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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

The 2000 kg cable car shown in FIGURE P7.42 descends a 200-m-high hill. In addition to its brakes, the cable car controls its speed by pulling an 1800 kg counterweight up the other side of the hill.
The 1.0 kg physics book in FIGURE P7.41 is connected by a string to a 500 g coffee cup.The book is given a push up the slope and released with a speed of 3.0 m/s. The coefficients of friction are
A 4.0 kg box is on a frictionless 35° slope and is connected via a massless string over a massless, frictionless pulley to a hanging 2.0 kg weight. The picture for this situation is similar to
FIGURE P7.39 shows a block of mass m resting on a 20° slope. The block has coefficients of friction Î¼s= 0.80 and Î¼k= 0.50 with the surface. It is connected via a
The coefficient of kinetic friction between the 2.0 kg block in FIGURE P7.38 and the table is 0.30. What is the acceleration of the 2.0 kg block? 2.0 kg 3.0 kg 1.0 kg FIGURE P7.38
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 T1to T5and the magnitude of force F. T4 T2 Ts т,
The block of mass M in FIGURE P7.36 slides on a frictionless surface. Find an expression for the tension in the string. Massless string Massless, fric- tionless pulley FIGURE P7.36
The coefficient of static friction is 0.60 between the two blocks in FIGURE P7.35. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force F causes both blocks to
The two blocks in FIGURE P7.34 are sliding down the incline. What is the tension in the massless string? 1.0 kg 2.0 kg Hx = 0.20 Hy =0.10 20° FIGURE P7.34
Two packages at UPS start sliding down the 20° ramp shown in FIGURE P7.33. Package A has a mass of 5.0 kg and a coefficient of friction of 0.20. Package B has a mass of 10 kg and a coefficient of
Bob, who has a mass of 75 kg, can throw a 500 g rock with a speed of 30 m/s. The distance through which his hand moves as he accelerates the rock from rest until he releases it is 1.0 m.a. What
Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can withstand only about 1.3 kN. Suppose a 140 g baseball traveling at 30 m/s strikes your head and stops
A Federation star ship (2.0 × 106 kg2) uses its tractor beam to pull a shuttle craft (2.0 × 104 kg2) aboard from a distance of 10 km away. The tractor beam exerts a constant force of 4.0 × 104 N
While driving to work last year, I was holding my coffee mug in my left hand while changing the CD with my right hand. Then the cell phone rang, so I placed the mug on the flat part of my dashboard.
A rope of length L and mass m is suspended from the ceiling.Find an expression for the tension in the rope at position y, measured upward from the free end of the rope.
FIGURE P7.27 shows a 6.0 N force pushing two gliders along an air track. The 200 g spring between the gliders is compressed. How much force does the spring exert on (a) Glider A(b) Glider B?The
FIGURE P7.26 shows two strong magnets on opposite sides of a small table. The long-range attractive force between the magnets keeps the lower magnet in place.(a) Draw an interaction diagram and draw
The 100 kg block in FIGURE EX7.25 takes 6.0 s to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless. 100 kg | 1.0 m
The 1.0 kg block in FIGURE EX7.24 is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic
A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.23. It is found that Î¸1= 20° when the center rope
A 2.0 kg rope hangs from the ceiling. What is the tension at the midpoint of the rope?
The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at 9.5 mph. The cable is driven by large motors at a central power station and extends,
Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of 6.0 kg, accelerates downward at 3/4 g.What is
A woman living in a third-story apartment is moving out. Rather than carrying everything down the stairs, she decides to pack her belongings into crates, attach a frictionless pulley to her balcony
A 2.0-m-long, 500 g rope pulls a 10 kg block of ice across a horizontal, frictionless surface. The block accelerates at 2.0 m/s2. How much force pulls forward on(a) The ice,(b) The rope?Assume that
A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with 80% efficiency. That is, 80% of the kinetic energy becomes electric
A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying a 40 kg backpack filled with gear. How much power does he need to reach the top in 55 s?
