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The earths 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... 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? 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 earth... How fast must a plane fly along the earths 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... 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... To withstand g-forces of up to 10 gs, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a human centrifuge. 10 gs is an acceleration of 98 m/s 2 . If the length of the... The radius of the earths very nearly circular orbit around the sun is 1.5 10 11 m. Find the magnitude of the earths (a) Velocity, (b) Angular velocity, and (c) Centripetal acceleration as it travels... A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s 2 . 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... FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshafts angular acceleration at (a) t = 1 s, (b) t = 3 s, and (c) t = 5 s? Figure Ex 4.37 w (rad/s) 250 -... FIGURE EX4.37 shows the angular acceleration graph of a turntable that starts from rest. What is the turntables angular velocity at (a) t = 1 s, (b) t = 2 s, and (c) t = 3 s? Figure Ex 4.37 a (rad/s)... 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... A wheel initially rotating at 60 rpm experiences the angular acceleration shown in FIGURE EX4.39. What is the wheels angular velocity, in rpm, at t = 3.0 s? Figure Ex 4.39 (rad/s?) 04 -t (s) 3 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... An electric fan goes from rest to 1800 rpm in 4.0 s. What is its angular acceleration? a. A projectile is launched with speed v 0 and angle . Derive an expression for the projectiles maximum height h. b. A baseball is hit with a speed of 33.6 m/s. Calculate its height and the distance... 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 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 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 net... 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 bulls-eye of a target at the same... 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... 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... FIGURE EX1.11 shows two dots of a motion diagram and vector 1 Copy this figure, then add dot 4 and the next velocity vector 2 if the acceleration vector at dot 3 (a) Points right and (b) Points left?... Breathing Oxygen. The density of air under standard laboratory conditions 1.29 kg/m 3 is and about 20% of that air consists of oxygen. Typically, people breathe about L of air per breath. (a) How... Compute the x- and y-components of the vectors A, B, C, and D in Fig. E1.28. Figure E1.28: B (15.0 m) 30.0 (10.0 m) 53.0 25.0 (12.0 m) V (8.00 m) 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... 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... (a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in g/day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of... Vector A has y-component A y = +13.0 m. A makes an angle of 32.0 o counterclockwise from the y-axis. (a) What is the x-component of A? (b) What is the magnitude of A? A rectangular piece of aluminum is 7.60 0.01 cm long and 1.90 0.01 cm wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional uncertainty in the... Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0 west of north, and the resultant of these two pulls is 460.0 N directly... (a) Find the magnitude and direction of the vector R that is the sum of the three vectors A, B, and C in Fig. E1.28. In a diagram, show how is formed from these three vectors. (b) Find the magnitude... A rocket fires two engines simultaneously. One produces a thrust of 480 N directly forward, while the other gives a 513-N thrust at 32.4 o above the forward direction. Find the magnitude and... Dislocated Shoulder. A patient with a dislocated shoulder is put into a traction apparatus as shown in Fig. P1.73. The pulls and have equal magnitudes and must combine to produce an outward traction... A dog in an open field runs 12.0 m east and then 28.0 m in a direction 50.0 o west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point? Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 26.0 m in a direction 60.0 o west of north. Jane... John, Paul, and George are standing in a strawberry field. Paul is 14.0 m due west of John. George is 36.0 m from Paul, in a direction 37.0 o south of east from Pauls location. How far is George from... Vectors A and B have scalar product -6.00 and their vector product has magnitude +9.00. What is the angle between these two vectors? When two vectors A and B are drawn from a common point, the angle between them is ɸ. (a) Using vector techniques, show that the magnitude of their vector sum is given by (b) If A and B... The scalar product of vectors A and B is +48.0 m 2 . Vector A has magnitude 9.00 m and direction 28.0 o west of south. If vector B has direction 39.0 o south of east, what is the magnitude of B? Three sleds are being pulled horizontally on friction less horizontal ice using horizontal ropes (Fig. E5.14). The pull is of magnitude 125 N. Find (a) The acceleration of the system and (b) The... All the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. Figure P1.101 shows the... Sam heaves a 16-lb shot straight upward, giving it a constant upward acceleration from rest of 35.0 m/s 2 for 64.0 cm. He releases it 2.20 m above the ground. You may ignore air