All Related Questions of Potential Energy

Q: In Fig. 10.1, what kind of energy does

In Fig. 10.1, what kind of energy does ball A possess initially when at rest at the top of the hill? What kind of energies are involved as ball A moves down the hill? What kind of energy does ball A p...

Q: The combustion of methane, CH4, is an exothermic process.

The combustion of methane, CH4, is an exothermic process. Therefore, the products of this reaction must possess (higher/ lower) total potential energy than do the reactants.

Q: In deriving the ideal-gas equation from the kineticmolecular model,

In deriving the ideal-gas equation from the kineticmolecular model, we ignored potential energy due to the earth’s gravity. Is this omission justified? Why or why not?

Q: (a). Compute the increase in gravitational potential energy for a

(a). Compute the increase in gravitational potential energy for a nitrogen molecule (molar mass 28.0 g/mol) for an increase in elevation of 400 m near the earth’s surface. (b). At what temperature is...

Q: An ideal spring of negligible mass is 12.00 cm long

An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a 3.15-kg weight from it, you measure its length to be 13.40 cm. If you wanted to store 10.0 J of pote...

Q: A force of 520 N keeps a certain spring stretched a distance

A force of 520 N keeps a certain spring stretched a distance of 0.200 m. (a) What is the potential energy of the spring when it is stretched 0.200 m? (b) What is its potential energy when it is compre...

Q: A uniform 2.00-m ladder of mass 9.

A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of 53.0° with the floor. A worker pushes the ladder up against the wall until it is vertical. What is t...

Q: A spring stores potential energy U0 when it is compressed a distance

A spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length. (a) In terms of U0, how much energy does the spring store when it is compressed (i) twice as much...

Q: A slingshot will shoot a 10-g pebble 22.0

A slingshot will shoot a 10-g pebble 22.0 m straight up. (a) How much potential energy is stored in the slingshot’s rubber band? (b) With the same potential energy stored in the rubber band, how high...

Q: (a) A book is lifted upward a vertical distance of

(a) A book is lifted upward a vertical distance of 0.800 m. During this displacement, does the gravitational force acting on the book do positive work or negative work? Does the gravitational potentia...

Q: (a) A block of wood is pushed against a spring

(a) A block of wood is pushed against a spring, which is compressed 0.080 m. Does the force on the block exerted by the spring do positive or negative work? Does the potential energy stored in the spr...

Q: A spring of negligible mass has force constant k = 800 N

A spring of negligible mass has force constant k = 800 N/m. (a) How far must the spring be compressed for 1.20 J of potential energy to be stored in it? (b) You place the spring vertically with one en...

Q: Since only changes in potential energy are important in any problem,

Since only changes in potential energy are important in any problem, a student decides to let the elastic potential energy of a spring be zero when the spring is stretched a distance x1. The student d...

Q: Figure 7.22a shows the potential ­ energy function for the

Figure 7.22a shows the potential ­ energy function for the force Fx = -kx. Sketch the potential ­ energy function for the force Fx = +kx. For this force, is x = 0 a point of equi...

Q: A spring of negligible mass has force constant k = 1600 N

A spring of negligible mass has force constant k = 1600 N/m. (a) How far must the spring be compressed for 3.20 J of potential energy to be stored in it? (b) You place the spring vertically with one e...

Q: Based on Fig. P7.82, how much elastic potential

Based on Fig. P7.82, how much elastic potential energy is stored in the DNA when it is stretched 50 nm? (a) 2.5 × 10-19 J; (b) 1.2 × 10-19 J; (c) 5.0 × 10-12 J...

Q: A 2.50-kg mass is pushed against a horizontal

A 2.50-kg mass is pushed against a horizontal spring of force constant 25.0 N/cm on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any...

Q: You are asked to design a spring that will give a 1160

You are asked to design a spring that will give a 1160-kg satellite a speed of 2.50 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00g. The...

Q: Two blocks have a spring compressed between them, as in Exercise

Two blocks have a spring compressed between them, as in Exercise 8.24. The spring has force constant 720 N/m and is initially compressed 0.225 m from its original length. For each block, what is (a) t...

