Two equal-sized newspapers have an overlap circulation of 10% (10% of the subscribers subscribe to both newspapers). Advertisers are willing to pay $15 to advertise in one newspaper but only $29 to advertise in both, because they're unwilling to pay twice to reach the same subscriber. Suppose the advertisers bargain by telling each newspaper that they're going to reach agreement with the other newspaper, whereby they pay the other newspaper $14 to advertise.

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Two equal-sized newspapers have an overlap circulation of 10% (10% of the subscribers subscribe to both newspapers). Advertisers are willing to pay $15 to advertise in one newspaper but only $29 to advertise in both, because they’re unwilling to pay twice to reach the same subscriber. Suppose the advertisers bargain by telling each newspaper that they’re going to reach agreement with the other newspaper, whereby they pay the other newspaper $14 to advertise.

According to the nonstrategic view of bargaining, each newspaper would earn

of the $14 in value added by reaching an agreement with the advertisers. The total gain for the two newspapers from reaching an agreement is

.

Suppose the two newspapers merge. As such, the advertisers can no longer bargain by telling each newspaper that they’re going to reach agreement with the other newspaper. Thus, the total gains for the two parties (the advertisers and the merged newspapers) from reaching an agreement with the advertisers are $14.

In what sense does the moon fall? · How does the force of gravity between two bodies change when the distance between them is tripled?

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· In what sense does the moon fall?
· How does the force of gravity between two bodies change when the distance between them is tripled?
· Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Accelerated downward? Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that moved upward at a constant velocity? In an elevator that moved downward at constant velocity?
· Explain why occupants of the International Space Station are firmly in the grip of Earth’s gravity, even though they have no weight.
· A stone is thrown up at an angle. Neglecting air resistance, what happens to the horizontal component of its velocity along its trajectory? The vertical component?
· A projectile is launched vertically at 100 m/s. If air resistance can be neglected, at what speed does it return to its initial level?
· What happens to an object close to Earth’s surface if it is given a speed exceeding 11.2km/s?

1) Billy Bob “Bubba” Hickman is working in his barn one day. He has a 25 kg hay bale suspended from the barn's rafters on a 2.44 meter long rope. Bubba pulls on another rope horizontally until the rope holding the hay bale makes an angle of 20 degrees with respect to the vertical. a) What force does Bubba have to exert on the rope to hold the hay bale in this position?

