What relationship must exist between an applied force and the velocity of a moving object if uniform circular motion is to result?

Transcription

1 1 What relationship must exist between an applied force and the velocity of a moving object if uniform circular motion is to result? 5 A mass m =.2 kg on a frictionless table is attached to a hanging mass M = 3 kg by a cord through a hole in the table shown in the figure. The mass m is roated in a circle with a radius of 1.5 m. Find the speed with which m must spin for M to stay at rest. Circular motion results when the direction of the force is constantly perpendicular to the instantaneous velocity of the object. 2 What is the direction of the force that acts on clothes in the spin cycle of a washing machine? 3 The walls of the tub push the clothes toward the center of the tub. Some of the water in the clothes is not pushed toward the center of the tub, and goes out through the holes in the wall of the tub. Check out the pattern in the clothes next to the wall right after the spin cycle stops. The royal antelope of western Africa has an average mass of only 3.2 kg. If this antelope runs with a tangential speed of 9.1 m/s in a circle with a radius of 30.0 m, how large is the force that maintains this circular motion? m/s The moon (mass = 7.36 x kg) orbits Earth at a range of 3.84 x 10 5 km with a period of approximately 28 days. Determine the force that maintains the circular motion of the moon. 1.9 x N N Mata Jagdamba of India had the longest hair in 1994; it was measured to be 4.23 m long. Suppose Jagdamba conducts experiments with her hair. First, she determines that one hair can support a mass of 25 g. She then attaches a smaller mass to the same hair and swings it in the horizontal plane. If the hair breaks when the tangential speed of the mass reaches 8.1 m/s, how large is the mass? 7 Pat Kinch cycled km in h. Suppose the entire distance was made by traveling once around a large circular path. If Kinch's mass is 72 kg, estimate the average force that maintains her circular motion. 2.6 N 15.8 g

2 8 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to a post and moving in a circle at constant speed on a frictionless horizontal surface. 12 In a cyclotron one type of particle the accelerator uses deuteron (an atom of atomic mass 2 u) which reaches a final velocity of 10% the speed of light while moving in a circular path of radius 0.48 m. The deuteron is maintained in a circular path by a magnetic force. What magnitude of force is required? Mass of Deuteron = 3.32 x kg. The speed of light is a constant that can be found in your text. F = x N 9 In the Bohr model of the hydrogen atom, the electron revolves in a circular orbit around the nucleus. If the radius is 5.3 x m and the electron makes 6.6 x rev/s, (a) Find the speed of the electron. (b) Find the acceleration (magnitude and direction) of the electron (c) Find the centripetal force acting on the electron. (This force is due to the attraction between the positively charged nucleus and the negatively charged electron.) The mass of the electron is 9.1 x kg What centripetal force is required to keep a 2-kg mass moving in a horizontal circle of radius 0.4 m at a speed of 3 m/s? 45 N A 3 kg mass attached to a light string rotates in a circular motion on a horizontal, frictionless table. The radius of the circle is 0.8 m and the string can support as mass of 25 kg before breaking. What range of speed can the mass have before the string breaks? (a) 2.2 x 10 6 m/s (b) 9.11 x m/s 2 toward the center (c) 8.29 x 10-8 N 10 Thanks to Earth's rotation, you move with uniform circular motion. What supplies the force that keeps you moving in this circle? Earth's Gravity 11 Sue whirls a yo-yo in a horizontal circle. The yo-yo has a mass of 0.20 kg and is attached to a string 0.80 m long. (a) If the yo-yo makes 1.0 complete revolution each second, what force does the string exert on it? (b) If Sue increases the speed of the yo-yo to 2.0 revolutions per second, what force does the string now exert? (c) What is the ratio of answer b to a? Why? 8.08 m/s (a) 6.3 N (b) 25 N (c) 4:1

3 15 In the Bohr model of the hydrogen atom the velocity of the electron is approximately 2.2 x 10 6 m/sec. ( Mass of an electron = x kg). (a) Find the centripetal force acting on the electron as it revolves in a circular orbit of radius 0.53 x m, (b) Find the centripetal acceleration of the electron. (c) Find the number of revolutions per second made by the electron. 18 It takes a 615-kg racing car 14.3 s to travel at a uniform speed around a circular racetrack of 50.0 m radius. (a) What is the acceleration of the car? (b) What average force must the track exert on the tires to produce this acceleration? (a) 9.65 m/s 2 (b) 5.94 x (a) 8.31 x 10-8 N (b) x m/s 2 (c) 6.61 x rev/sec Sue whirls a yo-yo horizontally above her head. What is the direction of the net force that acts on the yo-yo? 19 A coin is placed on a stereo record revolving at 33 1/3 revolutions per minute. (a) In what direction is the acceleration of the coin, if any? (b) Find the acceleration of the coin when it is placed 5.0, 10, and 15 cm from the center of the record. (c) What force accelerates the coin? (d) At which of the three radii listed in b would the coin be most likely to fly off? Why? 17 Along the string toward the center of the circle that the yoyo follows. A mass m = 5 kg on a frictionless table is attached to a hanging mass M = 8 kg by a cord of radius 0.5 m through a hole in the table shown in the figure. Find the speed with which m must spin for M to stay at rest. 20 (a) toward the Center (b) 0.61 m/s m/s m/s 2 (c) friction (d) 15 cm A child places a picnic basket on the outer rim of a merry-goround that has a radius of 4.6 m and revolves once every 30 s. (a) What is the speed of a point on the rim of the merry-goround? (b) How large must the coefficient of static friction be for the basket to stay on the merry-go-round? (a).96 m/s (b)

