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physics
mechanics
Physics 9th edition John D. Cutnell, Kenneth W. Johnson - Solutions
In Figure, a 0.400 kg ball is shot directly upward at initial speed 40.0 m/s. What is its angular momentum about P, 2.00 m horizontally from the launch point, when the ball is(a) At maximum height and(b) Halfway back to the ground? What is the torque on the ball about P due to the gravitational
At time t = 0, a 3.0 kg particle with velocity v = (5.0 m/s)î – (6.0 m/s)ĵ is at x = 3.0 m,y = 8.0 m. It is pulled by a 7.0 N force in the negative x direction. About the origin, what are(a) The particle's angular momentum,(b) The torque acting on the particle, and(c)
A particle is to move in an xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle if the magnitude of its angular momentum about the origin is(a) 4.0 kg · m2/s,(b) 4.0t2 kg · m2/s,(c) 4.0 √t kg · m2/s,
A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm, rotational inertia 5.0 × 10–3 kg · m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.0 m/s, and the lazy
Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia 3.30 kg · m2 about its central axis, is set spinning counterclockwise at 450 rev/min. The second
A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on a massless axle through its center (Figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg · m2. The wheel is initially at rest at the top of a
In Figure, a constant horizontal force Fapp of magnitude 12 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 10 kg, its radius is 0.10 m, and the cylinder rolls smoothly on the horizontal surface.(a) What is the magnitude of the
Two particles, each of mass 2.90 × 10–4 kg and speed 5.46 m/s, travel in opposite directions along parallel lines separated by 4.20 cm.(a) What is the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines?(b) Does the value of L change if the
In Figure, a nonuniform bar is suspended at rest in a horizontal position by two massless cords. One cord makes the angle θ = 36.9° with the vertical; the other makes the angle Ф = 53.1° with the vertical. If the length L of the bar is 6.10 m, compute the distance x from the left end
Figure shows a 70 kg climber hanging by only the crimp hold of one hand on the edge of a shallow horizontal ledge in a rock wall. (The fingers are pressed down to gain purchase.) Her feet touch the rock wall at distance H = 2.0 m directly below her crimped fingers but do not provide any support.
In Figure and the associated sample problem, let the coefficient of static friction µs between the ladder and the pavement be 0.53. How far (in percent) up the ladder must the firefighter go to put the ladder on the verge of sliding?
In Figure, two identical, uniform, and frictionless spheres, each of mass m, rest in a rigid rectangular container. A line connecting their centers is at 45° to the horizontal. Find the magnitudes of the forces on the spheres from(a) The bottom of the container,(b) The left side of the
If the (square) beam in Figure.a and the associated sample problem is of Douglas fir, what must be its thickness to keep the compressive stress on it to 1/6 of its ultimate strength?
We want to position a space probe along a line that extends directly toward the Sun in order to monitor solar flares. How far from Earth's center is the point on the line where the Sun's gravitational pull on the probe balances Earth's pull?
In Problem 1, what ratio m/M gives the least gravitational potential energy for the system?
In 1993 the spacecraft Galileo sent home an image (Figure) of asteroid 243 Ida and a tiny orbiting moon (now known as Dactyl), the first confirmed example of an asteroid-moon system.In the image, the moon, which is 1.5 km wide, is 100 km from the center of the asteroid, which is 55 km long. The
In Figure, two satellites, A and B, both of mass m = 125 kg, move in the same circular orbit of radius r = 7.87 × 106 m around Earth but in opposite senses of rotation and therefore on a collision course.(a) Find the total mechanical energy EA +
With what speed would mail pass through the center of Earth if falling in a tunnel through the center?
You inflate the front tires on your car to 28 psi. Later, you measure your blood pressure, obtaining a reading of 120/80, the readings being in mm Hg. In metric countries (which is to say, most of the world), these pressures are customarily reported in kilopascals (kPa). In kilopascals, what are(a)
Vesna Vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles, 551 yards. What is this distance in meters?
A bottle of wine known as a magnum contains a volume of 1.5 liters. A bottle known as a jeroboam contains 0.792 U.S. gallons. How many magnums are there in one jeroboam?
