University Physics with Modern Physics 13th edition Hugh D. Young, Roger A. Freedman, A. Lewis Ford - Solutions

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For many years Colonel John P. Step, USAF, held the world’s land speed record. On March 19, 1954, he rode a rocket-propelled sled that moved down a track at a speed of 632 mi/h. He and the sled were safely brought to rest in 1.40 s (Fig. P2.31). Determine (a) The negative acceleration he
A truck on a straight road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 20.0 m/s. Then the truck travels for 20.0 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.00 s. (a) How long is the truck in motion? (b)
An electron in a cathode ray tube (CRT) accelerates from 2.00 x 104 m/s to 6.00 x 106 m/s over 1.50 cm. (a) How long does the electron take to travel this 1.50 cm? (b) What is its acceleration?
In a 100-m linear accelerator, an electron is accelerated to 1.00% of the speed of light in 40.0m before it coasts for 60.0m to a target. (a) What is the electron’s acceleration during the first 40.0 m? (b) How long does the total flight take?
Within a complex machine such as a robotic assembly line, suppose that one particular part glides along a straight track. A control system measures the average velocity of the part during each successive interval of time ∆t0 =t0 - 0, compares it with the value vc it should be, and switches a
A glider on an air track carries a flag of length l through a stationary photo gate, which measures the time interval ∆td during which the flag blocks a beam of infrared light passing across the photo gate. The ratio vd l / ∆td is the average velocity of the glider over this part of its
A ball starts from rest and accelerates at 0.500 m/s2 while moving down an inclined plane 9.00 m long. When it reaches the bottom, the ball rolls up another plane, where, after moving 15.0 m, it comes to rest. (a) What is the speed of the ball at the bottom of the first plane? (b) How long does
Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at - 2.00 m/s 2 because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and at what
Solve Example 2.8, “Watch out for the Speed Limit!” by a graphical method. On the same graph plot position versus time for the car and the police officer, from the intersection of the two curves read the time at which the trooper overtakes the car
A golf ball is released from rest from the top of a very tall building. Neglecting air resistance, calculate (a) The position and (b) The velocity of the ball after 1.00, 2.00, and 3.00 s
Every morning at seven o’clock there’s twenty terriers drilling on the rock. The boss comes around and he says, “Keep still and bear down heavy on the cast-iron drill and drill, ye terriers, drill.” And drills, ye terriers, drill its work all day for sugar in your tea down beyond the
A ball is thrown directly downward, with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does the ball strike the ground?
A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister’s outstretched hand. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?
Emily challenges her friend David to catch a dollar bill as follows. She holds the bill vertically, as in Figure P2.44, with the center of the bill “between David” is index finger and thumb. David must catch the bill after Emily releases it without moving his hand downward. If his reaction time
In Mostar, Bosnia, the ultimate test of a young man’s courage once was to jump off a 400-year-old bridge (now destroyed) into the River Neretva, 23.0 m below the bridge. (a) How long did the jump last? (b) How fast was the diver traveling upon impact with the water? (c) If the speed of
A ball is dropped from rest from a height h above the ground. Another ball is thrown vertically upwards from the ground at the instant the first ball is released. Determine the speed of the second ball if the two balls are to meet at a height h/2 above the ground.
A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.00 s for the ball to reach its maximum height. Find (a) Its initial velocity and (b) The height it reaches.
It is possible to shoot an arrow at a speed as high as100 m/s. (a) If friction is neglected, how high would an arrow launched at this speed rise if shot straight up? (b) How long would the arrow be in the air?
A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of the saddle is 3.00 m. (a) What must be the horizontal distance between the saddle and limb when
A woman is reported to have fallen 144 ft from the 17th floor of a building, landing on a metal ventilator box, which she crushed to a depth of 18.0 in. She suffered only minor injuries. Neglecting air resistance, calculate (a) The speed of the woman just before she collided with the
The height of a helicopter above the ground is given by h = 3.00t 3, where h is in meters and t is in seconds. After 2.00 s, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground?
A freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall?
