{1}{2}mv^{2} \)) is the energy an object has due to its motion, while potential energy (e.g., gravitational potential energy \( PE = mgh \), elastic potential energy \( PE=\frac{1}{2}kx^{2} \)) is the energy an object has due to its position or state.

1. Calculating gravitational potential energy

The formula for gravitational potential energy near the Earth's surface is \( PE = mgh \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height of the object above a reference point.

ii. Systems that lose energy

Systems that can lose energy (due to non - conservative forces like friction) are known as "dissipative systems".

h. Average power

Average power is used to measure how much energy is "transferred" from one type to another over time.

i. Definition of power

Power is the "work" applied to something with a particular "rate" (more precisely, power \( P=\frac{W}{t} \), where \( W \) is work and \( t \) is time, so it's the rate at which work is done or energy is transferred).

Answer:

1. Work is what happens when you apply a \(\boldsymbol{\text{force}}\) over a certain \(\boldsymbol{\text{distance}}\) to a system.

a. A "system" refers to the object (or group of objects) under analysis (e.g., the box being pulled).
b. Work is expressed in units known as \(\boldsymbol{\text{joules (J)}}\).
c. To calculate the part of the force that's parallel to the floor, use \( F_{\parallel}=F\cos\theta \) (where \( F \) is the applied force and \(\theta\) is the angle between the force and the horizontal).
i. We typically designate an angle in a system as \(\boldsymbol{\theta}\) (theta).
d. One way physicists often write the equation for work is they'll set it equal to \(\boldsymbol{\text{force}}\) times \(\boldsymbol{\text{distance}}\) times the \(\boldsymbol{\text{cosine of the angle between them}}\).
e. To find the work done by a varying force, you just have to \(\boldsymbol{\text{integrate (find the area under the force - distance curve of)}}\) that force relative to the \(\boldsymbol{\text{distance}}\) the object moved.
f. Joules are often used as the units for something else: \(\boldsymbol{\text{energy}}\).
g. Energy is the ability to \(\boldsymbol{\text{do work}}\).
i. Kinetic energy is energy of motion (\(KE = \frac{1}{2}mv^{2}\)), potential energy is energy of position/state (e.g., \(PE=mgh\) for gravity).

1. Gravitational potential energy is calculated as \( \boldsymbol{PE = mgh}\) (where \(m\) = mass, \(g\) = acceleration due to gravity, \(h\) = height).

ii. Some systems can lose energy. These are known as \(\boldsymbol{\text{dissipative systems}}\).
h. Average power is used to measure how much energy is \(\boldsymbol{\text{transferred}}\) from type to another over time.
i. Power is the \(\boldsymbol{\text{work}}\) applied to something with a particular \(\boldsymbol{\text{rate (of doing work)}}\).