Physics Chapter 6

What is the value of the spring constant determined by?

-how the spring was formed -the material of the spring

If an applied force acts along the direction of the displacement then θ=____

0°

Derived formula for elastic potential energy of a spring

( ΔKE + ΔPE(g) + ΔPE(s) )f = ( ΔKE + ΔPE(g) + ΔPE(s) )i

The two types of mechanical energy

Kinetic energy Potential energy

You push very hard on a heavy desk, trying to move it. You do work on the desk:

Only if it starts moving.

Elastic potential energy

The energy stored in a stretched or compressed spring or other elastic material

Why cant the formula W = FΔx be used when the force applied is changing?

The formula only works when the magnitude and direction of force is constant.

The Moon revolves around the Earth in a nearly circular orbit, kept there by the gravitational force exerted by the Earth. Does gravity do (a) positive work, (b) negative work, or (c) no work on the Moon.

The gravitational force exerted by the Earth on the Moon acts toward the Earth and provides its centripetal acceleration, inward along the radius of the Moon's orbit. The Moon's displacement at any moment is tangent to the circle, in the direction of its velocity, perpendicular to the radius and perpendicular to the force of gravity. Therefore, θ is 90° . That means the work on the moon is nonexistent. This is why the Moon and other artificial satellites can stay in orbit without expenditure or fuel. NO NET WORK NEEDS TO BE DONE AGAINST THE FORCE OF GRAVITY.

Does one moving object have the ability to do work on another object?

Yes; a flying cannon can do work on a brick wall it knocks over, or a moving hammer does work on a second object which undergoes displacement.

What is the most common type of potential energy?

gravitational potential energy PE(g) = mgy The higher above the ground, the more PE(g) an object has

power is a ________________ quantity

scalar

The three key ingredients to work

•force •displacement •cause

How the spring was formed

-The diameter of the coil -The coil distances

What are the two parts a stationary jump consists of?

-extension -free flight

Work done against a nonconservative force cannot _____________________

Be easily be removed

The magnitude of the force would be

F = K X F = force K = a specific constant for the spring X = displacement

Area = Δa = ???

F(x)ΔX the work done by a variable force acting on an object that undergoes displacement is equal to the area under the F(x) versus X

If Fx is + and X is + then the W ________________ the mechanical energy of a system

Increases

For a stiff spring, k is ...

Large

Power instant formula

P(inst) = (ma^2+f(k)a) t

What does mechanical energy have an amount of within its system?

PE and KE (ΣE)

The speed of an object will increase if the network done on it is _______________________________________________________

Positive, because the final kinetic energy will be greater than the initial vice versa for decrease

For a flexible spring, k is ...

Small

What are some things KE(max) equal?

= F(input) = 0 = V = at maximum = a = 0

Resting length

A spring that is not compressed or stretched

Work on a body and/or system ______________ the energy of the body and/or system

Changes (Work = energy, energy = work)

What is an example of a force acting on an object, but no work being done?

Holding a heavy bag of groceries and moving. You may have a displacement, but the bag has no displacement, so no work is being done on the bag.

K formula

If Fs = -K X Then K = W/X

Hooke's Law

If a force is exerted on a spring that changes its shape and held in that position by a constant force, then the spring must be exerting an equal and opposite force F = -K X

V in KE is not velocity, why?

It is speed. Since energy is scalar, it is the magnitude of the distance traveled in a time period.

What is KE defined as

KE is defined as 1/2mv^2

Units in a watt

Nm/s = J/s = (1 kg)(m^2/s^3)

An object has stored energy by its ___________ or ____________

Shape; position

The simplified definition of energy

The ability to do work

What is the initial energy put into the Earth reciprocated into?

The bodies center of gravity.

The sign of work depends on ____________________

The direction of F relative to the displacement

Work-energy principle

The net work done on an object is equal to the change in the object's potential energy.

When is a force conservative?

When the work done moving an object between two points is the same no matter what path is taken

When is work negative?

Whenever the force acts in the direction opposite to the motion. Or whenever the force is trying to slow the object down.

What is the initial position of the extension phase?

a "pre-load" (lowering the center of gravity)

W = F (d) But if F is an angle W = F (cos θ) (d)

Work is done by a constant force in a direction

derived formula for the instantaneous power in terms of drag force, force, mass, acceleration, and time

ma = Fe-Fd Fe = ma+Fd PE = Fe/t = (ma+Fd)/t

Work

the product of the magnitude of the displacement times the component of the force parallel to the displacement.

Power

the rate of energy transfer with time

average power

the work done divided by the time interval

Italicized W is _______ Bold W is ________

work watt

The SI unit of work is the newton meter (Nm) or Joule (J)

1 Nm = 1 J (1 kg•m^-1/s^2)(m)

What is K approximately equal to when it is small?

100 N/m

What is K approximately equal to when it is large?

10000 N/m

What are some things PE(max) equal?