Automotive engineers refer to the time rate of change of acceleration as the “jerk.” If an object moves in one dimension such that its jerk J is constant, (a) Determine expressions for its acceleration ax (t), velocity vx (t), and position x (t), given that its initial acceleration, velocity,
A student drives a moped along a straight road as described by the velocity-versus-time graph in Figure P2.54. Sketch this graph in the middle of a sheet of graph paper. (a) Directly above your graph, sketch a graph of the position versus time, aligning the time coordinates of the two graphs.
The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = (- 5.00 x 107)t 2 + (3.00 x 105)t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero. (a) Determine the acceleration and
The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared, and is given (in SI units) by a = -3.00v 2 for v > 0. If the marble enters this fluid with a speed of 1.50 m/s, how long will it take before the marble’s speed is reduced to half of its initial
A car has an initial velocity v0 when the driver sees an obstacle in the road in front of him. His reaction time is ∆tr, and the braking acceleration of the car is a. Show that the total stopping distance is sstop = vo ∆tr – vo2/2a. Remember that a is a negative number.
The yellow caution light on a traffic signal should stay on long enough to allow a driver to either pass through the intersection or safely stop before reaching the intersection. A car can stop if its distance from the intersection is greater than the stopping distance found in the previous
The Acela is the Porsche of American trains. Shown in Figure P2.59a, the electric train whose name is pronounced ah-SELL-ah is in service on the Washington-New York- Boston run. With two power cars and six coaches, it can carry 304 passengers at 170 mi/h. The carriages tilt as much as 6- from the
Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60m long. The first moves past her in 1.50 s and the second in 1.10 s. find the constant acceleration of the train.
A dog’s hair has been cut and is now getting 1.04 mm longer each day. With winter coming on, this rate of hair growth is steadily increasing, by 0.132 mm/day every week. By how much will the dog’s hair grow during 5 weeks?
A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 80.0 m/s at ground level. Its engines then fire and it accelerates upward at 4.00 m/s2 until it reaches an altitude of 1 000 m. At that point its engines fail and the rocket goes into free fall, with an
A motorist drives along a straight road at a constant speed of 15.0 m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 2.00 m/s2 to overtake her. Assuming the officer maintains this acceleration, (a) Determine the time it takes the police officer to
In Figure 2.10b, the area under the velocity versus time curve and between the vertical axis and time t (vertical dashed line) represents the displacement. As shown, this area consists of a rectangle and a triangle. Compute their areas and compare the sum of the two areas with the expression on the
Setting a new world record in a 100-m race, Maggie and Judy cross the finish line in a dead heat, both taking 10.2 s. Accelerating uniformly, Maggie took 2.00 s and Judy 3.00 s to attain maximum speed, which they maintained for the rest of the race. (a) What was the acceleration of each sprinter?
A commuter train travels between two downtown stations. Because the stations are only 1.00 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the time interval ∆t between two stations by accelerating for a time interval ∆t1 at
A hard rubber ball, released at chest height, falls to the pavement and bounces back to nearly the same height. When it is in contact with the pavement, the lower side of the ball is temporarily flattened. Suppose that the maximum depth of the dent is on the order of 1 cm. Compute an
At NASA’s John H. Glenn research center in Cleveland, Ohio, free-fall research is performed by dropping experiment packages from the top of an evacuated shaft 145 m high. Free fall imitates the so-called micro gravity environment of a satellite in orbit. (a) What is the maximum time interval
An inquisitive physics student and mountain climber climbs a 50.0-m cliff that overhangs a calm pool of water. He throws two stones vertically downward, 1.00 s apart, and observes that they cause a single splash. The first stone has an initial speed of 2.00 m/s. (a) How long after release of the
A rock is dropped from rest into a well. The well is not really 16 seconds deep, as in Figure P2.70. (a) The sound of the splash is actually heard 2.40 s after the rock is released from rest. How far below the top of the well is the surface of the water? The speed of sound in air (at the ambient
To protect his food from hungry bears, a boy scout raises his food pack with a rope that is thrown over a tree limb at height h above his hands. He walks away from the vertical rope with constant velocity vboy, holding the free end of the rope in his hands (Fig. P2.71). (a) Show that the speed v
In Problem 71, let the height h equal 6.00 m and the speed vboy equal 2.00 m/s. Assume that the food pack starts from rest. (a) Tabulate and graph the speed–time graph. (b) Tabulate and graph the acceleration-time graph. Let the range of time be from 0 s to 5.00 s and the time intervals be
Kathy Kool buys a sports car that can accelerate at the rate of 4.90 m/s2. She decides to test the car by racing with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 1.00 s before Kathy. If Stan moves with a constant acceleration of 3.50 m/s2 and
The speed of sound in air is 331 m/s. During the next thunderstorm, try to estimate your distance from a lightning bolt by measuring the time lag between the flash and the thunderclap. You can ignore the time it takes for the light flash to reach you. Why?
