A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 80.0 N at an angle of 25.0° above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and floor is 0.300. (a) Find the acceleration of the box. (b) The student now starts moving the box up a 10.0° incline, keeping her 80.0 N force directed at 25.0° above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?
> An airplane maintains a speed of 630 km/h relative to the air it is flying through, as it makes a trip to a city 750 km away to the north. (a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 km/h toward t
> A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50 m/s2. (a) What is the acceleration of the bolt relative to the train car? (b) What is the acceleration of the bolt relative to the Earth? (c) Describe th
> A Coast Guard cutter detects an unidentified ship at a distance of 20.0 km in the direction 15.0° east of north. The ship is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat to intercept and investigat
> A jet airliner moving initially at 3.00 x 102 mi/h due east enters a region where the wind is blowing 1.00 x 102 mi/h in a direction 30.0° north of east. (a) Find the components of the velocity of the jet airliner relative to the air, v(JA. (b
> A car travels due east with a speed of 50.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 60.0° with the vertical. Find the velocity of the rai
> Suppose a boat moves at 12.0 m/s relative to the water. If the boat is in a river with the current directed east at 2.50 m/s, what is the boat’s speed relative to the ground when it is heading (a) East, with the current (b) West, against the current?
> A cruise ship sails due north at 4.50 m/s while a Coast Guard patrol boat heads 45.0° north of west at 5.20 m/s. What are (a) the x – component (b) y - component of the velocity of the cruise ship relative to the patrol boat?
> A graph of position versus time for a certain particle moving along the x - axis is shown in Figure P2.6. Find the instantaneous velocity at the instants (a) t = 1.00 s (b) t = 3.00 s (c) t = 4.50 s, and (d) t = 7.50 s. Figure P2.6
> A playground is on the flat roof of a city school, 6.00 m above the street below (Fig. P3.19). The vertical wall of the building is h 5 7.00 m high, to form a 1-m-high railing around the playground. A ball has fallen to the street below, and a passer-by
> A fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of θi = 30.0° above the horizontal as shown in Figure P3.18. If the speed of the stream as it leaves the hose is
> A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0° above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile’s velocity at the highest point of its trajectory? (b)
> An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x - and y - coordinates of the shell where it explodes, relative to its
> A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a cons
> From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.00 m/s and angle of 20.0° below the horizontal. It strikes the ground 3.00 s later. (a) If the base of the building is taken to be the origin
> A brick is thrown upward from the top of a building at an angle of 25° to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building?
> The record distance in the sport of throwing cowpats is 81.1 m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) The initial speed of the projecti
> A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0° to t
> A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal range R. (a) At what angle θ is the rock thrown? (b) In terms of the original range R, what is the range Rmax the rock can attain
> A paper in the journal Current Biology tells of some jellyfish-like animals that attack their prey by launching stinging cells in one of the animal kingdom’s fastest movements. High-speed photography showed the cells were accelerated from rest for 700. n
> The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height?
> One of the fastest recorded pitches in major league baseball, thrown by Tim Lin cecum in 2009, was clocked at 101.0 mi/h (Fig. P3.8). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached ho
> A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in Figure P3.7. (a) What are the coordinates of the initial position of the ston
> A rabbit is moving in the positive x - direction at 2.00 m/s when it spots a predator and accelerates to a velocity of 12.0 m/s along the negative y - axis, all in 1.50 s. Determine (a) The x – component (b) The y - component of the rabbit’s acceleration
> A car is traveling east at 25.0 m/s when it turns due north and accelerates to 35.0 m/s, all during a time of 6.00 s. Calculate the magnitude of the car’s average acceleration.