Q: A force parallel to the x-axis acts on a particle

A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy U(x) given by U(x)= ax4, where a = 0.630 J/m4. What is the force (magnitude and directio...

Q: A meter stick with a mass of 0.180 kg is

A meter stick with a mass of 0.180 kg is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released. As it swings th...

Q: The potential energy of a pair of hydrogen atoms separated by a

The potential energy of a pair of hydrogen atoms separated by a large distance x is given by U(x)= -C6>x6, where C6 is a positive constant. What is the force that one atom exerts on the other? Is this...

Q: The potential energy of two atoms in a diatomic molecule is approximated

The potential energy of two atoms in a diatomic molecule is approximated by U(r)=(a/r12)-1b/r62, where r is the spacing between atoms and a and b are positive constants. (a) Find the force F® on one a...

Q: Figure 7.22b shows the potential ­ energy function associated with

Figure 7.22b shows the potential ­ energy function associated with the gravitational force between an object and the earth. Use this graph to explain why objects always fall toward the eart...

Q: For a system of two particles we often let the potential energy

For a system of two particles we often let the potential energy for the force between the particles approach zero as the separation of the particles approaches infinity. If this choice is made, explai...

Q: The maximum height a typical human can jump from a crouched start

The maximum height a typical human can jump from a crouched start is about 60 cm. By how much does the gravitational potential energy increase for a 72­kg person in such a jump? Where does this energy...

Q: A crate of mass M starts from rest at the top of

A crate of mass M starts from rest at the top of a frictionless ramp inclined at an angle a above the horizontal. Find its speed at the bottom of the ramp, a distance d from where it started. Do this...

Q: Block A in Fig. E8.24 has mass 1.

Block A in Fig. E8.24 has mass 1.00 kg, and block B has mass 3.00 kg. The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level, frictionles...

Q: A 25.0-kg child plays on a swing having

A 25.0-kg child plays on a swing having support ropes that are 2.20 m long. Her brother pulls her back until the ropes are 42.0° from the vertical and releases her from rest. (a) What is her potential...

Q: Is it possible to have an arrangement of two point charges separated

Is it possible to have an arrangement of two point charges separated by a finite distance such that the electric potential energy of the arrangement is the same as if the two charges were infinitely f...

Q: An object with mass 0.200 kg is acted on by

An object with mass 0.200 kg is acted on by an elastic restoring force with force constant 10.0 N/m. (a) Graph elastic potential energy U as a function of displacement x over a range of x from -0.300...

Q: Ten days after it was launched toward Mars in December 1998,

Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass 629 kg) was 2.87 × 106 km from the earth and traveling at 1.20 × 104 km/h relative to the earth....

Q: A thin, uniform rod has length L and mass M.

A thin, uniform rod has length L and mass M. A small uniform sphere of mass m is placed a distance x from one end of the rod, along the axis of the rod (Fig. E13.34). (a) Calculate the gravitational...

Q: Consider the ring- shaped body of Fig. E13.35

Consider the ring- shaped body of Fig. E13.35. A particle with mass m is placed a distance x from the center of the ring, along the line through the center of the ring and perpendicular to its plane....

Q: A harmonic oscillator has angular frequency v and amplitude A.

A harmonic oscillator has angular frequency v and amplitude A. (a) What are the magnitudes of the displacement and velocity when the elastic potential energy is equal to the kinetic energy? (Assume th...

Q: A mass is oscillating with amplitude A at the end of a

A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic ene...

Q: A thrill-seeking cat with mass 4.00 kg is

A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion...

Q: The preceding problems in this chapter have assumed that the springs had

The preceding problems in this chapter have assumed that the springs had negligible mass. But of course no spring is completely massless. To find the effect of the spring’s mass, consider a spring wit...

Q: A rocket with mass 5.00 × 103 kg is in

A rocket with mass 5.00 × 103 kg is in a circular orbit of radius 7.20 × 106 m around the earth. The rocket’s engines fire for a period of time to increase that radius to 8.80 * 106 m, with the orbit...

Q: A shaft is drilled from the surface to the center of the

A shaft is drilled from the surface to the center of the earth. As in Example 13.10 (Section 13.6), make the unrealistic assumption that the density of the earth is uniform. With this approximation, t...