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1) Billy Bob “Bubba” Hickman is working in his barn one day. He has a 25 kg hay bale suspended from the barn’s rafters on a 2.44 meter long rope. Bubba pulls on another rope horizontally until the rope holding the hay bale makes an angle of 20 degrees with respect to the vertical.
a) What force does Bubba have to exert on the rope to hold the hay bale in this position?
b) The rope slips out of Bubba’s hands. The hay bale starts to swing. How long does it take for the hay bale to swing to the farthest distance from where it started (the farthest distance across the barn)?
c) Bubba runs to catch the hay bale. He tries to catch it at the bottom of the swing as it swings back towards him. How fast is the hay bale moving when it hits Bubba?
2) A narrow metal rod, of mass 1.22 kg and length 2.05 meters is free to rotate about one end of the rod.
a) What is the moment of inertia of the rod?
b) How much work is needed to make the rod go from rest to swinging at 10 revolutions per minute?
3) Bubba has a mass of 75.3 kilogram and stands in the center of a 4.12 meter long uniform board. The board has a mass of 16.2 kg. The board is supported on each end by cables, each of which can sustain a maximum tensile force of 564 Newtons before breaking. How far from the center of the board can Bubba walk before one of the cables breaks?
4) The elevator at a diamond mine is supported by a single steel cable of diameter 1.28cm. The total mass of the elevator and cable is 670kg. When the elevator is at surface level, it is 12m below the pulley holding the cable.
a) Determine the stress and strain on the cable when the elevator is at the surface level.
b) By how much does the cable stretch when the elevator has been lowered a distance of 350m below the surface of the ground.
c) What is the maximum mass that the elevator and its occupants may have before the cable breaks? (Neglect the mass of the cable.)
5) Ceres, the largest object in the asteroid belt, has a mass of 9.43×1020 kg and a radius of 487 km. a) What is the acceleration due to gravity at the surface of Ceres?
b) What would be the orbital period of a satellite if it were to orbit Ceres at a distance of 925 km above its surface?
6) A 425 gram mass is attached to a horizontal spring. The spring is known to have a spring constant of 84.6 N/m. The mass is free to slide along a frictionless surface.
a) The mass is then pulled to the side a distance of 5.67 cm and released. Determine the period and amplitude of the resulting oscillations.
b) Determine the magnitude of the maximum velocity of the mass, and state where it reaches that maximum velocity.
7) A harmonic oscillator moves according to the equation: x=(13.8 cm)cos(11.7s−1t+ 0.77) .
a) What is the period of this oscillation?
b) What is the amplitude of this oscillation?
c) What is the maximum velocity of this oscillation?
d) What is the maximum acceleration of this oscillation?
8) Bubba sets a 1.25kg solid sphere of diameter 11.5cm at the top end of a 1.75m long board that is inclined an angle of 15 degrees relative to the horizontal. The sphere rolls down the incline without slipping.
a) Determine the linear speed of the sphere at the bottom of the incline.
b) Determine the rotational rate of the sphere at the bottom of the incline.
c) Determine how many times the sphere executed a complete rotation before it reached the bottom of the incline.
9) Consider a solid iron hollow cylinder (inner diameter 10.4 cm, outer diameter 18.8 cm, and length 45.0cm). (The density of iron is 7.874 gm/cm3.) a) Determine the mass of the cylinder.
b) Determine the moment of inertia of the cylinder if it spins about its long axis.
c) If the cylinder were spinning at 76.6 rpm, and brake pads were applied to the inner surface of the cylinder (like in drum brakes), how much force would be needed pressing the pads into the cylinder walls to stop the cylinder in 12.3 seconds? Assume that the coefficient of kinetic friction between the pads and the cylinder is 0.445.
10) A rotating metal plate of length 26cm and width 21cm is spinning about its center of mass at 22.3 radians per second. The metal plate has mass 22.4 kg. A solid cylinder of mass 34.3 kg and diameter 16cm is dropped onto the center of the rotating plate.
a) Determine the final speed of rotation of the system.
b) Determine the change in kinetic energy of the system.
Material Properties
Properties of Aluminum (Al): Density: 2700 kg/m3 Young’s Modulus: 6.5×1010 N/m2 Specific Heat: 921 J/(kg C°) Ultimate Strength: 1.10×108 N/m2 Resistivity: 2.8×10-6 Ω∙cm Melting Point: 660° C Boiling Point: 2519° C Coefficient of Linear Thermal Expansion: 2.40×10-5 1/C°
Properties of Steel: Density: 7880 kg/m3 Young’s Modulus: 1.92×1011 N/m2 Specific Heat: 460 J/(kg C°) Ultimate Strength: 4.0×108 N/m2 Resistivity: 1.0×10-5 Ω∙cm Melting Point: ~ 1425° C Coefficient of Linear Thermal Expansion: 1.34×10-5 1/C°
Properties of Copper (Cu): Density: 8900 kg/m3 Young’s Modulus: 1.20×1011 N/m2 Specific Heat: 389 J/(kg C°) Ultimate Strength: 2.1×108 N/m2 Resistivity: 1.72×10-6 Ω∙cm Melting Point: 1085° C Boiling Point: 2562° C Coefficient of Linear Thermal Expansion: 1.68×10-5 1/C°
Properties of Lead (Pb): Density: 11,300 kg/m3 Young’s Modulus: 1.38×109 N/m2 Specific Heat: 129 J/(kg C°) Ultimate Strength: 1.2×107 N/m2 Resistivity: 2.065×10-5 Ω∙cm Melting Point: 327.5° C Boiling Point: 1749° C Coefficient of Linear Thermal Expansion: 2.89×10-5 1/C°
Properties of Water (H2O): Density: 1000 kg/m3 Specific Heat: 4186 J/(kg C°) Melting Point: 0° C Boiling Point: 100° C
Properties of Air (at STP): Density: 1.293 kg/m3 Specific Heat (Constant Pressure): 1000 J/(kg C°) Specific Heat (Constant Volume): 716 J/(kg C°)
Moments of Inertia:
Solid Disk or cylinder about a Solid Disk or cylinder about a central axis diameter: I = ½ MR2 I = ¼ MR2
Solid Sphere (or hemisphere) Thin hollow spherical Long rod about its through a diameter: shell: center of mass:
I = 2/5 MR2 I = 2/3 MR2 I = 1/12 ML2
Rectangular Plate about its Thin Hoop about a Thin Hoop about its center of mass: diameter: central axis:
I = 1/12 M (a2+b2) I = ½ MR2 I = MR2

1) Billy Bob “Bubba” Hickman is working in his barn one day. He has a 25 kg hay bale suspended from the barn's rafters on a 2.44 meter long rope. Bubba pulls on another rope horizontally until the rope holding the hay bale makes an angle of 20 degrees with respect to the vertical. a) What force does Bubba have to exert on the rope to hold the hay bale in this position?

