Question: A baseball is thrown from the outfield

> 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)

> 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

> 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?

> 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

> Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far mu

> A tennis player moves in a straight-line path as shown in Figure P2.8. Find her average velocity in the time intervals from (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to 5.0 s.

> A ball is thrown vertically upward. (a) What are its velocity and acceleration when it reaches its maximum altitude? (b) What is the acceleration of the ball just before it hits the ground?

> Figure CQ2.6 shows strobe photographs taken of a disk moving from left to right under different conditions. The time interval between images is constant. Taking the direction to the right to be positive, describe the motion of the disk in each case. For

> Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negli

> (a) Can the equations in Table 2.4 be used in a situation where the acceleration varies with time? (b) Can they be used when the acceleration is zero?

> A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine

> If the velocity of a particle is zero, can the particle’s acceleration be nonzero? Explain.

> As the tennis ball of Quick Quiz 2.6 travels through the air, does its speed Data from Quick Quiz 2.6 A tennis player on serve tosses a ball straight up. While the ball is in free fall, does its acceleration (a) Increase (b) Decrease (c) Decrease and t

> The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain.

> The nearest neutron star (a collapsed star made primarily of neutrons) is about 3.00 x 1018 m away from Earth. Given that the Milky Way galaxy (Fig. P1.81) is roughly a disk of diameter, ~1021 m and thickness, ~ 1019 m, estimate the number of neutron sta

> An average person sneezes about three times per day. Estimate the worldwide number of sneezes happening in a time interval approximately equal to one sneeze.

> (a) How many Earths could fit inside the Sun? (b) How many of Earth’s Moons could fit inside the Earth?

> Assume there are 100 million passenger cars in the United States and that the average fuel consumption is 20 mi/gal of gasoline. If the average distance travelled by each car is 10,000 mi/yr, how much gasoline would be saved per year if average fuel cons

> A sphere of radius r has surface area A = 4πr2 and volume V = (4/3) πr3. If the radius of sphere 2 is double the radius of sphere 1, what is the ratio of (a) the areas, A2/A1 and (b) the volumes, V2 /V1

> One gallon of paint (volume = 3.79 x 10-3 m3) covers an area of 25.0 m2. What is the thickness of the fresh paint on the wall?

> Assume it takes 7.00 minutes to fill a 30.0-gal gasoline tank. (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in ho

> The displacement of an object moving under uniform acceleration is some function of time and the acceleration. Suppose we write this displacement as s = kamtn, where k is a dimensionless constant. Show by dimensional analysis that this expression is sati

> (a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be 55 mi/h. Use the conversion factor from part (a) to find the speed in kilometers per hour. (

> A tennis player on serve tosses a ball straight up. While the ball is in free fall, does its acceleration (a) Increase (b) Decrease (c) Increase and then decrease (d) Decrease and then increase, or (e) Remain constant?

> A commuter airplane starts from an airport and takes the route shown in Figure P1.71. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150. km 20.0° west of north, to city B

> The helicopter view in Figure P1.70 shows two people pulling on a stubborn mule. Find (a) The single force that is equivalent to the two forces shown and (b) The force a third person would have to exert on the mule to make the net force equal to zero. Th

> The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 41.0 km/h. Three hours later the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is t

> A map suggests that Atlanta is 730. miles in a direction 5.00° north of east from Dallas. The same map shows that Chicago is 560. miles in a direction 21.0° west of north from Atlanta. Figure P1.68 shows the location of these three

> A vector has an x - component of -25.0 units and a y - component of 40.0 units. Find the magnitude and direction of the vector.

> A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight downfield, perpendicular to the li

> A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her final position relative to her starting location? (b) What is the length of the path she walked?

> A figure skater glides along a circular path of radius 5.00 m. If she coasts around one half of the circle, find (a) Her distance from the starting location and (b) The length of the path she skated.

> The magnitude of vector A( is 35.0 units and points in the direction 325° counterclockwise from the positive x - axis. Calculate the x - and y - components of this vector.

> A person walks 25.0° north of east for 3.10 km. How far due north and how far due east would she have to walk to arrive at the same location?

> Figure 2.14a is a diagram of a multiflash image of an air puck moving to the right on a horizontal surface. The images sketched are separated by equal time intervals, and the first and last images show the puck at rest. (a) In Figure 2.14b, which color g

> A vector A( has components Ax = -5.00 m and Ay = 9.00 m. Find (a) The magnitude and (b) The direction of the vector.

> Calculate (a) the x - component and (b) the y - component of the vector with magnitude 24.0 m and direction 56.0°.

> A roller coaster moves 2.00 x 102 ft horizontally and then rises 135 ft at an angle of 30.0° above the horizontal. Next, it travels 135 ft at an angle of 40.0° below the horizontal. Use graphical techniques to find the roller coaster’s displacement from

> A force F(1 of magnitude 6.00 units acts on an object at the origin in a direction θ = 30.0° above the positive x - axis (Fig. P1.58). A second force F(2 of magnitude 5.00 units acts on the object in the direction of the positive