Q: An electron and a positron are moving toward each other and each

An electron and a positron are moving toward each other and each has speed 0.500c in the lab frame. a. What is the kinetic energy of each particle? b. The e+ and e- meet head-on and annihilate. What...

Q: A beam of alpha particles is incident on a target of lead

A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in “head-on” to a particular lead nucleus and stops 6.50 * 10-14 m away from the center of the nucleus. (Th...

Q: The energy-level scheme for the hypothetical one electron element Searsium

The energy-level scheme for the hypothetical one electron element Searsium is shown in Fig. E39.25. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus....

Q: The radii of atomic nuclei are of the order of 5.

The radii of atomic nuclei are of the order of 5.0 * 10-15 m. a. Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus. b. Take this uncertainty in momentum...

Q: The radii of atomic nuclei are of the order of 5.

The radii of atomic nuclei are of the order of 5.0 * 10-15 m. a. Estimate the minimum uncertainty in the momentum of an electron if it is confined within a nucleus. b. Take this uncertainty in momen...

Q: A particle with mass m moves in a potential energy U(

A particle with mass m moves in a potential energy U(x)= A x , where A is a positive constant. In a simplified picture, quarks (the constituents of protons, neutrons, and other particles, as will be d...

Q: Consider a particle with mass m moving in a potential U =

Consider a particle with mass m moving in a potential U = 1/2 kx2, as in a mass–spring system. The total energy of the particle is E =(p2/2m)+ 1/2 kx2. Assume that p and x are approximately related by...

Q: When radium-226 decays radioactively, it emits an alpha particle

When radium-226 decays radioactively, it emits an alpha particle (the nucleus of helium), and the end product is radon-222. We can model this decay by thinking of the radium-226 as consisting of an al...

Q: Figure P23.57 shows eight point charges arranged at the corners

Figure P23.57 shows eight point charges arranged at the corners of a cube with sides of length d. The values of the charges are +q and -q, as shown. This is a model of one cell of a cubic ionic crysta...

Q: Current materials-science technology allows engineers to construct capacitors with much

Current materials-science technology allows engineers to construct capacitors with much higher values of C than were previously possible. A capacitor has C = 3000 F and is rated to withstand a maximum...

Q: Electrons in an electric circuit pass through a resistor. The wire

Electrons in an electric circuit pass through a resistor. The wire on either side of the resistor has the same diameter. (a). How does the drift speed of the electrons before entering the resistor com...

Q: A point charge q1 = 4.00 nC is placed at

A point charge q1 = 4.00 nC is placed at the origin, and a second point charge q2 = -3.00 nC is placed on the x-axis at x = +20.0 cm. A third point charge q3 = 2.00 nC is to be placed on the x-axis be...

Q: (a). Calculate the potential energy of a system of two

(a). Calculate the potential energy of a system of two small spheres, one carrying a charge of 2.00 µC and the other a charge of -3.50 µC, with their centers separated by a distance of 0.180 m. Assume...

Q: (a). Calculate the electric potential energy of the adenine–

(a). Calculate the electric potential energy of the adenine–thymine bond, using the same combinations of molecules (O-H-N and N-H-N) as in Exercise 21.21. Exercise 21.21: (a). Calculate the net for...

Q: Three equal 1.20-µC point charges are placed at

Three equal 1.20-µC point charges are placed at the corners of an equilateral triangle with sides 0.400 m long. What is the potential energy of the system? (Take as zero the potential energy of the th...

Q: A point charge q1 is held stationary at the origin. A

A point charge q1 is held stationary at the origin. A second charge q2 is placed at point a, and the electric potential energy of the pair of charges is +5.4 × 10-8 J. When the second charge is moved...

Q: Two large, parallel, metal plates carry opposite charges of equal

Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated by 45.0 mm, and the potential difference between them is 360 V. (a). What is the magnitude of the elect...

Q: In classical (Newtonian) mechanics, the total energy E of

In classical (Newtonian) mechanics, the total energy E of a particle can never be less than the potential energy U because the kinetic energy K cannot be negative. Yet in barrier tunneling (see Sectio...

