When a book slides along a tabletop, the force of friction does negative work on it. Can friction ever do positive work? Explain.
> A stone with mass 0.80 kg is attached to one end of a string 0.90 m long. The string will break if its tension exceeds 60.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. (a) Draw a f
> (a) In Example 5.18 (Section 5.3), what value of D is required to make vt = 42 m/s for the skydiver? (b) If the skydiver’s daughter, whose mass is 45 kg, is falling through the air and has the same D 10.25 kg/m2 as her father, what is the daughter’s term
> A large crate with mass m rests on a horizontal floor. The coefficients of friction between the crate and the floor are
> You throw a baseball straight upward. The drag force is proportional to v2. In terms of g, what is the y-component of the ball’s acceleration when the ball’s speed is half its terminal speed and (a) it is moving up? (b) It is moving back down?
> As shown in Fig. E5.34, block A (mass 2.25 kg) rests on a tabletop. It is connected by a horizontal cord passing over a light, frictionless pulley to a hanging block B (mass 1.30 kg). The coefficient of kinetic friction between block A and the tabletop i
> A box with mass m is dragged across a level floor with coefficient of kinetic friction mk by a rope that is pulled upward at an angle u above the horizontal with a force of magnitude F. (a) In terms of m, mk, u, and g, obtain an expression for the magnit
> You have two identical tennis balls and fill one with water. You release both balls simultaneously from the top of a tall building. If air resistance is negligible, which ball will strike the ground first? Explain. What if air resistance is not negligibl
> Two crates connected by a rope lie on a horizontal surface (Fig. E5.37). Crate A has mass mA, and crate B has mass mB. The coefficient of kinetic friction between each crate and the surface is mk. The crates are pulled to the right at constant velocity b
> A 25.0-kg box of textbooks rests on a loading ramp that makes an angle a with the horizontal. The coefficient of kinetic friction is 0.25, and the coefficient of static friction is 0.35. (a) As a is increased, find the minimum angle at which the box star
> (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 a car by locking the brakes when the car is traveling at 28.7 m/s (about 65 mi/h)? (b) On wet pavement the coefficient
> Consider the system shown in Fig. E5.34. Block A weighs 45.0 N, and block B weighs 25.0 N. Once block B is set into downward motion, it descends at a constant speed. (a) Calculate the coefficient of kinetic friction between block A and the tabletop. (b)
> You are lowering two boxes, one on top of the other, down a ramp by pulling on a rope parallel to the surface of the ramp (Fig. E5.33). Both boxes move together at a constant speed of 15.0 cm>s. The coefficient of kinetic friction between the ramp and
> A pickup truck is carrying a toolbox, but the rear gate of the truck is missing. The toolbox will slide out if it is set moving. The coefficients of kinetic friction and static friction between the box and the level bed of the truck are 0.355 and 0.650,
> A box with mass 10.0 kg moves on a ramp that is inclined at an angle of 55.0o above the horizontal. The coefficient of kinetic friction between the box and the ramp surface is mk = 0.300. Calculate the magnitude of the acceleration of the box if you push
> 12 m/s. The hill rises at 36° above the horizontal and has coefficients of kinetic friction and static friction of 0.45 and 0.65, respectively, with these rocks. (a) Find the acceleration of the rocks as they slide up the hill. (b) Once a rock reaches it
> 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 37.0° below the horizontal, and the chair slides along the floor. (a) Draw a clearly
> A .22-caliber rifle bullet traveling at 350 m/s strikes a large tree and penetrates it 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 required for the bullet to stop? (b) What force, in ne
> You throw a baseball straight upward. If you do not ignore air resistance, how does the time required for the ball to reach its maximum height compare to the time required for it to fall from its maximum height back down to the height from which you thre
> 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 labeled free-body diagram for the ball if (a) the trai
> You pull horizontally on block B in Fig. E4.26, causing both blocks to move together as a unit. For this moving system, make a carefully labeled free-body diagram of block A if (a) the table is frictionless and (b) there is friction between block B and t
> Crates A and B sit at rest side by side on a frictionless horizontal surface. They have masses mA and mB, respectively. When a horizontal force
> A student of mass 45 kg jumps off a high diving board. What is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9.8 m/s2? Use 6.0 × 1024 kg for the mass of the earth, and assume that the net force on th
> Boxes A and B are in contact on a horizontal, frictionless surface (Fig. E4.23). Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 250 N is exerted on box A. What is the magnitude of the force that box A exerts on box B? Fig. E4.23
> 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 magnitude and direction of the acceleration?
