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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

A concrete highway curve of radius 70 m is banked at a 15° angle. What is the maximum speed with which a 1500 kg rubber tired car can take this curve without sliding?
a. An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle θ. Find an expression for the angular velocity ω.b. A student ties a 500 g rock to a
You’ve taken your neighbor’s young child to the carnival to ride the rides. She wants to ride The Rocket. Eight rocket shaped cars hang by chains from the outside edge of a large steel disk. A
A 4.4-cm-diameter, 24 g plastic ball is attached to a 1.2-m-long string and swung in a vertical circle. The ball’s speed is 6.1 m/s at the point where it is moving straight up. What is the
A charged particle of mass m moving with speed v in a plane perpendicular to a magnetic field experiences a force F = (qvB, perpendicular to v), where q is the amount of charge and B is the magnetic
Two wires are tied to the 2.0 kg sphere shown in FIGURE P8.45. The sphere revolves in a horizontal circle at constant speed. a. For what speed is the tension the same in both wires?b. What is the
Two wires are tied to the 300 g sphere shown in FIGURE P8.46. The sphere revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in each of the wires?FIGURE P8.46 1.0 m
A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. FIGURE P8.47 shows that the string traces out
The 10 mg bead in FIGURE P8.48 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity Ï‰. If v is less than some critical value
In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then
The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched
In an amusement park ride called The Roundup, passengers stand inside a 16-m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in FIGURE
Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity ωmin you must maintain if you want the ball
A 30 g ball rolls around a 40-cm-diameter L-shaped track, shown in FIGURE P8.53, at 60 rpm. What is the magnitude of the net force that the track exerts on the ball? Rolling friction can be
FIGURE P8.54 shows a small block of mass m sliding around the inside of an L-shaped track of radius r. The bottom of the track is frictionless; the coefficient of kinetic friction between the block
The physics of circular motion sets an upper limit to the speed of human walking. (If you need to go faster, your gait changes from a walk to a run.) If you take a few steps and watch what’s
A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 5.0 N. A very
A 60 g ball is tied to the end of a 50-cm-long string and swung in a vertical circle. The center of the circle, as shown in FIGURE P8.57, is 150 cm above the floor. The ball is swung at the minimum
Elm Street has a pronounced dip at the bottom of a steep hill before going back uphill on the other side. Your science teacher has asked everyone in the class to measure the radius of curvature of
A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The
Scientists design a new particle accelerator in which protons (mass 1.7 × 10-27 kg) follow a circular trajectory given by r = c cos(kt2) î + c sin(kt2) ĵ, where c = 5.0 m and k = 8.0 × 104
A 1500 kg car starts from rest and drives around a flat 50-m-diameter circular track. The forward force provided by the car’s drive wheels is a constant 1000 N.a. What are the magnitude and
A 500 g steel block rotates on a steel table while attached to a 2.0-m-long massless rod. Compressed air fed through the rod is ejected from a nozzle on the back of the block, exerting a thrust force
a. Write a realistic problem for which this is the correct equation. Be sure that the answer your problem requests is consistent with the equation given.b. Finish the solution of the problem.60 N =
A 2.0 kg ball swings in a vertical circle on the end of an 80-cm-long string. The tension in the string is 20 N when its angle from the highest point on the circle is θ = 30°.a. What is the
a. Write a realistic problem for which this is the correct equation. Be sure that the answer your problem requests is consistent with the equation given.b. Finish the solution of the problem.(1500
Sam (75 kg) takes off up a 50-m-high, 10° frictionless slope on his jet-powered skis. The skis have a thrust of 200 N. He keeps his skis tilted at 10° after becoming airborne, as shown in
In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched
A small bead slides around a horizontal circle at height y inside the cone shown in FIGURE CP8.69. Find an expression for the bead€™s speed in terms of a, h, y, and g. a FIGURE CP8.69
A 500 g steel block rotates on a steel table while attached to a 1.2-m-long hollow tube as shown in FIGURE CP8.70. Compressed air fed through the tube and ejected from a nozzle on the back of the
If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.71, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the
Determine [B]-1 by row reduction.
Derive the stiffness matrix for a beam element with a nodal linkage€”that is, the shear is 0 at node i, but the usual shear and moment resistance are present at node j (see following
Determine [D]-1 by row reduction.