Q: a. Calculate the electric potential energy for a K+ ion

a. Calculate the electric potential energy for a K+ ion and a Br- ion separated by a distance of 0.29 nm, the equilibrium separation in the KBr molecule. Treat the ions as point charges. b. The ioniz...

Q: A fellow student proposes that a possible wave function for a free

A fellow student proposes that a possible wave function for a free particle with mass m (one for which the potential energy function U(x) is zero) is where κ is a positive constant. a....

Q: a. For the finite potential well of Fig. 40.

a. For the finite potential well of Fig. 40.13, what relationships among the constants A and B of Eq. (40.38) and C and D of Eq. (40.40) are obtained by applying the boundary condition that c be conti...

Q: Consider a hydrogen atom in the 1s state. a.

Consider a hydrogen atom in the 1s state. a. For what value of r is the potential energy U(r) equal to the total energy E? Express your answer in terms of a. This value of r is called the classical t...

Q: The one­dimensional calculation of Example 42.4 (Section

The one­dimensional calculation of Example 42.4 (Section 42.3) can be extended to three dimensions. For the three dimensional fcc NaCl lattice, the result for the potential energy of a pair...

Q: It can be a challenge to solve the Schrödinger equation for the

It can be a challenge to solve the Schrödinger equation for the bound-state energy levels of an arbitrary potential well. An alternative approach that can yield good approximate results f...

Q: Protons, neutrons, and many other particles are made of more

Protons, neutrons, and many other particles are made of more fundamental particles called quarks and antiquarks (the antimatter equivalent of quarks). A quark and an antiquark can form a bound state w...

Q: Consider a simple model of the helium atom in which two electrons

Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum Ä&...

Q: A coil with magnetic moment 1.45 A ∙ m2 is

A coil with magnetic moment 1.45 A ∙ m2 is oriented initially with its magnetic moment antiparallel to a uniform 0.835-T magnetic field. What is the change in potential energy of the coil when it is r...

Q: A small rubber ball (weight W = 450 Nm) is

A small rubber ball (weight W = 450 Nm) is attached by a rubber cord to a wood paddle (see figure). The natural length of the cord is Lo = 200 mm, its cross-sectional area is A = 1.6 mm2, and its modu...

Q: Consider the following reaction: / The following rate

Consider the following reaction: The following rate equation has been experimentally established for this process Rate = k[HO−][CH3CH2Br] An energy diagram for this process is show...

Q: Consider the relative energy diagrams for four different processes: /

Consider the relative energy diagrams for four different processes: a. Compare energy diagrams A and D. Assuming all other factors (such as concentrations and temperature) are identical for the two p...

Q: Suppose that a solid ball (a marble), a hollow ball

Suppose that a solid ball (a marble), a hollow ball (a squash ball), a solid cylinder (a steel bar), and a hollow cylinder (a lead pipe) roll down a slope. Which of these objects reaches the bottom fi...

Q: Sketch a potential energy diagram for a reaction that shows the effect

Sketch a potential energy diagram for a reaction that shows the effect of a catalyst on an endothermic reaction.

Q: Calculate the elastic potential energy of a spring with spring constant k

Calculate the elastic potential energy of a spring with spring constant k = 225 N/m that is (a) Compressed and (b) Stretched by 1.00 x 10-2 m.

Q: True or False: The elastic potential energy of a stretched or

True or False: The elastic potential energy of a stretched or compressed spring is always positive.

Q: Elastic potential energy depends on the spring constant and the distance the

Elastic potential energy depends on the spring constant and the distance the spring is stretched or compressed. By what factor does the elastic potential energy change if the spring’s stretch is (a) D...

Q: (a) Can the kinetic energy of a system be negative

(a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.

Q: Two stones, one with twice the mass of the other,

Two stones, one with twice the mass of the other, are thrown straight up and rise to the same height h. Compare their changes in gravitational potential energy (choose one): (a) They rise to the same...

Q: A 0.20 - kg stone is held 1.3

A 0.20 - kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Taking y = 0 at the top edge of the well, what is the gravitational potentia...