> 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 starting blocks to produce this acceleration? Which bod
> A small car of mass 380 kg is pushing a large truck of mass 900 kg due east on a level road. The car exerts a horizontal force of 1600 N on the truck. What is the magnitude of the force that the truck exerts on the car?
> At the surface of Jupiter’s moon Io, the acceleration due to gravity is g = 1.81 m/s2. A watermelon weighs 44.0 N at the surface of the earth. (a) What is the watermelon’s mass on the earth’s surface? (b) What would be its mass and weight on the surface
> (a) An ordinary flea has a mass of 210 mg. How many newtons does it weigh? (b) The mass of a typical froghopper is 12.3 mg. How many newtons does it weigh? (c) A house cat typically weighs 45 N. How many pounds does it weigh, and what is its mass in kilo
> You throw a baseball straight upward with speed v0. When the ball returns to the point from where you threw it, how does its speed compare to v0 (a) in the absence of air resistance and (b) in the presence of air resistance? Explain.
> 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?
> An astronaut’s pack weighs 17.5 N when she is on the earth but only 3.24 N when she is at the surface of a moon. (a) What is the acceleration due to gravity on this moon? (b) What is the mass of the pack on this moon?
> A small 8.00-kg rocket burns fuel that exerts a time- varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation F = A + Bt2. Measurements show that at t = 0, the force is 100.0
> A 4.50-kg experimental cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13 shows this acceleration as a function of time. (a) Find the maximum net force on this cart. When does this maximum force occur? (b) During what
> A crate with mass 32.5 kg initially at rest on a warehouse floor is acted on by a net horizontal force of 14.0 N. (a) What acceleration is produced? (b) How far does the crate travel in 10.0 s? (c) What is its speed at the end of 10.0 s?
> 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 x-axis; she continues to apply this force until t = 2.00
> 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 s. (a) What is the mass of the block of ice? (b) If the wor
> 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 2.20 m/s2, what is the mass of the box?
> You walk into an elevator, step onto a scale, and push the “up” button. You recall that your normal weight is 625 N. Draw a free-body diagram. (a) When the elevator has an upward acceleration of magnitude 2.50 m/s2, what does the scale read? (b) If you h
> A tennis ball drops from rest at the top of a tall glass cylinder—first with the air pumped out of the cylinder so that there is no air resistance, and again after the air has been readmitted to the cylinder. You examine multiflash photographs of the two
> A 68.5-kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. What force does friction exert on the skater?
> An electron (mass = 9.11 × 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 with a speed of 3.00 × 106 m/s. If the accelerating force
> Forces
> A man is dragging a trunk up the loading ramp of a mover’s truck. The ramp has a slope angle of 20.0°, and the man pulls upward with a force
> Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force? Fig. E4.
> To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E4.2. (a) Find the x- and y-components of each of the three pulls. (b) Use the components to find the magnitude and direction of the resul
> Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0°. If Rover exerts a force of 270 N and Fido exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with Rover’s rope.
> A 0.800-kg ball is tied to the end of a string 1.60 m long and swung in a vertical circle. (a) During one complete circle, starting anywhere, calculate the total work done on the ball by (i) the tension in the string and (ii) gravity. (b) Repeat part (a)
> A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force
> Two blocks are connected by a very light string passing over a massless and frictionless pulley (Fig. E6.7). Traveling at constant speed, the 20.0-N block moves 75.0 cm to the right and the 12.0-N block moves 75.0 cm downward. How much work is done (a) o
> While hovering, a typical flying insect applies an average force equal to twice its weight during each downward stroke. Take the mass of the insect to be 10 g, and assume the wings move an average downward distance of 1.0 cm during each stroke. Assuming
> You are applying a constant horizontal force
> Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.80 × 106 N, one 14° west of north and the other 14° east of north, as they pull the tanker 0.75 km toward the north. What is the total work they do on the supertanker?
> A ski tow operates on a 15.0° slope of length 300 m. The rope moves at 12.0 km/h and provides power for 50 riders at one time, with an average mass per rider of 70.0 kg. Estimate the power required to operate the tow.