= KE(max) = F(input) is at maximum = V = 0 = a = is at maximum

Scalar quantity

A number rather than a vector (therefore, it's easier to work with)

Conservation

A principle that the amount of a quantifiable physical entity such as energy, mass, momentum, or electrical charge within a system remains constant. What you start with is what you end up with.

Why is the potential energy of the spring always positive?

Because it is proportional to X^2 Always positive except at 0

If Fx - and X is - then the W ________________ the mechanical energy of a system

Decreases

A nonconservative force is generally ____________

Dissipative This means that nonconservative forces tends to randomly disperse the energy of bodies on which it acts

Elastic energy systems

Energy is only stored in an elastic object (spring) when it's stretched or compressed

Dispersal of energy often takes the form of:

Heat and/or sound

Formulas:

W = F cos θ d KE = (1/2) mv^2 W = ΔKE W = 1/2m(vf)^2-1/2m(vi)^2 KE = 1/2m(Vf^2-Vi^2)

If you can calculate the force applied over a small displacement, then you have:

W = F1ΔX1 + F2ΔX2 + F3ΔX3 ...

Work-energy theorem ***

W(net) = ΔKE W(net) = 1/2 m(vf)^2-1/2m(vi)^2 The net work done on an object by the force(s) acting on it is equal to the change in the KE of an object

When is a spring at max acceleration?

When it is completely stretched or compressed

When is the only time energy is stored in a spring?

When it is either stretched or compressed

The speed and KE of an object will change only if _______________________________

Work is done on the object by some external force(s)

Work is a ___________ quantity

Scalar

Work nonconservative formula***

W(nc) = ΔKE + ΔPE ***work done by all nonconservative forces equals the two change in the kinetic energy plus the change in potential energy

When is PE at maximum?

When it reaches maximum stretch of maximum compression

When does the free-flight phase begin?

When the jumper breaks contact with Earth

The material of the spring

-the thickness of the material wire -the inherent tensile strength

KE(max) will be at equilibrium the PE at equilibrium = _____

0

PE(max) then KE = ______

0

What is a kilowatt-hour

3.6 x 10^6 J Watt is a kilowatt-hour

To stretch or compress a spring, ___________________________

A force must be applied

Work describes __________________________________

Amount of of energy "applied" to a system

_____________ work originating _____________ from the center of gravity by _____________ contractions of the skeletal-muscular system occurs through "__________________," the force input into the Earth.

Internal Externally Internal De-loading

Can kinetic energy ever be negative?

No, it is always either positive or 0.

Another nonconservative force includes:

Propulsive forces (like forces exerted on by a jet engine, on a plane, or by a propeller on a submarine)

A car traveling 60 km/h can brake to a stop within a distance (d) of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping distance? (assume the maximum braking force is approximately independent of speed)

Since the stopping force F is approximately constant, the work needed to stop the car, Fd, is proportional to the distance traveled. We apply the work-energy principle, noting that F and d are in opposite directions and the final speed of the car is 0: W(net) = Fd (cos 180° ) = -Fd -Fd = ΔKE = (1/2)mv(f)^2 - (1/2)mv(i)^2 = 0 - (1/2)mv(i)^2

Transduction

•The various forms of energy are related to each other such that, when energy is transformed from one form to another, the total amount of energy remains the same (the change of energy) •The fact that the atoms that makeup matter are themselves concentrated bundles of energy reveals ΣE in a system remains regardless of the form or forms

Two water slides at a pool are shaped differently, but have the same length and start at the same height (h). Two riders, Paul and Kathleen, start from rest at the same time on different slides. (a) Which rider is traveling faster at the bottom? (b) Which rider makes it to the bottom first? IGNORE FRICTION

(a) Each rider's PE(i) gets transformed to KE, so the speed (v) at the bottom is obtained from (1/2)mv^2 = mgh. The mass cancels and so the speed will be the same, regardless of the mass of the rider. Since they descend the same vertical height, they will finish with the same speed. (b) Kathleen is consistently at a lower elevation than Paul at any instant, until the end. This means she has converted her potential energy to kinetic energy earlier. Consequently, she is traveling faster than Paul for the whole trip except toward the end where Paul finally gets up to the same speed. Since she was going faster for the whole trip, and the distance is the same, Kathleen gets to the bottom first.

x compression / x tension

x compression (max) = X(o) to X(compress max) X(c) <------ X(o) = X(T) ------> X(o) X(c) + X(o) = X(o) + X(T)

Conservative/non conservative force formulas

~w(net) = w(nc) + w(c) ~w(nc) + w(c) = 1/2m(vf)^2 - 1/2m(vi)^2 ~w(c) = mg(yi) - mg(yf)

The work done by an applied force is positive when the component of F cos θ is in the same direction as the displacement

• + when the applied force is in the same direction as displacement • - when the applied force is in the opposite direction as displacement

Energy

•Anything that can change the condition of matter. Commonly defined circularly as the ability to do work; actually only describable (the effect/work of a cause/energy) •Cannot be created nor destroyed; it may be transformed from one form into another, but the total amount of energy in a system never changes

Forms of Energy

•Mechanical •Chemical •Electromagnetic •Heat •Nuclear