Q: A block of mass 3.00 kg is placed against a

A block of mass 3.00 kg is placed against a horizontal spring of constant k = 875 N/m and pushed so the spring compresses by 0.070 0 m. (a) What is the elastic potential energy of the block–spring sys...

Q: A 60.0 - kg athlete leaps straight up into the

A 60.0 - kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.0 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum...

Q: A flea is able to jump about 0.5 m.

A flea is able to jump about 0.5 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100 - story building! When an animal jumps, it converts work done in contrac...

Q: A child of mass m starts from rest and slides without friction

A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserv...

Q: A roller - coaster car of mass 1.50 x 103

A roller - coaster car of mass 1.50 x 103 kg is initially at the top of a rise at point Ⓐ. It then moves 35.0 m at an angle of 50.0° below the horizontal to a lower point Ⓑ. (a) Find both the potentia...

Q: A 2.00 x 102 - g particle is released from

A 2.00 x 102 - g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R = 30.0 cm (Fig. P5.71). Calculate (a) Its gravitational potential energy at A relati...

Q: A 5.0 - kg block is pushed 3.0

A 5.0 - kg block is pushed 3.0 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of θ = 30° with the horizontal, as shown in Figur...

Q: After the Sun exhausts its nuclear fuel, its ultimate fate may

After the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be eq...

Q: A light rod of length 2L is free to rotate in a

A light rod of length 2L is free to rotate in a vertical plane about a frictionless pivot through its center. A particle of mass m1 is attached at one end of the rod, and a mass m2 is at the opposite...

Q: An object – spring system moving with simple harmonic motion has an

An object – spring system moving with simple harmonic motion has an amplitude A. (a) What is the total energy of the system in terms of k and A only? (b) Suppose at a certain instant the kinetic energ...

Q: A horizontal block – spring system with the block on a frictionless

A horizontal block – spring system with the block on a frictionless surface has total mechanical energy E = 47.0 J and a maximum displacement from equilibrium of 0.240 m. (a) What is the spring consta...

Q: A horizontal spring attached to a wall has a force constant of

A horizontal spring attached to a wall has a force constant of k = 8.50 x 102 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface as in Figure P1...

Q: An object executes simple harmonic motion with an amplitude A.

An object executes simple harmonic motion with an amplitude A. (a) At what values of its position does its speed equal half its maximum speed? (b) At what values of its position does its potential ene...

Q: A slingshot consists of a light leather cup containing a stone.

A slingshot consists of a light leather cup containing a stone. The cup is pulled back against two parallel rubber bands. It takes a force of 15.0 N to stretch either one of these bands 1.00 cm. (a) W...

Q: A 3.00-g copper coin at 25.0

A 3.00-g copper coin at 25.0°C drops 50.0 m to the ground. (a) Assuming 60.0% of the change in gravitational potential energy of the coin–Earth system goes into increasing the internal energy of the c...

Q: The apparatus shown in Figure P11.12 was used by Joule

The apparatus shown in Figure P11.12 was used by Joule to measure the mechanical equivalent of heat. Work is done on the water by a rotating paddle wheel, which is driven by two blocks falling at a co...

Q: A uniform electric field of magnitude 375 N/C pointing in

A uniform electric field of magnitude 375 N/C pointing in the positive x - direction acts on an electron, which is initially at rest. After the electron has moved 3.20 cm, what is (a) The work done by...

Q: Two point charges Q1 = +5.00 nC and Q2

Two point charges Q1 = +5.00 nC and Q2 = -3.00 nC are separated by 35.0 cm. (a) What is the electric potential at a point midway between the charges? (b) What is the potential energy of the pair of ch...

Q: A proton is located at the origin, and a second proton

A proton is located at the origin, and a second proton is located on the x - axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) A...

Q: An electric field does 1.50 x 103 eV of work

An electric field does 1.50 x 103 eV of work on a carbon nucleus of charge 9.61 x 10-19 C. Find the change in the nucleus’ (a) Electric potential and (b) Electric potential energy in joules.

