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physics
mechanics
Questions and Answers of
Mechanics
Projectile Motion on an Incline IL Refer to Challenge Problem 3.89. (a) An archer on ground that has a constant upward slope of 30.00 aims at a target 60.0 m farther up the incline. The arrow in
For no apparent reason, a poodle is running at a constant speed of v ~ 5.00 m/s in a circle with radius R = 2.50 m. Let VI be the velocity vector at time t" and let V2 be the velocity vector at time
A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 k/n above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed
Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 60 minutes, reaching a point 2.0 km farther upstream.
Two forces have the same magnitude F. What is the angle between the two vectors if their sum bas a magnitude of (a) 2F? (b) √2F? (c) zero? Sketch the three vectors in each case.
Instead of using the x- and y-axes of Fig. 4.8 to analyze the situation of Example 4.1, use axes rotated 37.0° counterclockwise, so the y-axis is parallel to the 250-N force. (a) For these axes
A warehouse worker pushes a crate along the floor, as shown in Fig. 4.31, with a force of 10 N that points downward at an angle of 450 below the horizontal. Find the horizontal and vertical
A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.00, and the man pulls upward with a force F whose direction makes an angle of30.0o with the ramp
Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.00. If dog A exerts a force of 270 N and dog B exerts a force of300 N, find the magnitude of the resultant
If a net horizontal force of 132 N is applied to a person with mass 60 kg who is resting on the edge of a swimming pool, what horizontal acceleration is produced?
Two forces, F1, and F2, act at a point. The magnitude of F1 is 9.00 N, and its direction is 60.00 above the x-axis in the second quadrant. The magnitude of F 2 is 6.00 N, and its direction is 53.10
What magnitude of net force is required to give a 135-kg refrigerator an acceleration of magnitude 1.40 m/S2?
A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude
A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00
A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to the puck, parallel to the
A crate with mass 325 kg initially at rest on a warehouse floor is acted on by a net horizontal force of 140 N. (a) What acceleration is produced? (b) How far does the crate travel in 10.0
A4.50-kg toy cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. 4.33 shows this acceleration as a function of time.(a) Find the maximum net force on this cart. When
A2.75-kg cat moves in a straight line (the x-axis). Figure 4.34 shows a graph of the x-component of this cat's velocity as a function of time.(a) Find the maximum net force on this cat. When does
A small 8.00-kg rocket bums fuel that exerts a time-varying upward force on the rocket. This force obeys the equation F = A + Bt2. Measurements show that at t = 0, the force is 100.0N, and at the end
An electron (mass = 9.11 X 10-31 kg) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.80 cm away. It reaches the grid
Superman throws a 2400-N boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of 12.0 m}S2?
A bowling ball weighs 71.2 N (16.0 Ib). The bowler applies a horizontal force of 160 N (36.0 lb) to the ball. What is the magnitude of the horizontal acceleration of the ball?
At the surface of Jupiter's moon 10, the acceleration due to gravity is g = 1.81 mfs2. A watermelon weighs 44.0 N at the surface of the earth. (a) What is the watermelon's mass on the earth's
An astronaut's pack weighs 17.5 N when she is on earth but only 3.24 N when she is at the surface of an asteroid. (a) What is the acceleration due to gravity on this asteroid? (b) What is the
World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude 15 m/s2. How much horizontal force must a 55-kg sprinter exert on the
Imagine that you are holding a book weighing 4 N at rest on the palm of your hand. Complete the following sentences: (a) A downward force of magnitude 4 N is exerted on the book by _____ . (b) An
A bottle is given a push along a tabletop and slides off the edge of the table. Do not ignore air resistance. (a) What forces are exerted on the bottle while it is falling from the table to the
The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the
A student with mass 45 kg jumps off a high diving board. Using 6.0 X l024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an
An athlete throws a ball of mass m directly upward, and it feels no appreciable air resistance. Draw a free-body diagram of this ball while it is free of the athlete's hand and (a) moving upward; (b)
Two crates, A and B, sit at rest side by side on a frictionless horizontal surface. The crates have masses mA and mB. A horizontal force F is applied to crate A and the two crates move off to the
A person pulls horizontally on block B in Fig. 4.35, causing both blocks to move together as a unit. While this system is moving, make a carefully labeled free-body diagram of block A if (a) The
A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly
A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your
A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 37.ft' below the horizontal
A skier of mass 65.0 kg is pulled up a snow-covered slope at constant speed by a tow rope that is parallel to the ground. The ground slopes upward at a constant angle of 26.0° above the horizontal,
A truck is pulling a car 00 a horizontal highway using a horizontal rope. The car is in neutral gear, so we can assume that there is no appreciable friction between its tires and the highway. As the