resistance. (a) What... In the treatment of spine injuries, it is often necessary to provide some tension along the spinal column to stretch the backbone. One device for doing this is the Stryker frame, illustrated in Fig.... An average person can reach a maximum height of about 60 cm when jumping straight up from a crouched position. During the jump itself, the persons body from the knees up typically rises a distance of... A 2.00-kg box is moving to the right with speed on a horizontal, friction less surface. At a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t) = (6.00... A 5.00-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position... In emergencies with major blood loss, the doctor will order the patient placed in the Trendelenburg position, in which the foot of the bed is raised to get maximum blood flow to the brain. If the... A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it is set moving. The coefficients of kinetic and static friction between the box and the... While a person is walking, his arms swing through approximately a 45 angle in s. As a reasonable approximation, we can assume that the arm moves with constant speed during each swing. A typical arm... A 5.00-kg box sits at rest at the bottom of a ramp that is 8.00 m long and that is inclined at 30.0 o above the horizontal. The coefficient of kinetic friction is k = 0.40, and the coefficient of... A 6.00-kg box sits on a ramp that is inclined at 37.0 o above the horizontal. The coefficient of kinetic friction between the box and the ramp is k = 0.30. What horizontal force is required to move... A 25,000-kg rocket blasts off vertically from the earths surface with a constant acceleration. During the motion considered in the problem, assume that g remains constant (see Chapter 13). Inside the... People who do chin-ups raise their chin just over a bar (the chinning bar), supporting themselves with only their arms. Typically, the body below the arms is raised by about 30 cm in a time of 1.0 s,... People (especially the elderly) who are prone to falling can wear hip pads to cushion the impact on their hip from a fall. Experiments have shown that if the speed at impact can be reduced to 1.3 m/s... In Fig. P5.34 block A has mass m and block B has mass 6.00 kg. The coefficient of kinetic friction between block A and the tabletop is μ k = 0.40. The mass of the rope connecting the... You are standing on a bathroom scale in an elevator in a tall building. Your mass is 64 kg. The elevator starts from rest and travels upward with a speed that varies with time according to u(t) =... A hammer is hanging by a light rope from the ceiling of a bus. The ceiling of the bus is parallel to the roadway. The bus is traveling in a straight line on a horizontal street. You observe that the... A 40.0-kg packing case is initially at rest on the floor of a 1500-kg pickup truck. The coefficient of static friction between the case and the truck floor is 0.30, and the coefficient of kinetic... A box with weight w is pulled at constant speed along a level floor by a force that is at an angle above the horizontal. The coefficient of kinetic friction between the floor and box is k . (a) In... An 8.00-kg package in a mail-sorting room slides 2.00 m down a chute that is inclined at 53.0 below the horizontal. The coefficient of kinetic friction between the package and the chutes surface is... A boxed 10.0-kg computer monitor is dragged by friction 5.50 m up along the moving surface of a conveyor belt inclined at an angle of 36.9 above the horizontal. If the monitors speed is a constant... You apply a constant force F = (68.0 N)i + (36.0 N)j to a 380-kg car as the car travels 48.0 m in a direction that is 240.0 counterclockwise from the +x-axis. How much work does the force you apply... A 1.50-kg book is sliding along a rough horizontal surface. At point A it is moving at 3.21 m s, and at point B it has slowed to 1.25 m s. (a) How much work was done on the book between A and B? (b)... (a) In the Bohr model of the atom, the ground-state electron in hydrogen has an orbital speed of 2190 km/s. What is its kinetic energy? (b) If you drop a 1.0-kg weight (about 2 lb) from a height of... A surgeon is using material from a donated heart to repair a patients damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a 16.0-cm strip of the... A 2.0-kg box and a 3.0-kg box on a perfectly smooth horizontal floor have a spring of force constant 250 N/m compressed between them. If the initial compression of the spring is 6.0 cm, find the... Three identical 6.40-kg masses are hung by three identical springs, as shown in Fig. E6.33. Each spring has a force constant of and was 12.0 cm long before any masses were attached to it. (a) Draw a... A crate on a motorized cart starts from rest and moves with a constant eastward acceleration of = 2.80 m/s 2 . A worker assists the cart by pushing on the crate with a force that is eastward and has... It is 5.0 km from your home to the physics lab. As part of your physical fitness program, you could run that distance at 10 km h (which uses up energy at the rate of 700 W), or you could walk it... A 20.0-kg crate sits at rest at the bottom of a 15.0-m-long ramp that is inclined at 34.0 above the horizontal. A constant horizontal force of 290 N is applied to the crate to push it up the ramp.... A 5.00-kg package slides 1.50 m down a long ramp that is inclined at 24.0 below the horizontal. The coefficient of kinetic