Milestone 2 info

Note: when it says "Your answer is equal to 10 to what power?", we want the value of P where answer = 10 P. Convert the following quantities as requested (no computation required): (a) 10 cg =  ___g (grams); Your answer is equal to 10 to what power?  (b) 0.1 ms =  ___s (seconds); Your answer is equal to 10 to what power?

We are now able to define a mathematical formula for gravitational potential energy. Near the Earth's surface, the gravitational potential energy of a system consisting of the earth and an object with a mass m is EP = mgh, where g is the acceleration of gravity (9.80 m/s2) and h is the height above ground level (positive upward). Note that the "ground level" could really be any height we choose, because what's really important is the change in potential energy. The difference between two heights always gives the same change in potential energy, regardless of where we set the "zero" of height. In other words, if we find the change in potential energy  ΔEP = EP,f − EP,i,  the final potential energy minus the initial, we have ΔEP = mghf − mghi = mgΔh. The change in gravitational potential energy is just mg times the change in height. Let's return to our ball-Earth example, only now let's examine a case where a ball is rising in the air. You toss a ball with a mass of 0.703 kg upward.…

When a electrical appliances whose power usage is X watts is run for Y seconds it uses X×Y joules of energy. The energy unit used by electrical utilities in their monthly bills is the kilowatt-hour (kwh, that is, 1 kilowatts used for 1 hour) how many joules are there in a kilowatt hour? If electricity cost per $0.09 per kilowatt hour, how much does it cost per megajoule?

What is the dot product A•B if A = 2x - 3y and B = 15x + 10y?

A&B plz

If the speed of a vehicle increases by 22%, by what factor does its kinetic energy increase? Kinetic formula is KE=1/2 mu^2. Thus, the amount of kinetic energy in a moving object is the product of the mass(m) of the object and the square of its speed(u)

What is the dot product of (3i + 3j - 3k) and (-2i + 2j -2k)?

ANALYSIS II Data Set 2. Imagine the following experiment: A cart is initially at rest. A force pulls the cart through a given distance and gives it an amount of kinetic energy K. At the end of this distance, the force goes to zero and the cart travels with a constant speed. The resulting speed is measured. The data table on the next page shows the measured kinetic energies and the measured speeds. K, Jv, m/s 0.50 0.48 1.50 0.76 3.00 1.10 4.50 1.30 6.00 1.55 7.50 1.70

A mass of 78g is placed on the end of a 5.3cm vertical spring. This causes the spring to extend to 9.3cm. If we then change the mass to 206g, what is the measured length of the spring (in m)?

If a particle is moving, it has kinetic energy. Kinetic energy is the energy of motion, and it depends on the speed and mass of the particle. It is given by the formula Ek = 1/2*mv2, where  Ek  is the kinetic energy, m is the mass, and v is the speed of the particle. The formula for kinetic energy has some important features to keep in mind. Kinetic energy, and every other type of energy as well, is a scalar quantity, given by only a single number. Energy does not have a "direction", unlike a vector quantity. (This is in contrast to the vector quantity momentum, which you might have already studied.) Kinetic energy, in particular, is always a positive number. (Note the speed v is the magnitude of the vector velocity, and therefore is positive. But even if it were a negative number, squaring it would always lead to a positive result.) Kinetic energy depends on the square of the speed. (This is in contrast to the magnitude of momentum, mv, a quantity you may have already studied, which…

The work W done when lifting an object varies jointly with the mass m of the object and the square of the height h that the object is lifted. Which equation represents the relationship between work, mass, and volume?

The kinetic energy K of an object of mass m moving with speed v is given by the formula K = mv2. The SI unit of kinetic energy is the joule, J. Use this formula to express the joule in terms of the fundamental SI quantities of mass, length, and time.

Since the initial potential energy and final kinetic energy are zero, our equation now becomes EP,f = EK,i. We can then substitute the formula for kinetic energy,  EK = 1/2mv2,  and the formula for gravitational potential energy,  EP = mgh, mghf = 1/2mvi2. Now it's just a matter of doing the algebra, solving for the final height  hf,  and substituting values to find  hf.  Notice that the mass m divides out of both sides of the equation, so the value of the mass is not needed to find the final height. Calculate the maximum height of the ball in meters. hf = __________ m

We have this equation in 1D.  If the terms confuse you, just follow the math: m d v/ d t − F = 0 Multiply everything by d x, identify d x / d t = v, and integrate.  You need only one constant of integration, E, and put it on the right side. The m and v term is called K (for "kinetic energy" or "energy of motion").  E is the energy ("total energy" or "total mechanical energy").  F isn't constant in general.  The F integral is identified with the potential energy: U = − ∫ F d x Write down the resulting equation (the "energy conservation equation").

