The 10.2 kg block in FIGURE P7.37 is held in place by a force applied to a rope passing over two massless, frictionless pulleys. Find the tensions T 1 to T 5 and the magnitude of force F. T4 T2 Ts ,...

An engineer at a pulp mill is considering the feasibility of removing chlorine gas (C1 2 , solute A) from an air steam using water, which will be reused for a pulp bleaching operation. The process...

At a particular location in a counter current stripper for removal of solute A from a liquid stream, the mole fraction of solute A in the gas phase is 0.010, and the mole fraction of this species in...

Consider the waste treatment process shown in the figure below. In this process, wastewater containing a dissolved TCE concentration of 50 gmole/m 3 enters a clarifier, which is essentially a...

Estimate the electric fields E 1 and E 2 at points 1 and 2 in Figure Q26.5. Dont forget that E is a vector. OV 10 V 20 V 30 V 40 V 2 0m 2 m 3 m 4 m FIGURE Q26.5

Consider a lightbulb circuit such as the one in Figure Q27.1. a. From the simple observations and measurements you can make on this circuit, can you distinguish a current composed of positive charge...

What is the difference between current and current density?

All the wires in Figure Q27.6 are made of the same material and have the same diameter. Rank in order, from largest to smallest, the currents I a to I d . Explain.

A system of two objects has K tot = 7 J and U int = -5 J. a. How much work is done by interaction forces? b. How much work is done by external forces?

A 1500 kg car traveling at 10 m/s suddenly runs out of gas while approaching the valley shown in FIGURE EX10.11. The alert driver immediately puts the car in neutral so that it will roll.What will be...

FIGURE EX10.24 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0 m. a. Will the particle move to the right or to the left? b. What is the particles maximum...

In FIGURE EX10.26, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm? U (J) 5- 4 3- 2- 0+ x (mm) 4 FIGURE EX10.26

A particle moving along the y-axis is in a system with potential energy U = 4y 3 J, where y is in m. What is the y-component of the force on the particle at y = 0 m, 1 m, and 2 m?

A particle moving along the x-axis is in a system with potential energy U = 10/x J, where x is in m. What is the x-component of the force on the particle at x = 2 m, 5 m, and 8 m?

What is the final kinetic energy of the system for the process shown in FIGURE EX10.38? E (J) 4 3 K; + U; + Wext = K; + U; + AE FIGURE EX10.38

A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the blocks speed after being lifted 2.00 m? Solve this problem using work and energy.

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?

A freight company uses a compressed spring to shoot 2.0 kg packages up a 1.0-m-high frictionless ramp into a truck, as FIGURE P10.51 shows. The spring constant is 500 N/m and the spring is compressed...

a. A 50 g ice cube can slide without friction up and down a 30 slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m....

The spring shown in FIGURE P10.54 is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student??s coefficient of kinetic...

In a physics lab experiment, a compressed spring launches a 20 g metal ball at a 30 angle. Compressing the spring 20 cm causes the ball to hit the floor 1.5 m below the point at which it leaves the...

The spring in FIGURE CP10.73 has a spring constant of 1000 N/m. It is compressed 15 cm, then launches a 200 g block. The horizontal surface is frictionless, but the blocks coefficient of kinetic...

What impulse does the force shown in FIGURE EX11.3 exert on a 250 g particle? F, (N) 1000- -t (ms) 6. 0+ 2 4 FIGURE EX11.3

FIGURE EX11.6 is an incomplete momentum bar chart for a collision that lasts 10 ms. What are the magnitude and direction of the average collision force exerted on the object? kg m/s 2 - 0- -2 - -4-...

A proton is traveling to the right at 2.0 10 7 m/s. It has a headon perfectly elastic collision with a carbon atom. The mass of the carbon atom is 12 times the mass of the proton. What are the speed...

FIGURE P11.71 shows a collision between three balls of clay. The three hit simultaneously and stick together. What are the speed and direction of the resulting blob of clay? 40 g JASO 45 4.0 m/s 3.0...

If the angular velocity Ï is held constant, by what factor must R change to double the rotational kinetic energy of the dumbbell in FIGURE Q12.2? , R M2 FIGURE Q12.2

A skater holds her arms outstretched as she spins at 180 rpm. What is the speed of her hands if they are 140 cm apart?

The moment of inertia of a uniform rod about an axis through its center is 1/12 mL 2 . The moment of inertia about an axis at one end is 1/3 mL 2 . Explain why the moment of inertia is larger about...

The three masses shown in Figure EX12.6 are connected by massless, rigid rods. What are the coordinates of the center of mass? 200 g B 10 cm 10 cm A 100 g 300 g FIGURE EX12.6

A student gives a quick push to a ball at the end of a massless, rigid rod, as shown in FIGURE Q12.9, causing the ball to rotate clockwise in a horizontal circle. The rods pivot is frictionless. a....

A drum major twirls a 96-cm-long, 400 g baton about its center of mass at 100 rpm. What is the batons rotational kinetic energy?