The average velocity of a particle moving in one dimension has a positive value. Is it possible for the instantaneous velocity to have been negative at any time in the interval? Suppose the particle started at the origin x ! 0. If its average velocity is positive, could the particle ever have been
If the average velocity of an object is zero in some time interval, what can you say about the displacement of the object for that interval
Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than the average velocity over a time interval containing the instant? Can it ever be less?
If an object’s average velocity is nonzero over some time interval, does this mean that its instantaneous velocity is never zero during the interval? Explain your answer.
If an object’s average velocity is zero over some time interval, show that its instantaneous velocity must be zero at some time during the interval. It may be useful in your proof to sketch a graph of x versus t and to note that vx(t ) is a continuous function.
If the velocity of a particle is nonzero, can its acceleration be zero? Explain.
If the velocity of a particle is zero, can its acceleration be nonzero? Explain.
Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car A exceeds the velocity of car B. Does this mean that the acceleration of A is greater than that of B? Explain.
Is it possible for the velocity and the acceleration of an object to have opposite signs? If not, state a proof. If so, give an example of such a situation and sketch a velocity–time graph to prove your point.
Consider the following combinations of signs and values for velocity and acceleration of a particle with respect to a one-dimensional x axis: Velocity Acceleration a. Positive Positive b. Positive Negative c. Positive Zero d. Negative Positive e. Negative Negative f. Negative Zero g. Zero
Can the equations of kinematics (Eqs. 2.9–2.13) be used in a situation where the acceleration varies in time? Can they be used when the acceleration is zero?
A stone is thrown vertically upward from the roof of a building. Does the position of the stone depend on the location chosen for the origin of the coordinate system? Does the stone’s velocity depend on the choice of origin? Explain your answers.
A child throws a marble into the air with an initial speed vi. Another child drops a ball at the same instant. Compare the accelerations of the two objects while they are in flight.
A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed, vi. How do the final velocities of the balls compare when they reach the ground
A 20-lb block slides down a 300 inclined plane with an initial velocity of 2 ft/s. Determine the velocity of the block in 3 s if the coefficient of kinetic friction between the block and the plane is uk = 0.25
A 2-lb ball is thrown in the direction shown with an initial speed VA = 18 ft/s. Determine the time needed for it to reach its highest point B and the speed at which it is traveling at B. Use the principle of impulse and momentum for the solution.
A 5-lb block is given an initial velocity of 10 ft/s up 45o smooth slope. Determine the time it will take to travel up the slope before it stops.
The 180-lb iron worker is secured by a fall-arrest system consisting of a harness and lanyard AB, which is fixed to the beam. If the lanyard has slack of 4 ft determine the average impulsive force developed in the lanyard if he happens to fall 4 feet. Neglect his size in the calculation and assume
The graph shows the vertical reaction force of the shoe-ground interaction as a function of time. The first peak acts on the heel, and the second peak acts on the forefoot. Determine the total impulse acting on the shoe during the interaction.
A man hits the 50-g golf ball such that it leaves the tee at an angle of 40o with the horizontal and strikes the ground at the same elevation a distance of 20 m in away. Determine the impulse of the club C on the ball. Neglect the impulse caused by the ball’s weight while the club is striking the
A hammer head H having a weight of 0.25 lb is moving vertically downward at 40 ft/s when it strikes the head of a nail of negligible mass and drives it into a block of wood. Find the impulse on the nail if it is assumed that the grip at A is loose, the handle has a negligible mass, and the hammer
During operation the breaker hammer develops on the concrete surface a force which is indicated in the graph. To achieve this the 2-lb spike S is fired from rest into the surface at 200 ft/s. Determine the speed of the spike just alter rebounding.