Q: In the classical model of a hydrogen atom, an electron orbits

In the classical model of a hydrogen atom, an electron orbits a proton with a kinetic energy of +13.6 eV and an electric potential energy of -27.2 eV. (a) Use the kinetic energy to calculate the class...

Q: Two positive charges each of charge q are fixed on the y

Two positive charges each of charge q are fixed on the y - axis, one at y = d and the other at y = -d as in Figure P16.70. A third positive charge 2q located on the x - axis at x = 2d is released from...

Q: If an electron is released from rest in a uniform electric field

If an electron is released from rest in a uniform electric field, does the electric potential energy of the charge – field system (a) Increase, (b) Decrease, or (c) Remain the same?

Q: Consider a collection of charges in a given region and suppose all

Consider a collection of charges in a given region and suppose all other charges are distant and have a negligible effect. Further, the electric potential is taken to be zero at infinity. If the elect...

Q: A person’s basal metabolic rate (BMR) is the rate at

A person’s basal metabolic rate (BMR) is the rate at which energy is expended while resting in a neutrally temperate environment. A typical BMR is 7.00 x 106 J/day. Convert this BMR to units of (a) Wa...

Q: An electric eel generates electric currents through its highly specialized Hunter’s organ

An electric eel generates electric currents through its highly specialized Hunter’s organ, in which thousands of disk - shaped cells called electrocytes are lined up in series, very much in the same w...

Q: An equation for potential energy states U = mgy. If U

An equation for potential energy states U = mgy. If U is in joules (J), with m in kg, y in m, and g in m/s2, find the combination of SI base units that is equivalent to joules.

Q: An equation for potential energy states U = mgh. If U

An equation for potential energy states U = mgh. If U is in kg·m2·s−2, m is in kg, and g is in m·s−2, what are the units of h? (a) s (b) s2 (c) m−1 (d) m (e) g-1

Q: For a hydrogen atom in its ground state, use the Bohr

For a hydrogen atom in its ground state, use the Bohr model to compute (a) The orbital speed of the electron, (b) The kinetic energy of the electron, and (c) The electrical potential energy of the ato...

Q: (a) Write an expression relating the kinetic energy KE of

(a) Write an expression relating the kinetic energy KE of the electron and the potential energy PE in the Bohr model of the hydrogen atom. (b) Suppose a hydrogen atom absorbs a photon of energy E, res...

Q: The “size” of the atom in Rutherford’s model is about

The “size” of the atom in Rutherford’s model is about 1.0 x 10-10 m. (a) Determine the attractive electrostatic force between an electron and a proton separated by this distance. (b) Determine (in eV)...

Q: An alpha particle (Z = 2, mass = 6.

An alpha particle (Z = 2, mass = 6.64 x 10-27 kg) approaches to within 1.00 x 10-14 m of a carbon nucleus (Z = 6). What are (a) The maximum Coulomb force on the alpha particle, (b) The acceleration of...

Q: Frito-Lay, the multi-billion-dollar snack food

Frito-Lay, the multi-billion-dollar snack food giant, requires vast amounts of water, electricity, natural gas, and fuel to produce its 41 well-known brands. In keeping with growing environmental conc...

Q: Consider the falling of a rock off a cliff into seawater,

Consider the falling of a rock off a cliff into seawater, and eventually settling at the bottom of the sea. Starting with the potential energy of the rock, identify the energy transfers and transforma...

Q: The temperature of air changes from 0 to 10°C while

The temperature of air changes from 0 to 10°C while its velocity changes from zero to a final velocity, and its elevation changes from zero to a final elevation. At which values of final air velocity...

Q: A 15.0 g conducting rod of length 1.30

A 15.0 g conducting rod of length 1.30 m is free to slide downward between two vertical rails without friction. The ends of the rod maintain electrical contact with the rails. The rails are connected...

Q: A charge Q = −50.0 nC is located 0

A charge Q = −50.0 nC is located 0.30 m from point A and 0.50 m from point B. (a) What is the potential at A? (b) What is the potential at B? (c) If a point charge q is moved from...

Q: An object oscillates up and down between y = +A and

An object oscillates up and down between y = +A and y = −A at the end of a stretched spring. (a) At what point(s) is the kinetic energy maximum? (Give the value(s) of y.) (b) At what point(s) is the...