The four masses shown in Figure EX12.13 are connected by massless, rigid rods. a. Find the coordinates of the center of mass. b. Find the moment of inertia about a diagonal axis that passes through...

A 4.0-m-long, 500 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end...

An athlete at the gym holds a 3.0 kg steel ball in his hand. His arm is 70 cm long and has a mass of 3.8 kg, with the center of mass at 40% of the arm length. What is the magnitude of the torque...

The two objects in Figure EX12.29 are balanced on the pivot. What is distance d? 2.0 m 1.0 m 4.0 kg- 1.0 kg FIGURE EX12.29

A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. a. What is the tires angular velocity, in rpm? b. What is the speed of a point at the top edge of the tire? c. What is the...

A 500 g, 8.0-cm-diameter can is filled with uniform, dense food. It rolls across the floor at 1.0 m/s. What is the cans kinetic energy?

An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25 incline. It rolls, without slipping, to the bottom. a. What is the spheres angular velocity at the bottom...

Evaluate the cross products A Ã B and C Ã D. (b) (a) A 45/ FIGURE EX12.37

Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end. Confirm that your answer agrees with Table 12.2 when d = 0...

In Figure P12.59, an 80 kg construction worker sits down 2.0 m from the end of a 1450 kg steel beam to eat his lunch.What is the tension in the cable? Cable 307 6.0 m

A 750 g disk and a 760 g ring, both 15 cm in diameter, are rolling along a horizontal surface at 1.5 m/s when they encounter a 15 slope. How far up the slope does each travel before rolling back down?

The 5.0 kg, 60-cm-diameter disk in FIGURE P12.72 rotates on an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the...

A thin, uniform rod of length L and mass M is placed vertically on a horizontal table. If tilted ever so slightly, the rod will fall over. a. What is the speed of the center of mass just as the rod...

The sphere of mass M and radius R in FIGURE P12.76 is rigidly attached to a thin rod of radius r that passes through the sphere at distance 1/2 R from the center. A string wrapped around the rod...

A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity...

A 200 g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20 g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a...

Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as...

What is the ratio of the suns gravitational force on you to the earths gravitational force on you?

The gravitational force of a star on orbiting planet 1 is F 1 . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F 2 ....

A rocket is launched straight up from the earths surface at a speed of 15,000 m/s. What is its speed when it is very far away from the earth?

A proposed space elevator would consist of a cable stretching from the earths surface to a satellite, orbiting far in space, that would keep the cable taut. A motorized climber could slowly carry...

a. At what height above the earth is the free-fall acceleration 10% of its value at the surface? b. What is the speed of a satellite orbiting at that height?

What is the total gravitational potential energy of the three masses in Figure P13.35? 5.0 kg 20 cm 10.0 kg 20.0 kg 10 cm FIGURE P13.35

An object of mass m is dropped from height h above a planet of mass M and radius R. Find an expression for the objects speed as it hits the ground.

The unexplored planet Alpha Centauri III has a radius of 7.0 10 6 m. A visiting astronaut drops a rock, from rest, into a 100 m deep crevasse. She records that it takes 6.0 s for the rock to reach...

A 4000 kg lunar lander is in orbit 50 km above the surface of the moon. It needs to move out to a 300-km-high orbit in order to link up with the mother ship that will take the astronauts home. How...

FIGURE P13.57 shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter. Find an exact expression for the...

FIGURE CP13.72 shows a particle of mass m at distance x from the center of a very thin cylinder of mass M and length L. The particle is outside the cylinder, so x > L/2. a. Calculate the...

Water flows through a 2.5-cm-diameter hose at 3.0 m/s. How long, in minutes, will it take to fill a 600 L childs wading pool?

A bucket is filled with water to a height of 23 cm, then a plug is removed from a 4.0-mm-diameter hole in the bottom of the bucket. As the water begins to pour out of the hole, how fast is it moving?

What does the top pressure gauge read in FIGURE EX14.30? 200 kPa 3.0 m/s 10 m Oil 2.0 m/s FIGURE EX14.30

A 2.0 mL syringe has an inner diameter of 6.0 mm, a needle inner diameter of 0.25 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine...

A 5.0-m-diameter solid aluminum sphere is launched into space. By how much does its diameter increase? Give your answer in m.

A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is 10.0 cm deep. How far upward from its initial position does the mercury in...

A plastic boat with a 25 cm 2 square cross section floats in a liquid. One by one, you place 50 g masses inside the boat and measure how far the boat extends below the surface. Your data are as...

The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos(10 t - /4), where t is in s. Determine: a. The amplitude. b. The period. c. The spring constant. d. The phase constant. e. The...

The 3.0-m-long pipe in FIGURE P18.50 is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the waters surface. What is the length L of...

In the alternate universe, how fast must an object be moving for it to have a kinetic energy equal to its rest mass? (a) 225 m/s; (b) 260 m/s; (c) 300 m/s; (d) The kinetic energy could not be equal...