When the 5-kg block is 6 m from the wall, it is sliding at v1 = 14 m/s. if the coefficient of kinetic friction between the block and the horizontal plane is uk = 0.3, determine the impulse of the wall on the block necessary to stop the block. Neglect the friction impulse acting on the block during
A man kicks the 200-g ball such that K leaves ground at an angle of 30o with the horizontal and strikes the ground at the same elevation a distance of 15 m away. Determine the impulse of his foot F on the ball. Neglect the impulse caused by the hull’s weight while its being kicked.
The particle P is acted upon by its weight of 3 lb and forces F1 and F2, where t is in seconds. If the particle originally has a velocity of v1 = {3i + 1j + 6k) ft/s, determine its speed after 2 s.
The twitch in a muscle of the arm develops a force which can be measured as a function of time as shown in the graph. If the effective contraction of the muscle lasts for a time t0, determine the impulse developed by the muscle.
Assuming that the force acting on a 2-g bullet, as it passes horizontally through the barrel of a rifle, varies with time in the manner shown, determine the maximum net force To, applied to the bullet when it is fired. The muzzle velocity is 500 m/s when t = 0.75 ms. Neglect friction between the
As indicated by the derivation, the principle of impulse and momentum is valid for observers in any inertial reference frame. Show that this is so, by considering the 10-kg block which rests on the smooth surface and is subjected to a horizontal force of 6 N. If observer A is in a fixed frame x,
The 4-lb cabinet is subjected to the force F =12(t + 1)^2 lb where t is in seconds. If the cabinet is initially moving up the plane with a velocity of 10 ft/s, determine how long it will take before the cabinet comes to a stop. F always acts parallel to the plane. Neglect the size of the rollers.
If it takes 35s for the 50-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest, determine the force of the rope on the tugboat. The propeller provides the propulsion force F winch gives the tugboat forward motion, whereas the barge moves freely. Also, determine F acting on the
The 5.5-Mg humpback whale is stuck on the there due to changes in the tide. In an effort to rescue a whale, 12-Mg tugboat is used to pull it fee using an inextensible rope tied to its tail. To overcome the frictional force of the sand on the whale, the tug backs up so that the rope becomes slack
The uniform beam has a weight of 5000 lb. Determine the average tension in each of the two cables AB and AC if the beam is given an upward speed of 8 ft/s in 1.5 s starting from rest. Neglect the mass of the cables.
The 5-kg block is moving downward at v1= 2 m/s when it is 8 m from the sandy surface. Determine the impulse of the sand on the block necessary to stop its motion. Neglect the distance the block dents into the sand and assume the block does not rebound. Neglect the weight of the block during the
The 5-kg block is falling downward at v1 2 m/s when it is 8 m from the sandy surface, Determine the average impulsive force acting on the block by the sand if the motion of the block is stopped in 0.9 s once the block strikes the sand. Neglect the distance the block dents into the sand and assume
A 30-tb block is initially moving along a smooth horizontal surface with a speed of v1 = 6 ft/s to the left. If it is acted upon by a force F, which varies in the manner shown, determine the velocity of the block in 15 s.
The rocket sled has a mass of 3 Mg and starts from rest when t = 0. If the engines provide a horizontal thrust T which varies as shown in the graph, determine the sled’s velocity in t = 4 s. Neglect air resistance, friction, and the loss of fuel during the motion.
A light string can support a stationary hanging load of 25.0 kg before breaking. A 3.00-kg object attached to the string rotates on a horizontal, frictionless table in a circle of radius 0.800 m, while the other end of the string is held fixed. What range of speeds can the object have before the
A curve in a road forms part of a horizontal circle. As a car goes around it at constant speed 14.0 m/s, the total force on the driver has magnitude 130 N. What is the total vector force on the driver if the speed is 18.0 m/s instead?