4 21 A 100-g disk sits on a horizontally rotating turntable. The turntable makes one revolution each second. The disk is located 10 cm from the axis of rotation of the turntable. (a) What is the frictional force acting on the disk? (b) The disk will slide off the turntable if it is located at a radius larger than 16 cm from the axis of rotation. What is the coefficient of static friction? 25 For each of the examples of two-body gravitational action below, find the missing quantity for the data given. (G = 6.7 x (Nm 2 /kg 2 ) (a) N (b) (a) 6.7 x 10 6 N (b) 1.94 x kg (c) 1.5 kg (d) 1.06 x m 22 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock riding on a horizontal disk that is rotating at constant speed about Its vertical axis. Friction prevents rock from sliding. 26 The mass of an electron is 9.1 x 10-3l kg. The mass of a proton is 1.7 x kg. They are about 1.0 x m apart in a hydrogen atom. What gravitational force exists between the proton and the electron of a hydrogen atom? 1.0 x N 27 Two 1.00-kg masses have their centers 1.00 m apart. What is the force of attraction between them? 6.67 x N 28 Two large spheres are suspended close to each other. Their centers are 4.0 m apart. One sphere weighs 9.8 x 10 2 N. The other sphere has a weight of 1.96 x 10 2 N. What is the gravitational force between them? 23 Identify the force that maintains the circular motion of a bicycle moving around a flat circular track 8.3 x 10-9 N friction between the tires and the track 29 If the centers of Earth and the moon are 3.9 x 10 8 m apart, the gravitational force between them is about 1.9 x N. What is the approximate mass of the moon? (Mass of Earth = 5.9 x ) 7.2 x kg 24 Racing on a flat track, a car going 32 m/s rounds a curve 56 m in radius. (a) What is the car's centripetal acceleration? (b) What would be the minimum coefficient of static friction between tires and road that would be needed for the car to round the curve without skidding? 30 Using Newton's Universal Law of Gravity (a) What is the gravitational force between two spherical 8.00 kg masses that are 5.0 m apart? (b) What is the gravitational force between them when they are 5.0 x 10 1 m apart? (a) 1.7 x N (b) 1.7 x N (a) 18 m/s 2 (b) 1.8

5 31 The gravitational force between two electrons 1.00 m apart is 5.42 x l0-71 N. Find the mass of an electron. 36 Draw the free body diagram of the forces on the rotating ball x kg 32 Compute the gravitational force the sun exerts on Jupiter x N 33 Two ships each of 10 8 kg mass are moored near each other. Assume the effective distance between them as far as gravitational attraction is concerned is 100 m. What gravitational force do they exert on one another? 671 N 34 From the data on the planetary data sheet, calculate the gravitational force on the earth due to the sun. It is this force which holds the earth in its orbit. 37 If you weigh 637 N on Earth's surface, how much would you weigh on the planet Mars? (Mars has a mass of 6.37 x kg and a radius of 3.43 x 10 5 m.) 235 N x N The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to point A by a string. The rock is moving in a horizontal circle at constant speed and not resting on a solid surface. 38 What would be the value of g, acceleration of gravity, if Earth's mass was double its actual value, but its radius remained the same? If the radius was doubled, but the mass remained the same? If both the mass and radius were doubled 19.6 m/s m/s m/s 2 39 What would be the strength of Earth's gravitational field at a point where an 80.0 kg astronaut would experience a 25% reduction in weight? 7.35 m/s 2 40 On the surface of the moon, a 91.0 kg physics teacher weighs only N. What is the value of the moon's gravitational field at its surface? 1.60 m/s 2 41 Two satellites of equal mass are put into orbit 30 m apart. The gravitational force between them is 2.0 x 10-7 N. (a) What is the mass of each satellite? (b) What is the initial acceleration given to each satellite by the gravitational force? (a) 1.6 x 10 3 kg (b) 1.3 x m/s 2