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1) Billy Bob “Bubba” Hickman is working in his barn one day. He has a 25 kg hay bale suspended from the barn’s rafters on a 2.44 meter long rope. Bubba pulls on another rope horizontally until the rope holding the hay bale makes an angle of 20 degrees with respect to the vertical.
a) What force does Bubba have to exert on the rope to hold the hay bale in this position?
b) The rope slips out of Bubba’s hands. The hay bale starts to swing. How long does it take for the hay bale to swing to the farthest distance from where it started (the farthest distance across the barn)?
c) Bubba runs to catch the hay bale. He tries to catch it at the bottom of the swing as it swings back towards him. How fast is the hay bale moving when it hits Bubba?
2) A narrow metal rod, of mass 1.22 kg and length 2.05 meters is free to rotate about one end of the rod.
a) What is the moment of inertia of the rod?
b) How much work is needed to make the rod go from rest to swinging at 10 revolutions per minute?
3) Bubba has a mass of 75.3 kilogram and stands in the center of a 4.12 meter long uniform board. The board has a mass of 16.2 kg. The board is supported on each end by cables, each of which can sustain a maximum tensile force of 564 Newtons before breaking. How far from the center of the board can Bubba walk before one of the cables breaks?
4) The elevator at a diamond mine is supported by a single steel cable of diameter 1.28cm. The total mass of the elevator and cable is 670kg. When the elevator is at surface level, it is 12m below the pulley holding the cable.
a) Determine the stress and strain on the cable when the elevator is at the surface level.
b) By how much does the cable stretch when the elevator has been lowered a distance of 350m below the surface of the ground.
c) What is the maximum mass that the elevator and its occupants may have before the cable breaks? (Neglect the mass of the cable.)
5) Ceres, the largest object in the asteroid belt, has a mass of 9.43×1020 kg and a radius of 487 km. a) What is the acceleration due to gravity at the surface of Ceres?
b) What would be the orbital period of a satellite if it were to orbit Ceres at a distance of 925 km above its surface?
6) A 425 gram mass is attached to a horizontal spring. The spring is known to have a spring constant of 84.6 N/m. The mass is free to slide along a frictionless surface.
a) The mass is then pulled to the side a distance of 5.67 cm and released. Determine the period and amplitude of the resulting oscillations.
b) Determine the magnitude of the maximum velocity of the mass, and state where it reaches that maximum velocity.
7) A harmonic oscillator moves according to the equation: x=(13.8 cm)cos(11.7s−1t+ 0.77) .
a) What is the period of this oscillation?
b) What is the amplitude of this oscillation?
c) What is the maximum velocity of this oscillation?
d) What is the maximum acceleration of this oscillation?
8) Bubba sets a 1.25kg solid sphere of diameter 11.5cm at the top end of a 1.75m long board that is inclined an angle of 15 degrees relative to the horizontal. The sphere rolls down the incline without slipping.
a) Determine the linear speed of the sphere at the bottom of the incline.
b) Determine the rotational rate of the sphere at the bottom of the incline.
c) Determine how many times the sphere executed a complete rotation before it reached the bottom of the incline.
9) Consider a solid iron hollow cylinder (inner diameter 10.4 cm, outer diameter 18.8 cm, and length 45.0cm). (The density of iron is 7.874 gm/cm3.) a) Determine the mass of the cylinder.
b) Determine the moment of inertia of the cylinder if it spins about its long axis.
c) If the cylinder were spinning at 76.6 rpm, and brake pads were applied to the inner surface of the cylinder (like in drum brakes), how much force would be needed pressing the pads into the cylinder walls to stop the cylinder in 12.3 seconds? Assume that the coefficient of kinetic friction between the pads and the cylinder is 0.445.
10) A rotating metal plate of length 26cm and width 21cm is spinning about its center of mass at 22.3 radians per second. The metal plate has mass 22.4 kg. A solid cylinder of mass 34.3 kg and diameter 16cm is dropped onto the center of the rotating plate.
a) Determine the final speed of rotation of the system.
b) Determine the change in kinetic energy of the system.
Material Properties
Properties of Aluminum (Al): Density: 2700 kg/m3 Young’s Modulus: 6.5×1010 N/m2 Specific Heat: 921 J/(kg C°) Ultimate Strength: 1.10×108 N/m2 Resistivity: 2.8×10-6 Ω∙cm Melting Point: 660° C Boiling Point: 2519° C Coefficient of Linear Thermal Expansion: 2.40×10-5 1/C°
Properties of Steel: Density: 7880 kg/m3 Young’s Modulus: 1.92×1011 N/m2 Specific Heat: 460 J/(kg C°) Ultimate Strength: 4.0×108 N/m2 Resistivity: 1.0×10-5 Ω∙cm Melting Point: ~ 1425° C Coefficient of Linear Thermal Expansion: 1.34×10-5 1/C°
Properties of Copper (Cu): Density: 8900 kg/m3 Young’s Modulus: 1.20×1011 N/m2 Specific Heat: 389 J/(kg C°) Ultimate Strength: 2.1×108 N/m2 Resistivity: 1.72×10-6 Ω∙cm Melting Point: 1085° C Boiling Point: 2562° C Coefficient of Linear Thermal Expansion: 1.68×10-5 1/C°
Properties of Lead (Pb): Density: 11,300 kg/m3 Young’s Modulus: 1.38×109 N/m2 Specific Heat: 129 J/(kg C°) Ultimate Strength: 1.2×107 N/m2 Resistivity: 2.065×10-5 Ω∙cm Melting Point: 327.5° C Boiling Point: 1749° C Coefficient of Linear Thermal Expansion: 2.89×10-5 1/C°
Properties of Water (H2O): Density: 1000 kg/m3 Specific Heat: 4186 J/(kg C°) Melting Point: 0° C Boiling Point: 100° C
Properties of Air (at STP): Density: 1.293 kg/m3 Specific Heat (Constant Pressure): 1000 J/(kg C°) Specific Heat (Constant Volume): 716 J/(kg C°)
Moments of Inertia:
Solid Disk or cylinder about a Solid Disk or cylinder about a central axis diameter: I = ½ MR2 I = ¼ MR2
Solid Sphere (or hemisphere) Thin hollow spherical Long rod about its through a diameter: shell: center of mass:
I = 2/5 MR2 I = 2/3 MR2 I = 1/12 ML2
Rectangular Plate about its Thin Hoop about a Thin Hoop about its center of mass: diameter: central axis:
I = 1/12 M (a2+b2) I = ½ MR2 I = MR2