A .22 rifle bullet, traveling at 350 m/s, strikes a large tree, which it penetrates to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume a constant retarding force. (a) How much time is
Two horses pull horizontally on ropes attached to a stump. The two forces F1, and F2 that they apply to the stump are such that the net (resultant) force R has a magnitude equal to that of F, and
You have just landed on Planet X. You take out a l00-g ball, release it from rest from a height of 10.0 m, and measure that it takes 2.2 s to reach the ground. You can ignore any force on the ball
Two adults and a child want to push a wheeled cart in the direction marked x in Fig. 4.36. The two adults Rush with~ horizontal forces F 1 and F 2 as shown in the figure. (a) Find the magnitude and
An oil tanker's engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of 1.5 m/s (Fig. 4.37). When the tanker is 500 m from the reef, the wind dies
A Standing Vertical Jump Basketball player Darrell Griffith is on record as attaining a standing vertical jump of 1.2 m (4 ft). (This means that he moved upward by 1.2 m after his feet left the
An advertisement claims that a particular automobile can "stop on a dime." What net force would actually be necessary to stop a 850-kg automobile traveling initially at 45.0 km/h in a distance equal
A 4.80-kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 75.0 N. (a) Draw the free-body force diagram for the bucket. In terms of the forces on your
A parachutist relies on air resistance (mainly on her parachute) to decrease her downward velocity. She and her parachute have a mass of 55.0 kg, and air resistance exerts a total upward force of 620
Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope (Fig. 4.38). A woman wearing golf shoes (so she can get
An astronaut is tethered by a strong cable to a spacecraft. The astronaut and her space snit have a total mass of 105 kg, while the mass of the cable is negligible. The mass of the spacecraft is 9.05
To study damage to aircraft that collide with large birds, you design a test gun that will accelerate chicken-sized objects so that their displacement along the gun barrel is given by x = (9.0 X 103
A spacecraft descends vertically near the surface of Planet X. An upward thrust of 25.0 kn from its engines slows it down at a rate of 1.20 m/S2, but it speeds up at a rate of 0.80 m}S2 with an
A 6.50-kg instrument is hanging by a vertical wire inside a space ship that is blasting off at the surface of the earth. This ship starts from rest and reaches an altitude of 276 min 15.0 s with
Suppose the rocket in Problem 4.47 is coming in for a vertical landing instead of blasting off. The captain adjusts the engine thrust so that the magnitude of the rocket's acceleration is the same as
A gymnast of mass m climbs a vertical rope attached to the ceiling. You can ignore the weight of the rope. Draw a free-body diagram for the gymnast. Calculate the tension in the rope if the gymnast
A loaded elevator with very worn cables has a total mass of 2200 kg, and the cables can withstand a maximum tension of 28,000 N. (a) Draw the free-body force diagram for the elevator. In terms of
Jumping to the Ground a 75.O-kg man steps off a platform 3.10 m above the ground, he keeps his legs straight as he falls, but at the moment his feet touch the ground his knees begin to bend and
A 4.9-N hammer head is stopped from an initial downward velocity of 3.2 m/s in a distance of 0.45 cm by a nail in a pine board. In addition to its weight, there is a 15-N downward force on the hammer
A uniform cable of weight w hangs vertically downward, supported by an upward force of magnitude w at its top end. What is the tension in the cable (a) At its top end; (b) At its bottom end;
The two blocks in Fig. 4.39 are connected by a heavy uniform rope with a mass of 4.00 kg. An upward force of 200 N is applied as shown. (a) Draw three free-body diagrams, one for the 6.00-kg block,
An athlete whose mass is 90.0 kg is performing weight-lifting exercises. Starting from the rest position, he lifts, with constant acceleration, a barbell that weighs 490 N. He lifts the barbell a
A hot-air balloon consists of a bas-t ket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating
A student tries to raise a chain consisting of three identical links. Each link has a mass of 300 g. The three-piece chain is connected to a string and then suspended vertically, with the student
The position of a 2.75 X 102 N training helicopter under test isgivenby1 = (0.020 m/s2)t2 + (2.2m/s)tj- (0.060m}S2)t2k, Find the net force on the helicopter at t = 5.0 s
An object with mass m moves along the x-axis. Its position as a function of time is given by x (t) = At – Bt3, where A and B are constants. Calculate the net force on the object as a function of
An object with mass m initially at rest is acted on by a force F = kli, + k2t3j, where kl and k2 are constants. Calculate the velocity v(t) of the object as a function of time.
If we know F(t), the force as a function of time, for straight-line motion, Newton's second law gives us a (t), the acceleration as a function of time. We can then integrate a (t) to find v (t) and x
An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force F (t) is applied that has components Fx (t) = kl + k2y Fy (t) = k3t where k1, k2, and k3 are constants. Calculate the
Two 25.0-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain that goes to the ceiling. (a) What is the tension in the
In Fig. 5.41 each of the suspended blocks has weight w. The pulleys are frictionless and the ropes have negligible weight. Calculate, in each case, the tension T in the rope in terms of the weight w.