> An elevator has mass 600 kg, not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 20.0 m (five floors) in 16.0 s, and it is driven by a motor that can provide up to 40 hp to the elevator. What is the max
> Your job is to lift 30-kg crates a vertical distance of 0.90 m from the ground onto the bed of a truck. How many crates would you have to load onto the truck in 1 minute (a) for the average power output you use to lift the crates to equal 0.50 hp; (b) fo
> When its 75-kW (100-hp) engine is generating full power, a small single-engine airplane with mass 700 kg gains altitude at a rate of 2.5 m/s (150 m/min, or 500 ft/min). What fraction of the engine power is being used to make the airplane climb? (The rema
> A tandem (two-person) bicycle team must overcome a force of 165 N to maintain a speed of 9.00 m/s. Find the power required per rider, assuming that each contributes equally. Express your answer in watts and in horsepower.
> A 20.0-kg rock is sliding on a rough, horizontal surface at 8.00 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.200. What average power is produced by friction as the rock stops?
> On December 27, 2004, astronomers observed the greatest flash of light ever recorded from outside the solar system. It came from the highly magnetic neutron star SGR 1806-20 (a magnetar). During 0.20 s, this star released as much energy as our sun does i
> A falling brick has a mass of 1.5 kg and is moving straight downward with a speed of 5.0 m/s. A 1.5-kg physics book is sliding across the floor with a speed of 5.0 m/s. A 1.5-kg melon is traveling with a horizontal velocity component 3.0 m/s to the right
> 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 leisurely at 3.0 km/h (which uses energy at 290 W). Which c
> How many joules of energy does a 100-watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of kinetic energy?
> A crate on a motorized cart starts from rest and moves with a constant eastward acceleration of a = 2.80 m/s2. A worker assists the cart by pushing on the crate with a force that is eastward and has magnitude that depends on time according to F(t)=(5.40
> A 75.0-kg painter climbs a ladder that is 2.75 m long and leans against a vertical wall. The ladder makes a 30.0° angle with the wall. (a) How much work does gravity do on the painter? (b) Does the answer to part (a) depend on whether the painter climbs
> A force in the +x-direction with magnitude F(x)= 18.0 N –(0.530 N/m)x is applied to a 6.00-kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box. If the box is initially at rest at x
> An ingenious bricklayer builds a device for shooting bricks up to the top of the wall where he is working. He places a brick on a vertical compressed spring with force constant k = 450 N/m and negligible mass. When the spring is released, the brick is pr
> A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 40.0° above the horizontal. The glider has mass 0.0900 kg. The spring has k = 640 N/m and negligible mass. When the spring is released, t
> (a) Suppose you cut a massless ideal spring in half. If the full spring had a force constant k, what is the force constant of each half, in terms of k? (b) If you cut the spring into three equal segments instead, what is the force constant of each one, i
> At a waterpark, sleds with riders are sent along a slippery, horizontal surface by the release of a large compressed spring. The spring, with force constant k = 40.0 N/cm and negligible mass, rests on the frictionless horizontal surface. One end is in co
> Suppose the 2.0-kg model car in Exercise 6.43 is initially at rest at x = 0 and
> Many terms from physics are badly misused in everyday language. In both cases, explain the errors involved. (a) A strong person is called powerful. What is wrong with this use of power? (b) When a worker carries a bag of concrete along a level constructi
> A force
> A 4.00-kg block of ice is placed against a horizontal spring that has force constant k = 200 N/m and is compressed 0.025 m. The spring is released and accelerates the block along a horizontal surface. Ignore friction and the mass of the spring. (a) Calcu
> (a) In Example 6.7 (Section 6.3) it was calculated that with the air track turned off, the glider travels 8.6 cm before it stops instantaneously. How large would the coefficient of static friction
> As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do 80.0
> Suppose the worker in Exercise 6.3 pushes downward at an angle of 30° below the horizontal. (a) What magnitude of force must the worker apply to move the crate at constant velocity? (b) How much work is done on the crate by this force when the crate is p
> A 6.0-kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work–energy theorem to find the maximum compression of the spring.
> A spring of force constant 300.0 N/m and unstretched length 0.240 m is stretched by two forces, pulling in opposite directions at opposite ends of the spring, that increase to 15.0 N. How long will the spring now be, and how much work was required to str
> Suppose the sled in Exercise 6.36 is initially at rest at x = 0. Use the work–energy theorem to find the speed of the sled at (a) x = 8.0 m and (b) x = 12.0 m. Ignore friction between the sled and the surface of the pond.