A horizontal spring with spring constant 250 N/m is compressed by 12 cm and then used to launch a 250 g box across the floor. The coefficient of kinetic friction between the box and the floor is
A spring of equilibrium length L1 and spring constant k1 hangs from the ceiling. Mass m1 is suspended from its lower end. Then a second spring, with equilibrium length L2 and spring constant k2, is
Two identical horizontal springs are attached to opposite sides of a box that sits on a frictionless table. The outer ends of the springs are clamped while the springs are at their equilibrium
When a 65 kg cheerleader stands on a vertical spring, the spring compresses by 5.5 cm. When a second cheerleader stands on the shoulders of the first, the spring compresses an additional 4.5 cm.What
A 50 g rock is placed in a slingshot and the rubber band is stretched. The magnitude of the force of the rubber band on the rock is shown by the graph in FIGURE P9.55. The rubber band is stretched 30
An electric dipole consists of two equal but opposite electric charges, +q and -q, separated by a small distance d. If another charge Q is distance x from the center of the dipole, in the plane
The gravitational attraction between two objects with masses m1 and m2, separated by distance x, is F = Gm1m2 /x2, where G is the gravitational constant.a. How much work is done by gravity when the
The force acting on a particle is Fx = F0e-x/L. How much work does this force do as the particle moves along the x-axis from x = 0 to x = L?
Hooke’s law describes an ideal spring. Many real springs are better described by the restoring force (FSp)s = -kΔs - q(Δs)3, where q is a constant. Consider a spring with k = 250 N/m and q = 800
You’re fishing from a tall pier and have just caught a 1.5 kg fish. As it breaks the surface, essentially at rest, the tension in the vertical fishing line is 16 N. Use work and energy to find the
A 50 kg ice skater is gliding along the ice, heading due north at 4.0 m/s. The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but μk = 0. Suddenly, a
A pile driver lifts a 250 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall of 1.5 m drives the pipe in 35 cm. What is the average force
A ball shot straight up with kinetic energy K0 reaches height h. What height will it reach if the initial kinetic energy is doubled?
A particle of mass m moving along the x-axis has velocity vx = v0 sin (πx/2L). How much work is done on the particle as it moves (a) From x = 0 to x = L(b) From x = 0 to x = 2L?
Susan’s 10 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30° above the floor.The tension is a constant 30 N and the coefficient of friction
a. Starting from rest, a crate of mass m is pushed up a frictionless slope of angle θ by a horizontal force of magnitude F. Use work and energy to find an expression for the crate’s speed v when
A 1000 kg elevator accelerates upward at 1.0 m/s2 for 10 m, starting from rest.a. How much work does gravity do on the elevator?b. How much work does the tension in the elevator cable do on the
The human heart pumps the average adult’s 6.0 L (6000 cm3) of blood through the body every minute. The heart must do work to overcome frictional forces that resist blood flow. The average adult
A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can go from rest to 20 m/s. What is the average power output of each? Average
A 50 kg sprinter, starting from rest, runs 50 m in 7.0 s at constant acceleration.a. What is the magnitude of the horizontal force acting on the sprinter?b. What is the sprinter’s power output at
At midday, solar energy strikes the earth with an intensity of about 1 kW/m2. What is the area of a solar collector that could collect 150 MJ of energy in 1 h? This is roughly the energy content of 1
How much energy is consumed by(a) A 1.2 kW hair dryer used for 10 min.(b) A 10 W night light left on for 24 h?
a. How much work must you do to push a 10 kg block of steel across a steel table at a steady speed of 1.0 m/s for 3.0 s?b. What is your power output while doing so?
a. How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m?b. How much power must the motor supply to do this in 50 s at constant speed?
Justin, with a mass of 30 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 11 m/s. How much thermal energy is created by friction during his descent?