A 75.0-kg wrecking ball hangs from a uniform heavy-duty chain having a mass of 26.0 kg. (a) Find the maximum and minimum tension in the chain. (b) What is the tension at a point three fourths of
An adventurous archaeologist crosses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 5.42). The rope
A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each
Solve the problem in Example 5.5 using coordinate axes where the y-axis is vertical and the x-axis is horizontal. Do you get the same answers using this different set of axes?
Certain streets in San Francisco make an angle of 17.5° with the horizontal. What force parallel to the street surface is required to keep a loaded 1967 Corvette of mass 1390 kg from rolling down
A large wrecking ball is held in place by two light steel cables (Fig. 5.43). If the mass m of the wrecking ball is 4090 kg, what are(a) The tension TB in the cable that makes an angle of 40°
Find the tension in each cord in Fig. 5.44 if the weight of the suspended object is w.
A 1130-kg car is held in place by a light cable on a very smooth (frictionless) ramp, as shown in Fig. 5.45. The cable makes an angle of31.0° above the surface of the ramp, and the ramp itself
A man pushes on a piano with mass 180 kg so that it slides at constant velocity down a ramp that is inclined at 11.00 above the horizontal floor. Neglect any friction acting on the piano. Calculate
In Fig. 5.46 the weight w is 60.0 N.(a) What is the tension in the diagonal string?(b) Find the magnitudes of the horizontal forces FI and F2 that must be applied to hold the system in the position
A solid uniform 45.0-kg ball of diameter 32.0 cm is supported against a vertical frictionless wall using a thin 30.0-cm wire of negligible mass, as shown in Fig. 5.47.(a) Make a free-body diagram for
Two blocks, each with weight w, are held in place on a frictionless incline (Fig. 5.48). In terms of w and the angle a of the incline, calculate the tension in(a) The rope connecting the blocks
A horizontal wire holds a solid uniform ball of mass m in place on a tilted ramp that rises 35.00 above the horizontal. The surface of this ramp is perfectly smooth, and the wire is directed away
A 125-kg (including all the contents) rocket bas an engine that produces a constant vertical force (the thrust) of 1720 N. Inside this rocket, a 15.5-N electrical power supply rests on the floor.
Genesis Crash On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210-kg capsule hit the ground at 311 km/b and penetrated the soil to a
Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. 5.50). The pull is horizontal and of magnitude 125 N. Find (a) The acceleration of the system
Atwood's Machine A 15.O-kg load of bricks hangs from one end of a rope that passes over a small, frictionless pulley. A 28.O-kg counterweight is suspended from the other end of the rope. As shown in
A 8.00.kg block of ice, released from rest at the top of a 1.50-m-long frictionless ramp, slides downhill, reaching a speed of 2.50 m/s at the bottom. (a) What is the angle between the ramp and the
A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, mass less pulley, and a block with mass m is
Runway Design A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 700 kg, and the total resistance (air drag plus friction
A 750.0-kg boulder is raised from a quarry 125 m deep by a long uniform chain having a mass of 575 kg. This chain is of uniform strength, but at any point it can support a maximum tension no greater
Apparent Weight, A 550-N physics student stands on a bathroom scale in an 850-kg (including the student) elevator that is supported by a cable. As the elevator stands moving, the scale reads 450 N.
A physics student playing with an air hockey table (a frictionless surface) finds that if she gives the puck a velocity of 3.80rn}s along the length (1.75 m) of the table at one end, by the time it
A 2540-kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force so that its vertical velocity as a function of time is given by v{t) = At +
Free-Body Diagrams the first two steps in the solution of Newton's second-law problems are to select an object for analysis and then to draw free-body diagrams for that object. Draw free-body
In a laboratory experiment on friction, a 135-N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to
A stockroom worker pushes a box with mass 11.2 kg on a horizontal surface with a constant speed of 3.50 m/s. The coefficient of kinetic friction between the box and the surface is 0.20. (a) What
A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (a) If no
A crate of 45.0-kg tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it and observe that the crate just begins to move when your force exceeds 313 N. After that
An 85-N box of oranges is being pushed across a horizontal floor. As it moves, it is slowing at a constant rate of 0.90 m/s each second. The push force has a horizontal component of 20 N and a
You are lowering two boxes, one on top of the other, down the ramp shown in Figure 5.53 by pulling on a rope parallel to the surface of the ramp. Both boxes move together at a constant speed of 15.0
Stopping Distance (a) If the coefficient of kinetic friction between tires and dry pavement is 0.80, what is the shortest distance in which you can stop an automobile by locking the brakes when
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