> An ant crawls on the floor along the curved path shown in Figure P3.4. The ant’s positions and velocities are indicated for times ti = 0 and tf = 5.00 s. Determine the x - and y - components of the ant’s (a) displaceme
> A miniature quadcopter is located at xi = 2.00 m and yi = 4.50 m at t = 0 and moves with an average velocity having components vav,x = 1.50 m/s and vav,y = -1.00 m/s. What are the (a) x – coordinate (b) y - coordinate of the quadcopter’s position at t =
> A hiker walks 2.00 km north and then 3.00 km east, all in 2.50 hours. Calculate the magnitude and direction of the hiker’s (a) Displacement (in km) (b) Average velocity (in km/h) during those 2.50 hours. (c) What was her average speed during the same tim
> As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 61.0 kg. If this
> Consider a solid metal sphere (S) a few centimeters in diameter and a feather (F). For each quantity in the list that follows, indicate whether the quantity is the same, greater, or lesser in the case of S or in that of F. Explain in each case why you ga
> To qualify for the finals in a racing event, a race car must achieve an average speed of 250. km/h on a track with a total length of 1.60 x 103. If a particular car covers the first half of the track at an average speed of 230. km/h, what minimum average
> Four forces act on an object, given by A( =40.0 N east, B( = 50.0 north, C( = 70.0 N west, and D( = 90.0 N south. (a) What is the magnitude of the net force on the object? (b) What is the direction of the force?
> A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 N, how long does it take to increase the speed of the train from rest to 80 km/h?
> Assume the three blocks portrayed in Figure P4.59 move on a frictionless surface and a 42-N force acts as shown on the 3.0-kg block. Determine (a) The acceleration given this system, (b) The tension in the cord connecting the 3.0-kg and the 1.0-kg blocks
> The systems shown in Figure P4.58 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline in Figure P4.58d are frictionless. Figure P4.58:
> Two blocks of masses m and 2m are held in equilibrium on a frictionless incline as in Figure P4.57. In terms of m and θ, find (a) The magnitude of the tension T1 in the upper cord and (b) The magnitude of the tension T2 in the lower cord con
> Two blocks each of mass m are fastened to the top of an elevator as in Figure P4.56. The elevator has an upward acceleration a. The strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b)
> A block of mass m1 = 16.0 kg is on a frictionless table to the left of a second block of mass m2 = 24.0 kg, attached by a horizontal string (Fig. P4.55). If a horizontal force of 1.20 x 102 N is exerted on the block m2 in the positive x - direction, (a)
> An Atwood’s machine (Fig. 4.38) consists of two masses: one of mass 3.00 kg and the other of mass 8.00 kg. When released from rest, what is the acceleration of the system? Figure 4.38:
> A setup similar to the one shown in Figure P4.53 is often used in hospitals to support and apply a traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted on the leg? Ass
> A hockey puck struck by a hockey stick is given an initial speed υ0 in the positive x - direction. The coefficient of kinetic friction between the ice and the puck is µk. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of pa
> Suppose you are driving a car at a high speed. Why should you avoid slamming on your brakes when you want to stop in the shortest possible distance? (Newer cars have antilock brakes that avoid this problem.)
> A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s2, find the force exerted by the rope on the bucket.
> A car is traveling at 50.0 km/h on a flat highway. (a) If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and t
> A bag of sugar weighs 5.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one sixth that on Earth? Repeat for Jupiter, where g is 2.64 times that on Earth. Find the mass of the bag of sugar in kilograms at ea
> The person in Figure P4.49 weighs 170. lb. Each crutch makes an angle of 22.0° with the vertical (as seen from the front). Half of the person’s weight is supported by the crutches, the other half by the vertical forces exerte
> A block of mass 12.0 kg is sliding at an initial velocity of 8.00 m/s in the positive x - direction. The surface has a coefficient of kinetic friction of 0.300. (a) What is the force of kinetic friction acting on the block? (b) What is the block’s accele
> To meet a U.S. Postal Service requirement, employees’ footwear must have a coefficient of static friction of 0.500 or more on a specified tile surface. A typical athletic shoe has a coefficient of 0.800. In an emergency, what is the minimum time interval
> A 3.00-kg block starts from rest at the top of a 30.0° incline and slides 2.00 m down the incline in 1.50 s. Find (a) The acceleration of the block (b) The coefficient of kinetic friction between the block and the incline (c) The frictional force acting
> An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f = bυ. Assume b = 15 kg/s and m = 50 kg. (a)
> Consider a large truck carrying a heavy load, such as steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, a 10000-kg lo
> Draw a free-body diagram for each of the following objects: (a) A projectile in motion in the presence of air resistance, (b) A rocket leaving the launch pad with its engines operating, and (c) An athlete running along a horizontal track.