Show that ([A] [B])T= [A]T[B]Tby using [b1 b12 b13 [B] = b21 b22 b23 α12 [4] = a22 a21
Determine the solution of the following simultaneous equations by the inverse method.1x1 + 3x2 = 54x1 - 1x2 = 12
Determine the solution of the following simultaneous equations by the inverse method.1x1 + 3x2 = 54x1 - 1x2 = 12
Solve the following system of simultaneous equations by Gaussian elimination.x1 + 4x2 - 5x3 = 43x2 + 4x3 = -1-2x1 -1x2 + 2x3 = -3
Given thatx1 = 2y1 - y2 z1 = -x1 - x2x2 = y1 - y2 z2 = 2x1 + x2a. Write these relationships in matrix form.b. Express [z] in terms of {y}.c. Express [y] in terms of [z].
Solve Problem B.1 by Gauss–Seidel iteration.Data from problem B.1Determine the solution of the following simultaneous equations by the inverse method.1x1 + 3x2 = 54x1 - 1x2 = 12
Solve Problems A.1 through A.6 using matrices [A], [B], [C], [D], and [E] given by(a) |A| + |B|(b) |A| + |B|(c) |A| |C|T(d) |D| {B}(e) |D| |C|(f) |C| |D| 3 1 01 -1 0 3 2 0 [4] [B] [C] -2 8 3 1 [D] =
Evaluate the matrix [B] for the quadratic quadrilateral element shown in Figure 10€“15 on page 521 (Section 10.5).(a)(b) 3. (20, 15) (12, 15) (10, 10)- (20, 10) (20, 20) (12, 16) (10, 10)
Determine the Jacobian matrix |J| and its determinant for the elements shown in Figure P10 11. Show that the determinant of |J|for rectangular and parallelogram shaped elements is equal to A/4, where
FIGURE EX1.11 shows two dots of a motion diagram and vector1Copy this figure, then add dot 4 and the next velocity vector2 if the acceleration vectorat dot 3(a) Points right and(b) Points
A rubber ball is dropped onto a ramp that is tilted at 20°, as shown in FIGURE P4.59. A bouncing ball obeys the €œlaw of reflection,€ which says that the ball leaves the
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground
A stunt man drives a car at a speed of 20 m/s off a 30-m-high cliff. The road leading to the cliff is inclined upward at an angle of 20°.a. How far from the base of the cliff does the car land?b.
A 35 g steel ball is held by a ceiling-mounted electromagnet 3.5 m above the floor. A compressed-air cannon sits on the floor, 4.0 m to one side of the point directly under the ball. When a button is
You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30° above horizontal, the ball hits the bull’s-eye of a target at the
A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20.0 m/s at an angle 5.0° above the horizontal. The horizontal distance to the net is 7.0 m, and the
A ball is thrown toward a cliff of height h with a speed of 30 m/s and an angle of 60° above horizontal. It lands on the edge of the cliff 4.0 s later.a. How high is the cliff?b. What was the
A gray kangaroo can bound across level ground with each jump carrying it 10 m from the takeoff point. Typically the kangaroo leaves the ground at a 20° angle. If this is so:a. What is its takeoff
A projectile is launched from ground level at angle θ and speed v0 into a headwind that causes a constant horizontal acceleration of magnitude a opposite the direction of motion.a. Find an
a. A projectile is launched with speed v0 and angle θ. Derive an expression for the projectile’s maximum height h.b. A baseball is hit with a speed of 33.6 m/s. Calculate its height and the
A projectile’s horizontal range over level ground is v02 sin 2θ/g. At what launch angle or angles will the projectile land at half of its maximum possible range?
Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?
A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.50 rad / s2.a. What is the wheel’s angular velocity, in rpm, 10
An electric fan goes from rest to 1800 rpm in 4.0 s. What is its angular acceleration?
