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# Energy

### kinetic energy of the cricket

It takes 4.186 of energy to raise the temperature of 1.00 of water by 1.00 degree. How fast would a 2.00 kg cricket have to jump to have that much kinetic energy? How fast would a 4.00 kg cricket have to jump to have the same amount of kinetic energy? v = ? m/s

### Superball Collides With a Table. To determine change in momentum.

As shown in the figure (see attachment), a superball with mass m equal to 50 grams is dropped from a height of h1= 1.5 m. It collides with a table, then bounces up to a height of h2= 1.0 m. The duration of the collision (the time during which the superball is in contact with the table) is tc= 15 ms. In this problem, take the

### Object with mass, initially at rest, explodes into two fragments

An object with mass m, initially at rest, explodes into two fragments, one with mass m_A and the other with mass m_B, where m_A + m_B = m. a). If energy Q is released in the explosion, how much kinetic energy does each fragment have immediately after the collision? Express your answers in terms of the variables m_A, m_B, an

### Force and Direction on a Particle

A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in the figure. The particle is released from rest at point A. a). What is the direction of the force on the particle when it is at point A? (Positive or Negativ

### difference between the tensions in the string

A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, th

### Angular Momentum Equal Mass

Please see attached. 1. The two spheres of equal mass m are able to slide along the rotating horizontal black rod. If they are initially latched in position a distance r from the axis of rotation with the assembly rotating freely with an angular velocity of Wo. Determine the new angular velocity Wf after the spheres are rele

### Calculate the maximum velocity of slider

Please see attached...solve using energy equations, ie, potential, kinetic Calculate the maximum velocity of slider B if the system is released from rest with X = Y (the red line is a frictionless, mass less linkage of length .9 m ) Motion is in the vertical plane. Friction is negligible and the masses of A and B are equal

### Spring Problem - Stored Energy

A block of mass m slides without friction on a table with speed v. It hits and compresses a spring of force constant k by a distance l. The spring then expands again ejecting the block in the opposite direction as it was originally traveling. Neglecting the mass of the spring, what is the speed of the object after it is ejected

### Springs and Slopes

A spring of constant k, compressed a distance x, is used to launch a mass m up a frictionless slope that makes an angle "theta" with the horizontal. Find an expression for the maximum distance along the slope that the mass moves after leaving the spring? How is the expression modified when you include kinetic friction in the pro

### Two problems on capacitors.

1. A controller on an electronic arcade game consists of a variable resistor connected across the plates of a 0.22 micro Farad capacitor. The capacitor is charged to 5.00V, then discharged through the resistor. The time for the potential difference across the plates to decrease to 0.800V is measured by a clock inside the game

### Excited States of Non-Interacting Fermion and Bose Systems

See attached file.

### Magnetic energy of solar flare

The problem reads as: "The magnetic field permeating a region of space represents stored energy. This energy is often quantified in terms of its density (magnetic energy per unit volume) given by B^2/(2*u) where u=4*pi X 10^(-7). Suppose an "X2" flare occurs within a volume of 10^12 km3 over a sunspot pair initially permeate

### the kinetic energy of the electrons in the beam

A beam of electrons, each with the same kinetic energy, illuminates a pair of slits separated by a distance of 52 nm. The beam forms bright and dark fringes on a screen located a distance 2.3 m beyond the two slits. The arrangement is otherwise identical to that used in the optical two-slit interference experiment. The brigh

### Charged spheres

1. A thin, spherical, conducting shell of radius R is mounted on an insulating support and charged to a potential of -125V. An electron is then fired directly toward the center of the shell, from point P at distance r from the center of the shell ( r>>R). What initial speed Vo is needed for the electron to just re

### minimum surface charge density on the plate to stop protons

Protons exit a high speed proton machine at a speed of 1.50 * 10^6 m/s. A device needs to stop the protons safely. Protons will embed themselves in a metal target, but protons traveling faster than 1.30 * 10^5 m/s emit dangerous x rays when they hit. The protons must be slowed down to an acceptable speed, then let them hit a

### A charged parallel plate capacitor with insertion of a dielectric slab.

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False. 1. Aft

### Special Relativity - Energy Problems

A particle of mass 3.5 MeV/c2 and kinetic energy 4.5 MeV collides with a stationary particle of mass 0.5 MeV/c2 . After the collision, the particles stick together. (part 1 of 5) Find the total energy of the first particle before the collision. Answer in units of MeV. (part 2 of 5) Find the speed of the first particl

### For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy.

For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy. Prove that the first order energy correction vanishes for all n = odd integer excited state levels.