> A crate of mass 45.0 kg is being transported on the flatbed of a pickup truck. The coefficient of static friction between the crate and the truck’s flatbed is 0.350, and the coefficient of kinetic friction is 0.320. (a) The truck accelerates forward on l
> A 276-kg glider is being pulled by a 1950-kg jet along a horizontal runway with an acceleration of a( = 2.20 m/s2 to the right as in Figure P4.41. Find (a) The thrust provided by the jet’s engines (b) The magnitude of the tension in the
> The leg and cast in Figure P4.40 weigh 220 N (w1). Determine the weight w2 and the angle a needed so that no force is exerted on the hip joint by the leg plus the cast. Figure P4.40:
> One or more external forces are exerted on each object enclosed in a dashed box shown in Figure 4.2. Identify the reaction to each of these forces. Figure 4.2
> A 150-N bird feeder is supported by three cables as shown in Figure P4.39. Find the tension in each cable. Figure P4.39:
> A certain orthodontist uses a wire brace to align a patient’s crooked tooth as in Figure P4.38. The tension in the wire is adjusted to have a magnitude of 18.0 N. Find the magnitude of the net force exerted by the wire on the crooked to
> (a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w? (b) When the elevator is moving at a
> The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much tension does the bird produce in the wire? Ignore the weig
> (a) Find the tension in each cable supporting the 6.00 x 102-N cat burglar in Figure P4.35. (b) Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the other cables increase, decrease, or stay the same? Why? Figure 4
> A crate of mass m = 32 kg rides on the bed of a truck attached by a cord to the back of the cab as in Figure P4.34. The cord can withstand a maximum tension of 68 N before breaking. Neglecting friction between the crate and truck bed, find the maximum ac
> A boat is heading due east at speed v when passengers onboard spot a dolphin swimming due north away from them, relative to their moving boat. Which of the following must be true of the dolphin’s motion relative to a stationary observer floating in the w
> A 75-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 825 N. What is the acceleration of the elevator?
> Two identical strings making an angle of θ = 30.0° with respect to the vertical support a block of mass m = 15.0 kg (Fig. P4.32). What is the tension in each of the strings? Figure 4.32:
> The coefficient of static friction between the 3.00-kg crate and the 35.0° incline of Figure P4.31 is 0.300. What minimum force F( must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? F
> Suppose the coefficient of static friction between a quarter and the back wall of a rocket car is 0.330. At what minimum rate would the car have to accelerate so that a quarter placed on the back wall would remain in place?
> A 6.0-kg object undergoes an acceleration of 2.0 m/s2. (a) What is the magnitude of the resultant force acting on it? (b) If this same force is applied to a 4.0-kg object, what acceleration is produced?
> A dockworker loading crates on a ship finds that a 20.0-kg crate, initially at rest on a horizontal surface, requires a 75.0-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 60.0 N is required to keep i
> A block of mass 55.0 kg rests on a slope having an angle of elevation of 25.0°. If pushing downhill on the block with a force just exceeding 187 N and parallel to the slope is sufficient to cause the block to start moving, find the coefficient of static
> A horse is harnessed to a sled having a mass of 236 kg, including supplies. The horse must exert a force exceeding 1240 N at an angle of 35.0° in order to get the sled moving. Treat the sled as a point particle. (a) Calculate the normal force on the sled
> A man exerts a horizontal force of 125 N on a crate with a mass of 30.0 kg. (a) If the crate doesn’t move, what’s the magnitude of the static friction force? (b) What is the minimum possible value of the coefficient of static friction between the crate a
> A rocket takes off from Earth’s surface, accelerating straight up at 72.0 m/s2. Calculate the normal force acting on an astronaut of mass 85.0 kg, including his space suit.
> Analyze the motion of a rock dropped in water in terms of its speed and acceleration as it falls. Assume a resistive force is acting on the rock that increases as the velocity of the rock increases.