A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T
A highway is to be built between two towns, one of which lies 35.0 km south and 72.0 km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west?
Three deer, A, B, and C, are grazing in a field. Deer B is located 62 m from deer A at an angle of 51° north of west. Deer C is located 77° north of east relative to deer A. The distance between deer B and C is 95 m. What is the distance between deer A and C?
(a) Two workers are trying to move a heavy crate. One pushes on the crate with a force A→, which has a magnitude of 445 new tons and is directed due west. The other pushes with a force B→, which has a magnitude of 325 new tons and is directed due north. What are the magnitude and direction of
Consider the following four force vectors:F1→50.0 new tons, due eastF2→10.0 new tons, due eastF3→40.0 new tons, due eastF4→30.0 new tons, due eastWhich two vectors add together to give a resultant with the smallest magnitude, and which two vectors add to give a resultant with the largest
A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the 30.0° angle. The magnitude of the force applied by each rope is 2900 new tons. Arrange the force vectors tail to head and use the graphical
Vector A→ points along the +y-axis and has a magnitude of 100.0 units. Vector B→ points at an angle of 60.00 above the +x-axis and has a magnitude of 200.0 units. Vector C→ points along the +x-axis and has a magnitude of 150.0 units. Which vector has? (a) The largest x component and (b) The
The x vector component of a displacement vector r→ has a magnitude of 125 m and points along the negative x-axis. The y vector component has a magnitude of 184 m and points along the negative y-axis. Find the magnitude and direction of r→ specify the direction with respect to the negative
The magnitude of the force vector F→ is 82.3 new tons. The x component of this vector is directed along the +x-axis and has a magnitude of 74.6 new tons. The y component points along the +y-axis.(a) Find the direction of F→ relative to the +x-axis.(b) Find the component of F→ along the
Consult Multiple-Concept Example 9 in preparation for this problem. A golfer, putting on a green, requires three strokes to “hole the ball.” During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20.0° north of east. The third putt is
A sailboat racecourse consists of four legs, defined by the displacement vectors A†’ B†’ C†’ and D†’ as the drawing indicates. The magnitudes of the first three vectors areA = 3.20 km,B = 5.10 km, andC = 4.80 km.The finish line of the course coincides with
The speed of an object and the direction in which it moves constitute a vector quantity known as the velocity. An ostrich is running at a speed of 17.0 m/s in a direction of 68.0° north of west. What is the magnitude of the ostrich’s velocity component that is directed? (a) Due north and (b) Due
A circus performer begins his act by walking out along a nearly horizontal high wire. He slips and falls to the safety net, 25.0 ft below. The magnitude of his displacement from the beginning of the walk to the net is 26.7 ft.(a) How far out along the high wire did he walk?(b) Find the angle that
Vector has a magnitude of 6.00 units and points due east. Vector points due north(a) What is the magnitude of B→ if the vector A→ + B→ points 60.00 north of east?(b) Find the magnitude of A→ + B→.
Due to continental drift, the North American and European continents are drifting apart at an average speed of about 3 cm per year. At this speed, how long (in years) will it take them to drift apart by another 1500 m (a little less than a mile)?
A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 22 minutes at an average speed of 7.2 m/s. During the second part, she rides for 36 minutes at an average speed of 5.1 m/s. Finally, during the
A jogger accelerates from rest to 3.0 m/s in 2.0 s. A car accelerates from 38.0 to 41.0 m/s also in 2.0 s.(a) Find the acceleration (magnitude only) of the jogger.(b) Determine the acceleration (magnitude only) of the car.(c) Does the car travel farther than the jogger during the 2.0 s? If so how
A jetliner, traveling northward, is landing with a speed of 69 m/s. Once the jet touches down, it has 750 m of runway in which to reduce its speed to 6.1 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing.
A cart is driven by a large propeller or fan, which can accelerate or decelerate the cart. The cart starts out at the position x = 0 m, with an initial velocity of +5.0 m/s and a constant acceleration due to the fan. The direction to the right is positive. The cart reaches a maximum position of x =
A locomotive is accelerating at 1.6 m/s2. It passes through a 20.0-m-wide crossing in a time of 2.4 s. After the locomotive leaves the crossing, how much time is required until its speed reaches 32 m/s?