A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s.a. Before slowing, what is the speed of a child on the rim?b. How many revolutions does the
A wheel initially rotating at 60 rpm experiences the angular acceleration shown in FIGURE EX4.39. What is the wheel€™s angular velocity, in rpm, at t = 3.0 s?Figure Ex 4.39 (rad/s?) 04 -t
FIGURE EX4.38 shows the angular- velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?Figure Ex 4.38 w (rad/s) 20- 10- 0+ -t
FIGURE EX4.37 shows the angular acceleration graph of a turntable that starts from rest. What is the turntable€™s angular velocity at(a) t = 1 s,(b) t = 2 s, and(c) t = 3 s?Figure Ex 4.37 a
FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshaft€™s angular acceleration at(a) t = 1 s,(b) t = 3 s, and(c) t = 5 s?Figure Ex 4.37 w (rad/s)
Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the
A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s2.a. What is the acceleration of a different speck of dust that is twice as far from the center of the disk?b. What would be
The radius of the earth’s very nearly circular orbit around the sun is 1.5 × 1011 m. Find the magnitude of the earth’s(a) Velocity,(b) Angular velocity, and(c) Centripetal acceleration as it
To withstand “g-forces” of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10 g’s is an acceleration of 98 m/s2. If the
Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the
A 3000-m-high mountain is located on the equator. How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earth’s radius is 6400 km.
How fast must a plane fly along the earth’s equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in
As the earth rotates, what is the speed of(a) A physics student in Miami, Florida, at latitude 26°, and(b) A physics student in Fairbanks, Alaska, at latitude 65°? Ignore the revolution of the
An old-fashioned single-play vinyl record rotates on a turntable at 45 rpm. What are(a) The angular velocity in rad/s and(b) The period of the motion?
The earth’s radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore
FIGURE EX4.25 shows the angular-velocity-versus-time graph for a particle moving in a circle, starting from Î¸0= 0 rad at t = 0 s. Draw the angular-position-versus-time graph. Include an
FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particle€™s angular velocity at(a) t = 1 s,(b) t = 4 s, and(c) t = 7 s?Figure Ex
FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?Figure Ex 4.23 w (rad/s) 20- 10- t (s) 0-
Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent’s speed relative to Susan’s reference frame?
A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker can paddle with a speed of 3.0 m/s.a. In
Mary needs to row her boat across a 100-m-wide river that is flowing to the east at a speed of 1.0 m/s. Mary can row with a speed of 2.0 m/s.a. If Mary points her boat due north, how far from her
When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the
A boat takes 3.0 hours to travel 30 km down a river, then 5.0 hours to return. How fast is the river flowing?
A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 4.0 m above the ground. The ball lands 25 m
A ball thrown horizontally at 25 m/s travels a horizontal distance of 50 m before hitting the ground. From what height was the ball thrown?
You have a remote-controlled car that has been programmed to have velocitywhere t is in s. At t = 0 s, the car is atWhat are the car€™s(a) Position vector and(b) Acceleration vector at t =
A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it
On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed
In the Olympic shot-put event, an athlete throws the shot with an initial speed of 12.0 m/s at a 40.0° angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground. How
A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point.a. What was the bullet’s flight time?b. What was the bullet’s speed as it left the
Sand moves without slipping at 6.0 m/s down a conveyer that is tilted at 15°. The sand enters a pipe 3.0 m below the end of the conveyer belt, as shown in FIGURE P4.56. What is the horizontal
You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground.
FIGURE Q4.13 shows three points on a steadily rotating wheel.a. Rank in order, from largest to smallest, the angular velocities Ï‰1, Ï‰2, and Ï‰3 of these points.
In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, the tangential component of velocity, the radial component of acceleration, the tangential
In FIGURE Q4.11, Yvette and Zack are driving down the freeway side by side with their windows down. Zack wants to toss his physics book out the window and have it land in Yvette€™s front
Zack is driving past his house in FIGURE Q4.10. He wants to toss his physics book out the window and have it land in his driveway. If he lets go of the book exactly as he passes the end of the
Anita is running to the right at 5 m/s in FIGURE Q4.8. Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anita, both balls are approaching her at 10 m/s.Which ball
A cart that is rolling at constant velocity on a level table fires a ball straight up.a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or
For a projectile, which of the following quantities are constant during the flight: x, y, r, vx, vy, v, ax, ay? Which of these quantities are zero throughout the flight?
A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0 m/s. A wise elder duck finally realizes that the solution is to
Tom is climbing a 3.0-m-long ladder that leans against a vertical wall, contacting the wall 2.5 m above the ground. His weight of 680 N is a vector pointing vertically downward. (Weight is measured
Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25°, and Paul is pulling a large crate up the ramp with a rope that angles 10° above the ramp. If Paul pulls

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