Q: A 230.0 g object on a spring oscillates on a

A 230.0 g object on a spring oscillates on a frictionless horizontal surface with frequency 2.00 Hz and amplitude 8.00 cm. Its position as a function of time is given by x = A sin ωt. (a) Sketch a gr...

Q: The potential energy associated with surface tension is much like the elastic

The potential energy associated with surface tension is much like the elastic potential energy of a stretched spring or a balloon. Suppose we do work on a puddle of liquid, spreading it out through a...

Q: A beam of electrons of mass me is deflected vertically by the

A beam of electrons of mass me is deflected vertically by the uniform electric field between two oppositely charged, parallel metal plates. The plates are a distance d apart, and the potential differe...

Q: A satellite is placed in a noncircular orbit about Earth. The

A satellite is placed in a noncircular orbit about Earth. The farthest point of its orbit (apogee) is 4.0 Earth radii from the center of Earth, while its nearest point (perigee) is 2.0 Earth radii fro...

Q: A particle is confined to & finite box of length L.

A particle is confined to & finite box of length L. In the nth state, the wave function has n − 1 nodes. The wave function must make a smooth transition from sinusoidal inside th...

Q: (a) If the bottom of a thundercloud has a potential

(a) If the bottom of a thundercloud has a potential of −1.00 × 109 V with respect to Earth and a charge of −20.0 C is discharged from the cloud to Earth during a lightning strike, how much electric po...

Q: Emil is tossing an orange of mass 0.30 kg into

Emil is tossing an orange of mass 0.30 kg into the air. (a) Emil throws the orange straight up and then catches it, throwing and catching it at the same point in space. What is the change in the pote...

Q: An arrangement of two pulleys, as shown in the figure,

An arrangement of two pulleys, as shown in the figure, is used to lift a 48.0 kg crate a distance of 4.00 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections a...

Q: What is the potential energy if a third point charge q =

What is the potential energy if a third point charge q = −4.2 nC is placed at point a?

Q: (a) In the diagram, what are the potentials at

(a) In the diagram, what are the potentials at points a and b? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q3 = +2.00 nC is moved from point a to poin...

Q: (a) In the diagram, what are the potentials at

(a) In the diagram, what are the potentials at points b and c? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q3 = +2.00 nC is moved from point b to poin...

Q: The gravitational potential energy of a pendulum is U = mgy.

The gravitational potential energy of a pendulum is U = mgy. (a) Taking y = 0 at the lowest point, show that y = L(1 − cos θ), where θ is the angle the stri...

Q: What is the potential energy if a third point charge q =

What is the potential energy if a third point charge q = −4.2 nC is placed at point c?

Q: Find the electric potential energy for the following array of charges:

Find the electric potential energy for the following array of charges: charge q1 = +4.0 µC is located at (x, y) = (0.0, 0.0) m; charge q2 = +3.0 µC is located at (4.0, 3.0) m; and charge q3 = −1.0 µC...

Q: (a) Calculate the change in potential energy of 1 kg

(a) Calculate the change in potential energy of 1 kg of water as it passes over Niagara Falls (a vertical descent of 50 m). (b) At what rate is gravitational potential energy lost by the water of the...

Q: Resilin is a rubber-like protein that helps insects to fly

Resilin is a rubber-like protein that helps insects to fly more efficiently. The resilin, attached from the wing to the body, is relaxed when the wing is down and is extended when the wing is up. As t...

Q: What is the potential energy for these two charges?

What is the potential energy for these two charges?

Q: How much energy is converted by the muscles of an 80.

How much energy is converted by the muscles of an 80.0 kg person in climbing a vertical distance of 15 m? Assume that muscles have an efficiency of 22%; that is, the increase in gravitational potentia...

Q: Justin moves a desk 5.0 m across a level floor

Justin moves a desk 5.0 m across a level floor by pushing on it with a constant horizontal force of 340 N. (It slides for a negligibly small distance before coming to a stop when the force is removed....