The mean free path of a molecule in a gas is 300 nm. What will the mean free path be if the gas temperature is doubled at (a) Constant volume (b) Constant pressure?

A heat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. The same engine running backward is called a heat pump if its purpose is to exhaust...

What mass of aluminum has a total nuclear charge of 1.0 C? Aluminum has atomic number 13.

What is the force F on the 1.0 nC charge in Figure EX22.19? Give your answer as a magnitude and a direction. 1.0 nC 1.0 cm ,' 1.0 cm 60 60% 1.0 cm 2.0 nC 2.0 nC FIGURE EX22.19

Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. a. What is the...

What is the force F on the 1.0 nC charge at the bottom in FIGURE P22.45? Give your answer in component form. -6.0 nC 2.0 nC, 2.0 nC +) +. 5.0 cm, 45 45 , 5.0 cm +, 1.0 nC FIGURE P22.45

The identical small spheres shown in FIGURE CP22.75 are charged to +100 nC and -100 nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere? 10 10 50 cm 50 cm E 100 nC...

Reproduce FIGURE Q23.2 on your paper. For each part, draw a dot or dots on the figure to show any position or positions (other than infinity) where E = 0. a. b. +'+

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.4? Specify the direction as an angle above or below horizontal. +) 3.0 nC 5.0 cm 10 cm...

The electric field strength 10.0 cm from a very long charged wire is 2000 N/C. What is the electric field strength 5.0 cm from the wire?

Two parallel plates 1.0 cm apart are equally and oppositely charged. An electron is released from rest at the surface of the negative plate and simultaneously a proton is released from rest at the...

a. An infinitely long sheet of charge of width L lies in the xy plane between x = -L/2 and x = L/2. The surface charge density is . Derive an expression for the electric field E along the x-axis for...

What is the net electric flux through the two cylinders shown in FIGURE EX24.16? Give your answer in terms of R and E. a. b. 2R 2R

A very long, uniformly charged cylinder has radius R and linear charge density . Find the cylinders electric field strength (a) Outside the cylinder, r R, (b) Inside the cylinder, r R. (c) Show...

A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r R) is E(r) = r 4 E max /R 4 . a. What is E max in terms of Q and R? b. Find an expression...

What is the electric potential energy of the group of charges in FIGURE EX25.7? -4.0 nC 3.0 nC + 3.0 cm 14.0 cm 3.0 nC FIGURE EX25.7

FIGURE EX25.10 shows the potential energy of an electric dipole. Consider a dipole that oscillates between ?60?. a. What is the dipole??s mechanical energy?b. What is the dipole??s kinetic energy...

Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level. One electron volt, abbreviated eV, is defined as the amount of kinetic energy...

In FIGURE EX25.26, a proton is fired with a speed of 200,000 m/s from the midpoint of the capacitor toward the positive plate. a. Show that this is insufficient speed to reach the positive plate.b....

a. What is the electric potential at points A, B, and C in FIGURE EX25.27? b. What are the potential differences ÎV AB = V B - V A and ÎV CB = V B - V C ? 2,0 cm, 1.0 cm +, 2.0 nC

Living cells pump singly ionized sodium ions, Na + , from the inside of the cell to the outside to maintain a membrane potential V membrane = V in - V out = - 70 mV. It is called pumping because work...

A room with 3.0-m-high ceilings has a metal plate on the floor with V = 0 V and a separate metal plate on the ceiling. A 1.0 g glass ball charged to +4.9 nC is shot straight up at 5.0 m/s. How high...

Honeybees acquire a charge while flying due to friction with the air. A 100 mg bee with a charge of +23 pC experiences an electric force in the earths electric field, which is typically 100 N/C,...

The electron drift speed is 2.0 10 -4 m/s in a metal with a mean time between collisions of 5.0 10 -14 s. What is the electric field strength?

A 2.0 10 -3 V/m electric field creates a 3.5 10 17 electrons/s current in a 1.0-mm-diameter aluminum wire. What are (a) The drift speed (b) The mean time between collisions for electrons in this...

Wires 1 and 2 are made of the same metal. Wire 2 has twice the length and twice the diameter of wire 1. What are the ratios (a) 2 / 1 of the resistivities (b) R 2 /R 1 of the resistances of the two...

The two segments of the wire in Figure EX27.24 have equal diameters but different conductivities Ï 1 and Ï 2 . Current I passes through this wire. If the conductivities have the ratio...

A thin metal cylinder of length L and radius R 1 is coaxial with a thin metal cylinder of length L and a larger radius R 2 . The space between the two coaxial cylinders is filled with a material that...

An oscillator circuit is important to many applications. A simple oscillator circuit can be built by adding a neon gas tube to an RC circuit, as shown in FIGURE CP28.83. Gas is normally a good...

What power is dissipated by the 2 resistor in FIGURE CP28.78? 15 VE 203 12 V FIGURE CP28.78