friction between the package and the ramp is Calculate (a) The work done on... When a car is hit from behind, its passengers undergo sudden forward acceleration, which can cause a severe neck injury known as whiplash. During normal acceleration, the neck muscles play a large... A block of ice with mass 4.00 kg is initially at rest on a frictionless, horizontal surface. A worker then applies a horizontal force F to it. As a result, the block moves along the x-axis such that... You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200-kg car moving at 0.65 m/s is to compress the spring no more than 0.090 m before stopping. What should... All birds, independent of their size, must maintain a power output of 1025 watts per kilogram of body mass in order to fly by flapping their wings. (a) The Andean giant hummingbird (Patagona gigas)... The food calorie, equal to 4186 J, is a measure of how much energy is released when food is metabolized by the body. A certain brand of fruit-and-cereal bar contains 140 food calories per bar. (a) If... The maximum energy that a bone can absorb without breaking depends on its characteristics, such as its cross-sectional area and its elasticity. For healthy human leg bones of approximately 6.0 cm2... Tendons are strong elastic fibers that attach muscles to bones. To a reasonable approximation, they obey Hookes law. In laboratory tests on a particular tendon, it was found that, when a 250-g object... A 2.50-kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0300 m. The spring has force constant 840 N/m. The coefficient of kinetic friction between the... Consider the glider of Example 7.7 and Fig. 7.16. As in the example, the glider is released from rest with the spring stretched 0.100 m. What is the displacement x of the glider from its equilibrium... Consider the glider of Example 7.7 and Fig. 7.16. (a) As in the example, the glider is released from rest with the spring stretched 0.100 m. What is the speed of the glider when it returns to x = 0?... (a) For the elevator of Example 7.9, what is the speed of the elevator after it has moved downward 1.00 m from point 1 in Fig. 7.17? (b) When the elevator is 1.00 m below point 1 in Fig. 7.17, what... A 15.0-kg stone slides down a snow-covered hill (Fig. P7.49), leaving point A with a speed of 10.00 m/s. There is no friction on the hill between points A and B, but there is friction on the level... A 0.300-kg potato is tied to a string with length 2.50 m, and the other end of the string is tied to a rigid support. The potato is held straight out horizontally from the point of support, with the... A sled with rider having a combined mass of 125 kg travels over the perfectly smooth icy hill shown in Fig. 7.68. How far does the sled land from the foot of the cliff? Figure 7.68: 11.0m Cliff 22.5... A 3.00-kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 900 N/m. The spring initially is neither stretched nor compressed. The fish is released... A basket of negligible weight hangs from a vertical spring scale of force constant 1500 N/m. (a) If you suddenly put a 3.0-kg adobe brick in the basket, find the maximum distance that the spring will... A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in Fig. P7.86. The particle is... The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 30 ms. (This number can also vary, depending... Experimental tests have shown that bone will rupture if it is subjected to a force density of 1.03 10 8 N/m 2 . Suppose a 70.0-kg person carelessly rollerskates into an overhead metal beam that hits... To warm up for a match, a tennis player hits the 57.0-g ball vertically with her racket. If the ball is stationary just before it is hit and goes 5.50 m high, what impulse did she impart to it? Two identical 1.50-kg masses are pressed against opposite ends of a light spring of force constant compressing the spring by 20.0 cm from its normal length. Find the speed of each mass when it has... In a volcanic eruption, a 2400-kg boulder is thrown vertically upward into the air. At its highest point, it suddenly explodes (due to trapped gases) into two fragments, one being three times the... A 1500-kg blue convertible is traveling south, and a 2000-kg red SUV is traveling west. If the total momentum of the system consisting of the two cars is 7200 kg m/s directed at 60.0 west of south,... An 8.00-kg block of wood sits at the edge of a frictionless table, 2.20 m above the floor. A 0.500-kg blob of clay slides along the length of the table with a speed of 24.0 m/s, strikes the block of... A small wooden block with mass 0.800 kg is suspended from the lower end of a light cord that is 1.60 m long. The block is initially at rest. A bullet with mass 12.0 g is fired at the block with a... A 5.00-kg chunk of ice is sliding at 12.0 m/s on the floor of an ice-covered valley when it collides with and sticks to another 5.00-kg chunk of ice that is initially at rest. Since the valley is... (a) When an object is in a circular orbit of radius r around the earth (mass ), the period of the orbit is T, given by Eq. (13.12), and the orbital speed is given by Eq. (13.10). Show that when the... A shaft is drilled from the surface to the center of the earth (see Fig. 13.24). As in Example 13.10 (Section 13.6), make the unrealistic assumption that the density of the earth is uniform. With... A 5000-kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the...
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