The greatest height reported for a jump into an airbag is 99.4 m by stuntman Dan Koko. In 1948, he jumped from rest from the top of the Vegas World Hotel and Casino. He struck the airbag at a speed of 39 m/s (88 mi/h). To assess the effects of air resistance, determine how fast he would have been
An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of +15 m/s and measures a time of 20.0 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet?
From her bedroom window, a girl drops a water-filled balloon to the ground, 6.0 m below. If the balloon is released from rest, how long is it in the air?
Consult Multiple-Concept Example to explore a model for solving this problem.(a) Just for fun, a person jumps from rest from the top of a tall cliff overlooking a lake. In falling through a distance H, she acquires a certain speed v. assuming free-fall conditions, how much farther must she fall in
A cement block accidentally falls from rest from the ledge of a 53.0-m-high building. When the block is 14.0 m above the ground, a man, 2.00 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way?
A person who walks for exercise produces the position–time graph given with this problem.(a)Without doing any calculations, decide which segments of the graph (A, B, C, or D) indicate positive, negative, and zero average velocities.(b) Calculate the average velocity for each segment to
Two runners start one hundred meters apart and run toward each other. Each runs ten meters during the first second. During each second thereafter, each runner runs ninety percent of the distance he ran in the previous second. Thus, the velocity of each person changes from second to second. However,
In preparation for this problem, review Conceptual Example. From the top of a cliff, a person uses a slingshot to fire a pebble straight downward, which is the negative direction. The initial speed of the pebble is 9.0 m/s. (a) What is the acceleration (magnitude and direction) of the pebble during
A speed ramp at an airport is basically a large conveyor belt on which you can stand and be moved along. The belt of one ramp moves at a constant speed such that a person who stands still on it leaves the ramp 64 s after getting on. Clifford is in a real hurry, however, and skips the speed ramp.
A woman and her dog are out for a morning run to the river, which is located 4.0 km away. The woman runs at 2.5 m/s in a straight line. The dog is unleashed and runs back and forth at 4.5 m/s between his owner and the river, until the woman reaches the river. What is the total distance run by the
In a quarter-mile drag race, two cars start simultaneously from rest, and each accelerates at a constant rate until it either reaches its maximum speed or crosses the finish line. Car A has an acceleration of 11.0 m/s2 and a maximum speed of 106 m/s. Car B has an acceleration of 11.6 m/s2 and a
Two trees have perfectly straight trunks and are both growing perpendicular to the flat horizontal ground beneath them. The sides of the trunks that face each other are separated by 1.3 m. A frisky squirrel makes three jumps in rapid succession. First, he leaps from the foot of one tree to a spot
In diving to a depth of 750 m, an elephant seal also moves 460 m due east of his starting point. What is the magnitude of the seal’s displacement?
A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar screen shows the satellite to be 162 km away. The radar antenna is pointing upward at an angle of 62.30 from the ground. Find the x and y components (in km) of the position vector of the satellite, relative to
A skateboarder, starting from rest, rolls down a 12.0-m ramp. When she arrives at the bottom of the ramp her speed is 7.70 m/s.(a) Determine the magnitude of her acceleration, assumed constant.(b) If the ramp is inclined at 25.0° with respect to the ground, what is the component of her
A volleyball is spiked so that it has an initial velocity of 15 m/s directed downward at an angle of 550 below the horizontal. What is the horizontal component of the ball’s velocity when the opposing player fields the ball?
A spider crawling across a table leaps onto a magazine blocking its path. The initial velocity of the spider is 0.870 m/s at an angle of 35.0° above the table, and it lands on the magazine 0.0770 s after leaving the table. Ignore air resistance. How thick is the magazine? Express your answer in
In the aerials competition in skiing, the competitors speed down a ramp that slopes sharply upward at the end. The sharp upward slope launches them into the air, where they perform acrobatic maneuvers. The end of a launch ramp is directed 630 above the horizontal. With this launch angle, a skier
As preparation for this problem, review Conceptual Example. The drawing shows two planes each about to drop an empty fuel tank. Now of release each plane has the same speed of 135 m/s, and each tank is at the same height of 2.00 km above the ground. Although the speeds are the same, the velocities
A fire hose ejects a stream of water at an angle of 35.00 above the horizontal. The water leaves the nozzle with a speed of 25.0 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?