An 8.0 kg crate is pulled 5.0 m up a 30° incline by a rope angled 18° above the incline. The tension in the rope is 120 N, and the crate’s coefficient of kinetic friction on the incline is
A baggage handler throws a 15 kg suitcase along the floor of an airplane luggage compartment with a speed of 1.2 m/s. The suitcase slides 2.0 m before stopping. Use work and energy to find the
A 55 kg softball player slides into second base, generating 950 J of thermal energy in her legs and the ground. How fast was she running?
One mole (6.02 × 1023 atoms) of helium atoms in the gas phase has 3700 J of microscopic kinetic energy at room temperature.If we assume that all atoms move with the same speed, what is that speed?
A horizontal spring with spring constant 85 N/m extends outward from a wall just above floor level. A 1.5 kg box sliding across a frictionless floor hits the end of the spring and compresses it 6.5
A 5.0 kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in FIGURE EX9.29. The scale reads in newtons.a. What does the spring scale read just before the mass
A 60 kg student is standing atop a spring in an elevator as it accelerates upward at 3.0 m/s2. The spring constant is 2500 N/m. By how much is the spring compressed?
A 10-cm-long spring is attached to the ceiling. When a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm.a. What is the spring constant?b. How long is the spring when a 3.0 kg
A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?
A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing?
A 150 g particle at x = 0 is moving at 2.00 m/s in the +x-direction. As it moves, it experiences a force given by Fx = (0.250 N) sin (x/2.00 m). What is the particle’s speed when it reaches x =
A particle moving on the x-axis experiences a force given by Fx = qx2, where q is a constant. How much work is done on the particle as it moves from x = 0 to x = d?
A 2.0 kg particle moving along the x-axis experiences the force shown in FIGURE EX9.22. The particle€™s velocity is 4.0 m/s at x = 0 m. What is its velocity at x = 2 m and x = 4 m? F; (N)
A 500 g particle moving along the x-axis experiences the force shown in FIGURE EX9.21. The particle€™s velocity is 2.0 m/s at x = 0 m. What is its velocity at x = 3 m? F; (N) 15 - 10- 5- -x
What is the angle θ between vectors A u and Bu in each part of Exercise 12?Exercise 12a. A = 3î + 4ĵ and B = 2î - 6ĵ.b. A = 3î - 2ĵ and B = 6î + 4ĵ.
Evaluate the dot product A · B ifa. A = 3î + 4ĵ and B = 2î - 6ĵ.b. A = 3î - 2ĵ and B = 6î + 4ĵ.
The left end of a spring is attached to a wall. When Bob pulls on the right end with a 200 N force, he stretches the spring by 20 cm.The same spring is then used for a tug-of-war between Bob and
Evaluate the dot product A · B ifa. A = 4î - 2ĵ and B = -2î - 3ĵ.b. A = -4î + 2ĵ and B = 2î + 4ĵ.