A baby carriage is sitting at the top of a hill that is 21 m high.  The carriage with the baby has a mass of 1.5 kg.  The carriage has _____ Joules of energy. PLEASE USE COMMAS IN YOUR ANSWERS IF NEEDED! The formula for potential energy is: PE = mgh v = velocity or speed in m/s m = mass in kg    g = 10m/s (this is really 9.8 m/s on earth but we will use 10 for simplicity) h = height in meters

The purpose of this experiment is to fully explain how starting height and mass affect an object’s potential and kinetic energy. Potential energy is stored energy. Potential energy related to an object’s height is called gravitational potential energy. The formula for calculating gravitational potential energy is Gravitational potential energy = Weight × Height. Kinetic energy is the energy an object has due to motion. The formula for calculating kinetic energy is Kinetic Energy = ½ × Mass × Velocity. Speed of an object is the distance the object travels per unit of time. The formula for calculating speed is Speed = Distance ÷ Time.  How does the starting height of an object affect an object's kinetic and potential energy ? The independent variable is the object's height. The dependent variable is the kinetic energy and potential energy. The hypothesis is if an object's height is shorter or taller than it won't affect kinetic and potential energy because it doesn't affect energy. Is…

The work required to launch an object from the surface of Earth to outer space is given by W = F(x)dx, where R=6370 km is the approximate radius of Earth, GM, M2 F(x) = x2 is the gravitational force between Earth and the object, G is the gravitational constant, M, is the mass of the Earth, M, is the mass of the object, and the product GM, is equal to 4x 1014 m3 /s?. Answer parts (a)-(c). .... a. Find the work required to launch an object in terms of M2. The work required is W = m² /s² (Simplify your answer. Round to three decimal places as needed. Use scientific notation. Use the multiplication symbol in the math palette as needed. Type an expression using M, as the variable.)

If g(v) is the fuel efficiency, in miles per gallon, of a car going at v miles per hour, what are the units of g′(90)? What is the practical meaning of g′(55)=−0.54?

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"Energy per unit time" is a quantity called Power.  Which of the following combinations has the same units as power? A   length squared times mass over time squared B   persimmons. C   speed times mass times acceleration over time D   Force times acceleration E   {potential energy minus kinetic energy} times time F   Force times velocity G   speed squared times mass H   mass time acceleration I   mass squared times acceleration.

A retailer buys Dalmatian stuffies for $6 each. (Assume that the retailer has no other variable costs). The retailer can only charge by the dollar so no need to consider cents -- e.g., $3 is a price you could choose, $3.11 or $2.99 are not. The potential customers have the following WTP. Student (1= yes) Parent (1=yes) Cat Lover (yes =1) Over 65? (1=yes) WTP 1 $20 O $20 1 $18 1 $15 O $15 O $14 O $14 1 $14 O $14 1 $13 O $10 1 1 1 1 1 1 1 1 O $8 O $8 1 $7 1 1 $7 1 $5 O $5 1 1 1 1 $5 O $4 1 $3 1 1 1 If you can only charge a single price what is the best price to maximize revenue?

In this problem we are going to consider two different examples of the dot product between two vectors, a force F and a displacement Δr.  If the force vector has a magnitude of F = 14.5 N, the displacement has a length of Δr = 0.75 m, and the angle between the vectors is 45°, what will the dot product between the vector F and the vector Δr be? You can answer in joules (which is the same as newton-meters).   If the force vector has components Fx = 7.5 N and Fy = 13.8 N, and the displacement vector has components Δrx = 0.25 m and Δry = 0.63 m, what is the dot product between them? Again, enter your answer in joules.

Newton's law of universal gravitation is represented by F= G* Mm/ T where F is the gravitational force, M and m are masses, and r is a length. Force has the Sl units kg • m/s?. What are the Sl units of the proportionality constant G? Show the work.

A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby has a mass of 1.5 kg. The carriage has Joules of energy. PLEASE USE COMMAS IN YOUR ANSWERS IF NEEDED! The formula for potential energy is: PE = mgh v = velocity or speed in m/s m = mass in kg g=10m/s (this is really 9.8 m/s on earth but we will use 10 for simplicity) h = height in meters

Evaluate the dot product A · Bif A = 9i +3j and B = 5i – 5j. %3| ? A-B =

Given v=-2i-9j and w=10i-j, find the angle between v and w

No. 3

what was the total for the division problem: S= 3 x (4.5x10^24kg) & 4(3.14)x (6.05x10^6)

The fuel efficiency E (in kilometres per litre) of a certain car driven at a speed v (in kilometres per hour) is approximated by E(v)=1,500v/v2+1,600. If the speed limit is 100 km/h, determine the legal speed that will maximize fuel efficiency.

Suppose that 5 Joules of work is needed to stretch a spring from its natural length of 11 cm to a length of 32 cm. a) How much work is needed to stretch the spring from 16 cm to 27 cm? W = =ff(x)dx, where f(x) = W = J. Note: You a= and b b) How far (in meters) beyond its natural length would a force of 35 N keep the spring stretched? m.

Given three vectors A = -72 + 93 – 4k,B = –6î + 33+ 12k and C = 152 – 47 + 7k which of the following is true? %3D O |(Ã+ B) – Č| > [(Ã – B) + Č| O |(Ã + Ë) – Č| < |(Ã – B) + Č| O |(Ä + B) – Č| < [(Ã + B) + Č| O |(Ã + B) + Č| < [(Ã – B) + Č|