An eagle is flying horizontally at 6.0 m/s with a fish in its claws. It accidentally drops the fish.(a) How much time passes before the fish’s speed doubles?(b) How much additional time would be required for the fish’s speed to double again?
An airplane with a speed of 97.5 m/s is climbing upward at an angle of 50.00 with respect to the horizontal. When the plane’s altitude is 732 m, the pilot releases a package.(a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the
An airplane is flying with a velocity of 240 m/s at an angle of 30.0° with the horizontal, as the drawing shows. When the altitude of the plane is 2.4 km, a flare is released from the plane. The flare hits the target on the ground. What is the angleθ?
The drawing shows an exaggerated view of a rifle that has been “sighted in†for a 91.4 meter target. If the muzzle speed of the bullet is v0 = 427 m/s, what are the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target?
From the top of a tall building, a gun is fired. The bullet leaves the gun at a speed of 340 m/s, parallel to the ground. As the drawing shows, the bullet puts a hole in a window of another building and hits the wall that faces the window. Using the data in the drawing, determine the distances D
A swimmer, capable of swimming at a speed of 1.4 m/s in still water (i.e., the swimmer can swim with a speed of 1.4 m/s relative to the water), starts to swim directly across a 2.8-km-wide river. However, the current is 0.91 m/s, and it carries the swimmer downstream. (a) How long does it take the
Two passenger trains are passing each other on adjacent tracks. Train A is moving east with a speed of 13 m/s, and train B is traveling west with a speed of 28 m/s. (a) What is the velocity (magnitude and direction) of train A as seen by the passengers in train B? (b) What is the velocity
Mario, a hockey player, is skating due south at a speed of 7.0 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 11.0 m/s and is moving in a direction of 22° west of south, relative to the ice. What are the magnitude and direction (relative to due south) of the
Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.00 m/s relative to the shore. Relative to boat 1, boat 2 is moving 30.0° north of east at a speed of 1.60 m/s. A passenger on boat 2 walks due east across the deck at a speed of 1.20 m/s relative to boat 2. What is the
Multiple-Concept Example provides useful background for this problem. A diver runs horizontally with a speed of 1.20 m/s off a platform that is 10.0 m above the water. What is his speed just before striking the water?
As preparation for this problem, review Conceptual Example. The two stones described there have identical initial speeds of v0 = 13.0 m/s and are thrown at an angle θ = 30.0°, one below the horizontal and one above the horizontal. What is the distance between the points where the stones strike
A person in a kayak starts paddling, and it accelerates from 0 to 0.60 m/s in a distance of 0.41 m. If the combined mass of the person and the kayak is 73 kg, what is the magnitude of the net force acting on the kayak?
A 1580-kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 50.0 m?
Two forces F→A and F→B are applied to an object whose mass is 8.0 kg. The larger force is F→A. When both forces point due east, the object’s acceleration has a magnitude of 0.50 m/s2. However, when F→A points due east and F→B points due west, the acceleration is 0.40 m/s2, due east.
A rocket of mass 4.50 × 105 kg is in flight. Its thrust is directed at an angle of 55.00 above the horizontal and has a magnitude of 7.50 × 106 N. Find the magnitude and direction of the rocket’s acceleration. Give the direction as an angle above the horizontal.
A 325-kg boat is sailing 15.0° north of east at a speed of 2.00 m/s. Thirty seconds later; it is sailing 35.0° north of east at a speed of 4.00 m/s. During this time, three forces act on the boat: a 31.0-N force directed 15.0° north of east (due to an auxiliary engine), a 23.0-N force directed
A bowling ball (mass = 7.2 kg, radius = 0.11 m) and a billiard ball (mass = 0.38 kg, radius = 0.028 m) may each be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other?
Synchronous communications satellites are placed in a circular orbit that is 3.59 × 107 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?
The mass of a robot is 5450 kg. This robot weighs 3620 N more on planet A than it does on planet B. Both planets have the same radius of 1.33 × 107 m. What is the difference MA - MB in the masses of these planets?