Q: The bottom of a thundercloud is at a potential of −1

The bottom of a thundercloud is at a potential of −1.00 × 108 V with respect to Earth's surface. If a charge of −25.0 C is transferred to Earth during a lightning strike, find the electric potential e...

Q: Human feet and legs store elastic energy when walking or running.

Human feet and legs store elastic energy when walking or running. They are not nearly as efficient at doing so as kangaroo legs, but the effect is significant nonetheless. If not for the storage of el...

Q: The particle has a total mechanical energy of −100 J.

The particle has a total mechanical energy of −100 J. At time t = 0, the particle is located at x = 8.0 cm and is moving to the left. (a) What is the particle’s potential energy at t = 0? What is its...

Q: A spring used in an introductory physics laboratory stores 10.0

A spring used in an introductory physics laboratory stores 10.0 J of elastic potential energy when it is compressed 0.20 m. Suppose the spring is cut in half. When one of the halves is compressed by 0...

Q: Use this method to find how the speed with which animals of

Use this method to find how the speed with which animals of similar shape can run up a hill depends on the size of the animal. Let L represent some characteristic length, such as the height or diamete...

Q: Multiple-Choice Questions 7–12 refer to a situation in

Multiple-Choice Questions 7–12 refer to a situation in which a golf ball is projected straight upward in the +y-direction. Ignore air resistance. The answer choices are found in the...

Q: Questions 11–20. See the graph of vx(t

Questions 11–20. See the graph of vx(t) for an object in SHM. Answer choices for each question: (a) 1 s, 2 s, 3 s (b) 5 s, 6 s, 7 s (c) 0 s, 1 s, 7 s, 8 s (d) 3 s, 4 s, 5 s (e) 0 s,...

Q: Three point charges are placed at the corners of an equilateral triangle

Three point charges are placed at the corners of an equilateral triangle having sides of 0.150 m. (a) What is the total electric force on the 2.50 µC charge? (b) What is the electric pot...

Q: Two point charges (+10.0 nC and −10.

Two point charges (+10.0 nC and −10.0 nC) are located 8.00 cm apart. (a) What is the change in electric potential energy when a third point charge of −4.2 nC is mo...

Q: The length of a spring increases by 7.2 cm from

The length of a spring increases by 7.2 cm from its relaxed length when a mass of 1.4 kg is hanging in equilibrium from the spring. (a) What is the spring constant? (b) How much elastic potential en...

Q: An above-ground swimming pool is filled with water (total

An above-ground swimming pool is filled with water (total mass M) to a height h. Explain why the gravitational potential energy of the water (taking U = 0 at ground level) is /. Where does the factor...

Q: What is the potential energy if a third point charge q =

What is the potential energy if a third point charge q = −4.2 nC is placed at point b?

Q: A point charge moves to a region of higher potential and yet

A point charge moves to a region of higher potential and yet the electric potential energy decreases. How is this possible?

Q: A negatively charged particle with charge −q is far away from

A negatively charged particle with charge −q is far away from a positive charge +Q that is fixed in place. As −q moves closer to +Q, (a) does the electric field do positive or negative work? (b) Does...

Q: Sean climbs a tower that is 82.3 m high to

Sean climbs a tower that is 82.3 m high to make a jump with a parachute. The mass of Sean plus the parachute is 68.0 kg. If U = 0 at ground level, what is the potential energy of Sean and the parachut...

Q: 1. After getting on the Santa Monica Freeway, a sports

1. After getting on the Santa Monica Freeway, a sports car accelerates from 30 mi/h to 90 mi/h. Its kinetic energy (a) increases by a factor of /. (b) increases by a factor of 3. (c) increases by a...

Q: An electron is released from rest and falls under the influence of

An electron is released from rest and falls under the influence of gravity. In the first centimeter, what fraction of the potential energy lost is radiated away?

Q: A charged particle, traveling in from /along the x axis

A charged particle, traveling in from /along the x axis, encounters a rectangular potential energy barrier Show that, because of the radiation reaction, it is possible for the particle to tunnel throu...

Q: The drag on the hull of a ship depends in part on

The drag on the hull of a ship depends in part on the height of the water waves produced by the hull. The potential energy associated with these waves therefore depends on the acceleration of gravity...