In the Bohr model of the hydrogen atom, the speed of the electron is approximately 2.20 x 106 m/s. Find (a) the force acting on the electron as it revolves in a circular orbit of radius 0.530 ) 10─10 m and (b) the centripetal acceleration of the electron.
In a cyclotron (one type of particle accelerator), a deuteron (of atomic mass 2.00 u) reaches a final speed of 10.0% of the speed of light while moving in a circular path of radius 0.480 m. The deuteron is maintained in the circular path by a magnetic force. What magnitude of force is required?
A coin placed 30.0 cm from the center of a rotating horizontal turntable slips when its speed is 50.0 cm/s. (a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable? (b) What is the coefficient of static friction between coin and turntable?
Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 100 km above the surface of the Moon, where the acceleration due to gravity is 1.52 m/s2. The radius of the Moon is 1.70) 106 m. Determine (a) The astronaut’s
A crate of eggs is located in the middle of the flat bed of a pickup truck as the truck negotiates an un-banked curve in the road. The curve may be regarded as an arc of a circle of radius 35.0 m. If the coefficient of static friction between crate and truck is 0.600, how fast can the truck be
The cornering performance of an automobile is evaluated on a skidpad where the maximum speed that a car can maintain around a circular path on a dry, flat surface is measured. Then the centripetal acceleration, also called the lateral acceleration, is calculated as a multiple of the free-fall
Consider a conical pendulum with an 80.0-kg bob on a 10.0-m wire making an angle of 5.00° with the vertical (Fig. P6.9). Determine (a) the horizontal and vertical components of the force exerted by the wire on the pendulum and (b) the radial acceleration of the bob.
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in Figure P6.10. The length of the arc ABC is 235 m, and the car completes the turn in 36.0 s. (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer
A 4.00-kg object is attached to a vertical rod by two strings, as in Figure P6.11. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) The upper string and (b) The lower string.
Casting of molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings and many other structures. A variety of sophisticated techniques have been invented, but the basic idea is as illustrated in Figure P6.12. A cylindrical enclosure is
A 40.0-kg child swings in a swing supported by two chains, each 3.00 m long. If the tension in each chain at the lowest point is 350 N, find (a) The child’s speed at the lowest point and (b) The force exerted by the seat on the child at the lowest point. (Neglect the mass of the seat.)
A child of mass m swings in a swing supported by two chains, each of length R. If the tension in each chain at the lowest point is T, find (a) The child’s speed at the lowest point and (b) The force exerted by the seat on the child at the lowest point. (Neglect the mass of the seat.)
Tarzan (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.0 m long, and his speed at the bottom of the swing (as he just clears the water) will be 8.00 m/s. Tarzan doesn’t know that the vine has a breaking strength of 1 000 N. Does he make it safely across the river?
A hawk flies in a horizontal arc of radius 12.0m at a constant speed of 4.00 m/s. (a) Find its centripetal acceleration. (b) It continues to fly along the same horizontal arc but increases its speed at the rate of 1.20 m/s2. Find the acceleration (magnitude and direction) under these conditions.
A pail of water is rotated in a vertical circle of radius 1.00 m. What is the minimum speed of the pail at the top of the circle if no water is to spill out?
A 0.400-kg object is swung in a vertical circular path on a string 0.500 m long. If its speed is 4.00 m/s at the top of the circle, what is the tension in the string there?
A roller coaster car (Fig.P6.19) has a mass of 500 kg when fully loaded with passengers. (a) If the vehicle has a speed of 20.0 m/s at point θ, what is the force exerted by the track on the car at this point? (b) What is the maximum speed the vehicle can have at " and still remain on the
An object of mass 5.00 kg, attached to a spring scale, rests on a frictionless, horizontal surface as in Figure P6.21. The spring scale, attached to the front end of a boxcar, has a constant reading of 18.0 N when the car is in motion. (a) If the spring scale reads zero when the car is at rest,

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University Physics with Modern Physics 13th edition Hugh D. Young, Roger A. Freedman, A. Lewis Ford - Solutions

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