When a metal is heated its density decreases. There are two sources that give rise to this diminishment of ρ: (1) the thermal expansion of the solid, and (2) the formation of vacancies (Section 5.2). Consider a specimen of gold at room temperature (20?C) that has a density of 19.320 g/cm3. (a) Determine its density upon heating to 800?C when only thermal expansion is considered.

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When a metal is heated its density decreases. There are two sources that give rise to this diminishment of ρ: (1) the thermal expansion of the solid, and (2) the formation of vacancies (Section 5.2). Consider a specimen of gold at room temperature (20?C) that has a density of 19.320 g/cm3.
(a) Determine its density upon heating to 800?C when only thermal expansion is considered.
(b) Repeat the calculation when the introduction of vacancies is taken into account. Assume that the energy of vacancy formation is 0.98 eV/atom, and that the volume coefficient of thermal expansion, αv is equal to 3αl.
thin film of oil (no = 1.50)with varying thickness floats on water (nw = 1.33)When it is illuminated from above by white light, the reflected colors are as shown in Fig. 24–60. In air, the wavelength of yellow light is 580 nm. (a) Why are there no reflected colors at point A? (b) What is the oil’s thickness t at point B?

A closed, nonreactive system contains species 1 and 2 in vapor/liquid equilibrium. Species 2 is a very light gas, essentially insoluble in the liquid phase. The vapor phase contains both species 1 and 2. Some additional moles of species 2 are added to the system, which is then restored to its initial T and P. As a result of the process, does the total number of moles of liquid increase, decrease, or remain unchanged?

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A closed, nonreactive system contains species 1 and 2 in vapor/liquid equilibrium. Species 2 is
a very light gas, essentially insoluble in the liquid phase. The vapor phase contains both species 1
and 2. Some additional moles of species 2 are added to the system, which is then restored to its
initial T and P. As a result of the process, does the total number of moles of liquid increase,
decrease, or remain unchanged?
A positive charge +q is located at the point
x=0, y=−a and a negative charge −q is located at the point x=0, y=+a.
Derive an expression for the potential V at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the charges.
A man wishes to vacuum his car with a canister vacuum cleaner marked 535 W at 120 V. The car is parked far from the building, so he uses an extension cord 15.0 m long to plug the cleaner into a 120-V source. Assume that the cleaner has constant resistance. (a) If the resistance of each of the two conductors of the extension cord is 0.900, what is the actual power delivered to the cleaner? (b) If, instead, the power is to be at least 525 W, what must be the diameter of each of two identical copper conductors in the cord the young man buys? (c) Repeat part (b) if the power is to be at least 532 W.