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Energy required to create a rabbit "out of thin air".

This figure indicates the energy required to conjure up the rabbit "out of thin-air". Evidently it takes more than energy, U=E, of the rabbit. Please explain, and also tell me why these energies are called "Free". In other words, why did scientists give them such a name? Which figure is correct or are they both correct ?

Non-Elastic Collision: Conservation of linear momentum

8. A 69.0 kg person running at an initial speed of v1 = 4.00 m/s jumps onto a m = 138 kg cart initially at rest. (Figure P8.47) The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.400. Friction between the cart and g

Amplitude, total energy and speed of object

A 0.5kg object is connected to a light spring with a spring constant of 25N/m and oscillates on a frictionless horizontal surface. the amplitude of motion is 3 cm. Find the total energy of the system. What is the speed of the object when the displacement is 2cm?

Temperature and Heat of Metal

A metal ball of mass 0.65 kg with initial temperature of 30 oC is dropped into a container of 1.29 kg of water at 20 oC. If the final temperature is 20.4 oC, what is the specific heat of the metal to the nearest tenth of a J/kg·K?

Helium Electrons

The energy levels for the helium ion He^+ are given by a formula similar to that for the hydrogen atom: 9.7 x 10^-18/n^2 J and the radii of the stationary electron orbits are at r_n=2.65 x 10^-11 n^2 What is the difference between a He^+ ion and a helium atom? Calculate the radii of the n=2 and n=3 orbits of He^+ and show

Frequency of Motion

Solid, uniform cylinder of mass m and radius R is fitted with a frictionless axle along the cylinder's long axis. A horizontal spring (spring constant k) is attached to this axle. Under the influence of the spring, the cylinder rolls back and forth without slipping on a horizontal surface. What is the frequency of this motion?

Pulley Setup and Kinetic Energy

A m1 = 49.0 kg block and an m2 = 103.0 kg block are connected by a string as in Figure P7.28. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between the 49.0 kg block and incline is 0.250. Determine the change in the kinetic energy of the 49.0 kg block as it moves from A to B, a distance o

Solving for the Kinetic Energy

A thin hoop with a radius of 10 cm and a mass of 3kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy?

Calculating kinetic energy

What is the kinetic energy of a cylindrical shaft with a mass of 2.0 kg and a radius of 10 cm rotating about its central axis at 600 rads?

Solving for Height

An 11 kg bowling ball is dropped into a tub containing a mixture of ice and water. A short time later, when a new equilibrium has been established, there are 5.0 g less ice. From what height was the ball dropped? Part A Assume the bowling ball has an initial temperature of 0 degreesC, and that no water or ice splashes out.

Block Problems

1) A stationary block explodes into two pieces that slide along a frictionless floor and then into regions with friction, where they stop. The first piece, with a mass of 2.0 kg, encounters a coefficient of kinetic friction of 0.40 and slides to a stop in a distance 0.15 m. The second piece encounters a coefficient of kinetic fr

Photons of energy impinging upon helium ions

Photons of energy 65.561eV and 52.324eV impinge upon a collection of helium ions (He* , Z = 2). a. Can the photons of energy 65.561eV be absorbed by the helium ions without ejecting the electron from the ions if the electron is initially in the ground state? If so, to which state is the electron promoted? If not, why not?

Proton with Energy

(See attached file for full problem description) --- - Proton with energy 1.3 MeV is moving along a straight line ("0 degrees" in the figure) in the vacuum tube...

Photoelectric Effect: Photo-Tubes

Photo-tubes cut off (don't respond to photons) at sufficiently small wavelengths. This is because the photo-tube's glass does not transmit UV. They also cut off at sufficiently large wavelengths, where the glass does transmit the light. Why?

Mechanics: Conservation of momentum, friction, kinetic energy and motion.

A 62.0 kg person running at an initial speed of v1 = 3.90 m/s jumps onto a m = 124 kg cart initially at rest. (Figure) The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.350. Friction between the cart and ground can

Energy and Momentum: Rolling, Collision and Project

The task is to determine where the metal ball will land. First ball will begin at rest and travel through a track and elastically collide with the metal ball. This metal ball will then is defenestrated and drop down. Also determine where the metal ball will land. Clear explanation of each step is needed. When it is done, it is a

Potential energy and waves

A pulsed laser produces brief bursts of light. One such laser emits pulses that carry 0.350J of energy but last only 225fs. a) What is the average power during one of these pulses? b) Assuming the energy is emitted in a cylindrical beam of light 2.00mm in diameter, calculate the average intensity of one of the pulses? c) W

Momentum and Collisions on a Frictionless Surface

Please help me with this question: On a frictionless horizontal air table, puck A (with mass .250 kg) is moving toward puck B (with mass .350 kg), which is initially at rest. After the collision, puck A has a velocity of .120 m/s to the left, and puck B has velocity .650 m/s to the right. a) What was the speed of puck A b

Rotational Inertia Problem

A uniform solid sphere of mass 5 kg and radius of 30 cm is rotating about an axis through its center at a rate of 180 rev/min. Find the kinetic energy of the sphere. The rotational inertia of the sphere is 2/d MR^2.

Rotational Motion: Rod released on smooth horizontal plane

A thin rod of length h and mass M is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then released to fall freely. Determine the speed of its center of mass just before it hits the horizontal surface. Use h, M, and g for length, mass, and gravitational acceleration respectively. (b)

3 Physics Problems

(See attached files for full problem description with units and diagrams) --- A package of mass is released from rest at a warehouse loading dock and slides down a 3.0-m-high frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2 , from

Motion in a vertical circle: conservation of energy

A pendulum consists of a string of length L and a bob of mass M. The string is brought to a horizontal position and given the minimum initial speed enabling a pendulum to make a full turn in the vertical plane. a) what is the maximum kinetic energy K of the bob? b) what is the tension in the string when the kinetic energy is

Find compression of spring at bottom of incline

A block of mass m starts from rest at a height h and slides down a frictionless plane inclined at theta with the horizontal. The block strikes a spring of force constant k. Find the compression of the spring when the block is momentarily at rest.

Calculating the Power of a Pump

Question: A pump is required to lift 800 kg of water (about 210 gallons) per minute from a well 14.0m deep and eject it with a speed of 18.0 m/s. a) How much work is done per minute in lifting the water? b) How much in giving the water the kinetic energy it has when ejected? c) What must be the power outpu

How to calculate spring constant force

If an object with a mass of xkg on the end of a spring with a mass of ykg, is pulled 0.2 m away from equilibrium on a horizontal table and released where it achieves a max velocity of Zm/s at X=0, how do you calculate the spring constant?