You need to raise a heavy block by pulling it with a massless rope.You can either (a) Pull the block straight up height h,(b) Pull it up a long, frictionless plane inclined at a 15° angle until
FIGURE CP7.58 shows three hanging masses connected by massless strings over two massless, frictionless pulleys.(a) Find the acceleration constraint for this system. It is a single equation relating
FIGURE CP7.57 shows a 200 g hamster sitting on an 800 g wedge-shaped block. The block, in turn, rests on a spring scale. An extra-fine lubricating oil having Î¼s= Î¼k= 0 is
A 40-cm-diameter, 50-cm-tall, 15 kg hollow cylinder is placed on top of a 40-cm-diameter, 30-cm-tall, 100 kg cylinder of solid aluminum, then the two are sent sliding across frictionless ice. The
What is the acceleration of the 3.0 kg block in FIGURE CP7.55 across the frictionless table?FIGURE CP7.55 3.0 kg| Frictionless 1.0 kg
In FIGURE CP7.54, find an expression for the acceleration of m1. The pulleys are massless and frictionless.FIGURE CP7.54 тy Frictionless т,
The lower block in FIGURE CP7.53 is pulled on by a rope with a tension force of 20 N. The coefficient of kinetic friction between the lower block and the surface is 0.30. The coefficient of kinetic
a. Write a realistic problem for which these are the correct freebody diagrams. Be sure that the answer your problem requests is consistent with the diagrams shown.b. Finish the solution of the
a. Write a realistic problem for which these are the correct freebody diagrams. Be sure that the answer your problem requests is consistent with the diagrams shown.b. Finish the solution of the
A rocket burns fuel at a rate of 5.0 kg/s, expelling the exhaust gases at a speed of 4.0 km/s relative to the rocket. We would like to find the thrust of the rocket engine.(a) Model the fuel burning
What is the equivalent capacitance of the three capacitors in Figure EX26.27? 10 μF 10 μF 20 μF FIGURE EX26.27
What is the equivalent capacitance of the three capacitors in Figure EX26.28? 20 μF 13 μF 30 μF FIGURE EX26.28
You need a capacitance of 50 μF, but you don’t happen to have a 50 μF capacitor. You do have a 30 μF capacitor. What additional capacitor do you need to produce a total capacitance of 50 μF?
You need a capacitance of 50 μF, but you don’t happen to have a 50 μF capacitor. You do have a 75 μF capacitor. What additional capacitor do you need to produce a total capacitance of 50 μF?
To what potential should you charge a 1.0 μF capacitor to store 1.0 J of energy?
50 pJ of energy is stored in a 2.0 cm × 2.0 cm × 2.0 cm region of uniform electric field. What is the electric field strength?
A 2.0-cm-diameter parallel-plate capacitor with a spacing of 0.50 mm is charged to 200 V. What are(a) The total energy stored in the electric field(b) The energy density?
The 90 μF capacitor in a defibrillator unit supplies an average of 6500 W of power to the chest of the patient during a discharge lasting 5.0 ms. To what voltage is the capacitor charged?
Two 5.0 mm × 5.0 mm electrodes are held 0.10 mm apart and are attached to a 9.0 V battery. Without disconnecting the battery, a 0.10-mm-thick sheet of Mylar is inserted between the electrodes. What
A typical cell has a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outside surface, thus making the cell wall a capacitor. What is the
FIGURE P26.41 is an edge view of three charged metal electrodes. Let the left electrode be the zero point of the electric potential. What are V and E at (a) X = 0.5 cm, (b) X = 1.5 cm, (c) X = 2.5
Use the on-axis potential of a charged disk from Chapter 25 to find the on-axis electric field of a charged disk.
a. Use the methods of Chapter 25 to find the potential at distance x on the axis of the charged rod shown in FIGURE P26.43.b. Use the result of part a to find the electric field at distance x on the
It is postulated that the radial electric field of a group of charges falls off as Er = C/rn, where C is a constant, r is the distance from the center of the group, and n is an unknown exponent. To
Engineers discover that the electric potential between two electrodes can be modeled as V(x) = V0 ln(1 + x/d), where V0 is a constant, x is the distance from the first electrode in the direction of
The electric potential in a region of space is V = 200/√x2 + y2, where x and y are in meters. What are the strength and direction of the electric field at (x, y) = (2.0 m, 1.0 m)? Give the
Consider a large, thin, electrically neutral conducting plate in the xy-plane at z = 0 and a point charge q on the z-axis at distance zcharge = d. What is the electric field on and above the
Metal sphere 1 has a positive charge of 6.0 nC. Metal sphere 2, which is twice the diameter of sphere 1, is initially uncharged. The spheres are then connected together by a long, thin metal wire.
The metal spheres in FIGURE P26.50 are charged to ±300 V. Draw this figure on your paper, then draw a plausible contour map of the potential, showing and labeling the -300 V, -200 V, -100 V, .
The potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity. How much excess charge is on the sphere?

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