> A block of mass m = 5.8 kg is pulled up a θ = 25° incline as in Figure P4.24 with a force of magnitude F = 32 N. (a) Find the acceleration of the block if the incline is frictionless. (b) Find the acceleration of the block if the
> A 1.00 x 103-N crate is being pushed across a level floor at a constant speed by a force F( of 3.00 x 102 N at an angle of 20.0° below the horizontal, as shown in Figure P4.23a. (a) What is the coefficient of kinetic friction between the crate
> A student of mass 60.0 kg, starting at rest, slides down a slide 20.0 m long, tilted at an angle of 30.0° with respect to the horizontal. If the coefficient of kinetic friction between the student and the slide is 0.120, find (a) The force of kinetic fri
> A car of mass 875 kg is traveling 30.0 m/s when the driver applies the brakes, which lock the wheels. The car skids for 5.60 s in the positive x - direction before coming to rest. (a) What is the car’s acceleration? (b) What magnitude force acted on the
> A horizontal force of 95.0 N is applied to a 60.0-kg crate on a rough, level surface. If the crate accelerates at 1.20 m/s2, what is the magnitude of the force of kinetic friction acting on the crate?
> A football punter accelerates a football from rest to a speed of 10 m/s during the time in which his toe is in contact with the ball (about 0.20 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
> Calculate the magnitude of the normal force on a 15.0-kg block in the following circumstances: (a) The block is resting on a level surface. (b) The block is resting on a surface tilted up at a 30.0° angle with respect to the horizontal. (c) The block is
> What would be the acceleration of gravity at the surface of a world with twice Earth’s mass and twice its radius?
> A force of 30.0 N is applied in the positive x - direction to a block of mass 8.00 kg, at rest on a frictionless surface. (a) What is the block’s acceleration? (b) How fast is it going after 6.00 s?
> The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N east. If the boat (including its crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?
> A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true? (a) Its velocity and its acceleration are both zero. (b) Its velocity is not zero, but its acceleration is zero. (c) Its velocit
> An airplane in a holding pattern flies at constant altitude along a circular path of radius 3.50 km. If the airplane rounds half the circle in 1.50 x 102 s, determine the magnitude of its (a) Displacement (b) Average velocity during that time. (c) What i
> A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130. km in 2.00 h. (a) What is his total displacement? (b) What is his average velocity? Answer: (a) Displacement = &Delta
> A graph of position versus time for a certain particle moving along the x - axis is shown in Figure P2.6. Find the average velocity in the time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e) 0 to 8.00
> A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). (a) How long does the race take? (b) What is
> A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min rest stop. If the person’s average speed is 77.8 km/h, (a) How much time is spent on the trip and (b) How far does the person travel?
> A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true? (a) The car travels a distance υt. (b) The average speed of the car is υ/2
> A skydiver jumps out of a hovering helicopter. A few seconds later, another skydiver jumps out, so they both fall along the same vertical line relative to the helicopter. Assume both skydivers fall with the same acceleration. Does the vertical distance b
> The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 45 m in a straight line, reaching a final speed of 72 km/h. (a) Determine the cheetah’s average acceleration during the
> A ball is thrown straight up in the air. For which situation are both the instantaneous velocity and the acceleration zero? (a) On the way up (b) At the top of the flight path (c) On the way down (d) Halfway up and halfway down (e) None of these.
> A jet plane has a takeoff speed of υto = 75 m/s and can move along the runway at an average acceleration of 1.3 m/s2. If the length of the runway is 2.5 km, will the plane be able to use this runway safely? Defend your answer.
> Express the location of the fly in Problem 40 in polar coordinates. Data from Problem 40: A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.
> True or False? (a) A car must always have an acceleration in the same direction as its velocity. (b) It’s possible for a slowing car to have a positive acceleration. (c) An object with constant nonzero acceleration can never stop and remain at rest.
> Figure 2.4 shows the unusual path of a confused football player. After receiving a kickoff at his own goal, he runs downfield to within inches of a touchdown, then reverses direction and races back until he’s tackled at the exact locati
> A football player runs from his own goal line to the opposing team’s goal line, returning to the fifty-yard line, all in 18.0 s. Calculate (a) His average speed, and (b) The magnitude of his average velocity.
> Light travels at a speed of about 3 x 108 m/s. (a) How many miles does a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye? (b) Compare this distance to the diameter of Earth.
> An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x - direction, determine her average velocities symbolically in (a) The first half of the s