> A child applies a force
> Three identical 8.50-kg masses are hung by three identical springs (Fig. E6.35). Each spring has a force constant of 7.80 kN/m and was 12.0 cm long before any masses were attached to it. (a) Draw a free-body diagram of each mass. (b) How long is each spr
> You swing a ball on the end of a lightweight string in a horizontal circle at constant speed. Can the string ever be truly horizontal? If not, would it slope above the horizontal or below the horizontal? Why?
> A ball is held at rest at position A in Fig. P5.115 by two light strings. The horizontal string is cut, and the ball starts swinging as a pendulum. Position B is the farthest to the right that the ball can go as it swings back and forth. What is the rati
> In Fig. P5.114 masses m1 and m2 are connected by a light string A over a light, frictionless pulley B. The axle of pulley B is connected by a light string Cover a light, frictionless pulley D to a mass m3. Pulley D is suspended from the ceiling by an att
> A wedge with mass M rests on a frictionless, horizontal tabletop. A block with mass m is placed on the wedge, and a horizontal force
> A wedge with mass M rests on a frictionless, horizontal tabletop. A block with mass m is placed on the wedge (Fig. P5.112a). There is no friction between the block and the wedge. The system is released from rest. (a) Calculate the acceleration of the wed
> A block of ice with mass 2.00 kg slides 1.35 m down an inclined plane that slopes downward at an angle of 36.9° below the horizontal. If the block of ice starts from rest, what is its final speed? Ignore friction.
> A factory worker pushes a 30.0-kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25. (a) What magnitude of force must the worker a
> A little red wagon with mass 7.00 kg moves in a straight line on a frictionless horizontal surface. It has an initial speed of 4.00 m>s and then is pushed 3.0 m in the direction of the initial velocity by a force with a magnitude of 10.0 N. (a) Use the w
> A soccer ball with mass 0.420 kg is initially moving with speed 2.00 m/s. A soccer player kicks the ball, exerting a constant force of magnitude 40.0 N in the same direction as the ball’s motion. Over what distance must the player’s foot be in contact wi
> A 12-pack of Omni-Cola (mass 4.30 kg) is initially at rest on a horizontal floor. It is then pushed in a straight line for 1.20 m by a trained dog that exerts a horizontal force with magnitude 36.0 N. Use the work–energy theorem to find the final speed o
> A mass m slides down a smooth inclined plane from an initial vertical height h, making an angle a with the horizontal. (a) The work done by a force is the sum of the work done by the components of the force. Consider the components of gravity parallel an
> A curve in a road has a bank angle calculated and posted for 80 km/h. However, the road is covered with ice, so you cautiously plan to drive slower than this limit. What might happen to your car? Why?
> In the conical pendulum of Example 5.20 (Section 5.4), which of the forces do work on the bob while it is swinging? Example 5.20: An inventor designs a pendulum clock using a bob with mass m at the end of a thin wire of length L. Instead of swinging ba
> A rookie quarterback throws a football with an initial upward velocity component of 12.0 m>s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (a) How much time is required for the football to reach the highest point of the trajecto
> Crickets Chirpy and Milada jump from the top of a vertical cliff. Chirpy drops downward and reaches the ground in 2.70 s, while Milada jumps horizontally with an initial speed of 95.0 cm/s. How far from the base of the cliff will Milada hit the ground? I
> A daring 510-N swimmer dives off a cliff with a running horizontal leap, as shown in Fig. E3.10. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below t
> A squirrel has x- and y-coordinates (1.1 m, 3.4 m) at time t1 = 0 and coordinates (5.3 m, -0.5 m) at time t2 = 3.0 s. For this time interval, find (a) the components of the average velocity, and (b) the magnitude and direction of the average velocity.
> A ball moves in a straight line (the x-axis). The graph in Fig. E2.9 shows this ball’s velocity as a function of time. (a) What are the ball’s average speed and average velocity during the first 3.0 s? (b) Suppose that
> A bird is flying due east. Its distance from a tall building is given by x(t)= 28.0 m +(12.4 m/s)t –(0.0450 m/s3)t3. What is the instantaneous velocity of the bird when t = 8.00 s?