### Loop the loop speed

See attached file for full problem description. A small object, released from a height of 15m slides along the frictionless loop-the-loop with a diameter of 4.3m. What is its speed at the top of the loop?

### Measuring the speed of a bullet

You need to verify which gun fired a bullet in a police investigation with a very limited budget. There are two guns involved in a crime; both could fire bullets of the same kind of mass (0.1kg). One is an assault rifle which fires the bullet at speed of 300m/s; the other is a hand gun which fires the same bullet with speed of 2

### emissivity and radiation

A.) The filament of a light bulb has a temperature of 3.1 103 °C and radiates 70 watts of power. The emissivity of the filament is 0.38. Find the surface area of the filament. B.) A car parked in the sun absorbs energy at a rate of 550 watts per square meter of surface area. The car reaches a temperature at which it radiat

### Heat intensity

A dish of lasagna is being heated in a microwave oven. The effective area of the lasagna that is exposed to the microwaves is 1.6 10-2 m2. The mass of the lasagna is 0.26 kg, and its specific heat capacity is 3400 J/(kg°C). The temperature rises by 80.0°C in 7.0 minutes. What is the intensity of the microwaves in the oven?

### Possibility of Perpetual Motion Machine

Physicists say that it is impossible to create a perpetual motion machine, a machine whose own activity keeps it running perpetually. What energy principle precludes the possibility of a perpetual motion machine?

### Water skiing: determining height

A water skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of 16.4 m/s. As the drawing indicates, the skier has a speed of 13.0 m/s at the highest point of the jump. Ignoring air resistance, determine the skier's height H above the top of the ramp at the highest point.

### Relativistic Electric Potential Difference

For this question you need to know that an electron accelerated through an electric potential difference of V volts acquires a kinetic energy of V eV. (This question is best done by not converting to joules, but by exploiting the fact that mec2 is given as 0.511 MeV). i) What is v/c for an electron? a) Striking the screen

### A Parallel Plate Air Capacitor

The plates of a parallel plate air capacitor are 1.2 nm apart and area of each plate is 20 x 10^-4 m^2. Find the capacitance. It is connected to a 40 V battery. (i) What is the charge on each plate? (ii) What is the energy stored in the capacitor? Repeat the calculations for the same capacitor with the air gap re

### Determine the Speed of the Gear Rack

The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed of the rack when s = 600 mm. The gears are free to turn about their centers, A and B. (See attached file for fig. and

### A .15kg block of ice is placed on a horizontal table. It is pushed back compressing a spring .045m, and the spring's constant is 1900N/m. The spring's mass is negligible. The tabletop is 1.2m above the floor. When the spring is released, the block slides off the table and onto the floor. With negligible friction between the block and the table, what is the speed of the block when it hits the floor?

A .15kg block of ice is placed on a horizontal table. It is pushed back compressing a spring .045m, and the spring's constant is 1900N/m. The spring's mass is negligible. The tabletop is 1.2m above the floor. When the spring is released, the block slides off the table and onto the floor. With negligible friction between the

### Electrostatic Energy and Capacitance

A capacitor has a charge of 30 uC (fancy u). The potential difference between the conductors is 400 is V. What is the capacitance?

### Electrostatic Energy

A cylindrical capacitor consists of a long wire of radius R, and length L with a charge +Q and a concentric outer cylindrical shell of radius Rsub2, length L, and a charge -Q. (a) find the electric field and energy density at any point in space. b(b) how much energy resides in cylindrical shell between the conductors of radius