The sun is more massive than the moon, but the sun is farther from the earth. Which one exerts a greater gravitational force on a person standing on the earth? Give your answer by determining the ratio Fsun /Fmoon of the magnitudes of the gravitational forces. Use the data on the inside of the
A 60.0-kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.760 and 0.410, respectively. What horizontal pushing force is required to? (a) Just start the crate moving and (b) Slide the crate across the dock at a constant speed?
A 6.00-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.360. Determine the kinetic frictional force that acts on the box when the elevator is (a) Stationary, (b) Accelerating upward with an acceleration whose
A person is trying to judge whether a picture (mass = 1.10 kg) is properly positioned by temporarily pressing it against a wall. The pressing force is perpendicular to the wall. The coefficient of static friction between the picture and the wall is 0.660. What is the minimum amount of pressing
Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity?
A worker stands still on a roof sloped at an angle of 36° above the horizontal. He is prevented from slipping by a static frictional force of 390 N. Find the mass of the worker.
A 44-kg chandelier is suspended 1.5 m below a ceiling by three wires, each of which has the same tension and the same length of 2.0 m (see the drawing). Find the tension in eachwire.
A bicyclist is coasting straight down a hill at a constant speed. The combined mass of the rider and bicycle is 80.0 kg, and the hill is inclined at 15.0° with respect to the horizontal. Air resistance opposes the motion of the cyclist. Later, the bicyclist climbs the same hill at the same
A 15-g bullet is fired from a rifle. It takes 2.50 × 10-3 s for the bullet to travel the length of the barrel, and it exits the barrel with a speed of 715 m/s. assuming that the acceleration of the bullet is constant, find the average net force exerted on the bullet.
Only two forces act on an object (mass = 4.00 kg), as in the drawing. Find the magnitude and direction (relative to the x-axis) of the acceleration of theobject.
A student is skateboarding down a ramp that is 6.0 m long and inclined at 180 with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.6 m/s Neglect friction and find the speed at the bottom of the ramp.
Two objects (45.0 and 21.0 kg) are connected by a mass less string that passes over a mass less frictionless pulley. The pulley hangs from the ceiling. Find (a) The acceleration of the objects and (b) The tension in the string.
A person whose weight is 5.20 × 102 N is being pulled up vertically by a rope from the bottom of a cave that is 35.1 m deep. The maximum tension that the rope can withstand without breaking is 569 N. What is the shortest time, starting from rest, in which the person can be brought out of the cave?
A penguin slides at a constant velocity of 1.4 m/s down an icy incline. The incline slopes above the horizontal at an angle of 6.9°. At the bottom of the incline, the penguin slides onto a horizontal patch of ice. The coefficient of kinetic friction between the penguin and the ice is the same for
A 55-kg bungee jumper has fallen far enough that her bungee cord is beginning to stretch and resist her downward motion. Find the force (magnitude and direction) exerted on her by the bungee cord at an instant when her downward acceleration has a magnitude of 7.6 m/s2. Ignore the effects of air
A 95.0-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is?(a) Accelerating upward with an acceleration of 1.80 m/s2,(b) Moving upward at a constant speed, and(c) Accelerating downward with an acceleration of 1.30 m/s2?
A student presses a book between his hands, as the drawing indicates. The forces that he exerts on the front and back covers of the book are perpendicular to the book and are horizontal. The book weighs 31 N. The coefficient of static friction between his hands and the book is 0.40. To keep the
A 1380-kg car is moving due east with an initial speed of 27.0 m/s. After 8.00 s the car has slowed down to 17.0 m/s. find the magnitude and direction of the net force that produces the deceleration.
The drawing shows Robin Hood (mass = 77.0 kg) about to escape from a dangerous situation. With one hand, he is gripping the rope that holds up a chandelier (mass = 195 kg).When he cuts the rope where it is tied to the floor, the chandelier will fall, and he will be pulled up toward a balcony above.
At an airport, luggage is unloaded from a plane into the three cars of a luggage carrier, as the drawing shows. The acceleration of the carrier is 0.12 m/s2, and friction is negligible. The coupling bars have negligible mass. By how much would the tension in each of the coupling bars A, B, and C
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