6 42 43 The asteroid Ceres has a mass 7 x kg and a radius of 500 km. (a) What is g on the surface? (b) How much would a 85-kg astronaut weigh on Ceres? (a) 0.2 m/s 2 (b) 2 x 10 1 N The radius of Earth is about 6.40 x 10 3 km. A 7.20 x 10 3 N spacecraft is traveling away from Earth. (a) What is the weight of the spacecraft 6.40 x 10 3 km from the Earth's surface? (b) What is the weight of the spacecraft 1.28 x 10 4 km from the Earth's surface? 49 The mass and radius of the moon are 7.3 x kg and 1.74 x 10 5 m respectively. (a) Calculate the value of g on the moon (b) Calculate the weight of a 50 kg boy on the earth (c) Calculate the weight of a 50 kg boy on the moon (d) Calculate the time it takes of an object to fall 4.9 m on the moon. (e) Calculate the time it takes of an object to fall 4.9 m both on the earth (f) Many physics students would like to change the magnitude of g from 9.8 m/s 2 to 10 m/s 2. To do this how should the mass and the radius of the earth be changed? (g) How could the same change in g be accomplished, theoretically, without any change in the mass or radius of the earth? 44 (a) 1.80 x 10 3 N (b) 800 N How high does a rocket have to go above Earth's surface until its weight is half what it would be on Earth? (a) 1.6 m/s 2 (b) F earth = 490 N (c) F moon = 80 N (d) 2.4 sec Moon (e) 1 second Earth (f) Only if G is not constant g x 10 5 m 45 The instrument-carrying payload of a rocket weighs 1058 newtons on the earth. What does it weigh x 10 4 km above the earth? 42 N 50 Use the Universal Law of Gravity to determine the following: (a) What is the weight of a 1.0 kg mass one earth radius from the surface of the earth (Radius of the earth = 6.4 x 10 5 m or 4000 miles). (b) At what distance from the surface is the weight of any mass reduced one-half? 46 Find the weight of a 100 kg man on Jupiter. (a) 2.5 N (b) 1.4 Earth radii from the center of the earth.4 radii from the surface of the earth 2469 N 51 Why does the water remain in a pail that is whirled in a vertical path, as shown in the figure below? 47 Calculate the theoretical value for the acceleration due to gravity at a point 1.00 x 10 7 m from the center of the earth m/s 2 48 At what height above the earth's surface will a rocket experience just a quarter the pull from the earth that it feels at the earth's surface? 1.28 x 10 7 m 2 Earth radii from the center of the Earth 1 Earth radius above the surface of the earth water tends to follow a straight-line path; pail exerts force that maintains circular motion

7 52 A certain string can withstand a maximum tension of 9.0 N. without breaking. A child ties a 0.82 N. stone to one end. Holding the other end, he whirls the stone in a vertical circle of radius 3.0 m slowly increasing the speed until the string breaks. (a) Where is the stone on its path when the string breaks? (b) What is the speed of the stone as the string breaks? 56 A 150 N. student on a steadily rotating Ferris wheel has an apparent weight (F N ) of 125 N. at the highest point. (a) What is his apparent weight (F N ) at the lowest point? (b) What would be his apparent weight (F N ) at the highest point if the speed of the Ferris wheel were doubled? (a) At the bottom of circle (b) 17.1 m/s (a) 175 (b) Tarzan (m = 85 kg) tries to cross a river by swinging from a 10.0 m long vine. His speed at the bottom of the swing, just as he clears the water, is 8.0 m/s. Tarzan doesn't know that the vine has a breaking strength of 1.0 x 10 3 N. Does he make it safely across the river? justify your answer. 57 A jet plane traveling 1800 km/hr (500 m/s) pulls out of a dive by moving in an arc of radius 3.0 km. What is the plane's acceleration in g's m/s = 9.5 g's no, 1.37 x 10 3 N > 1.0 x 10 3 N 54 With an average mass of only 30.0 g, the mouse lemur of Madagascar is the smallest primate on Earth. Suppose this lemur is swinging on a light vine with a length of 2.4 m so that the lemur's tangential speed at the bottom point is 2.8 m/s. Calculate the tension in the vine at that point. 58 What minimum speed must a roller coaster be traveling when upside down at the top of a circle if the passengers are not to fall out? Assume a radius of curvature of 8.0 m. v = m/s N In 1992, a team of 12 athletes from Great Britain and Canada rappelled 446 m down the CN Tower in Toronto, Canada. Suppose an athlete with a mass of 75 kg, having reached the ground, takes a joyful swing on the 446 m long rope. (a) If the speed of the athlete at the bottom point of the swing is 12 m/s, what is the force that maintains the athlete's circular motion? (b) What is the tension in the rope? Neglect the rope's mass. 59 A carnival clown rides a motorcycle down a ramp and around a "loop-the-loop." If the loop has a radius of 18 m, what is the slowest speed the rider can have at the top of the loop to avoid falling? Hint: At this slowest speed, at the top of the loop, the clown's weight is equal to the centripetal force. 10 m/s 24 N 760 N

8 60 A roller coaster moves through a vertical loop at a constant speed, suspending its passengers upside down. In what direction is the force that causes the coaster and its passengers to move in a circle? What provides this force? 63 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to point B and moving downward in a vertical circle with string horizontal. toward the center of the track; the track 61 A girl at a state fair swings a ball in a vertical circle at the end of a string. Is the force applied by the string greater than the weight of the ball at the bottom of the ball's path? Yes, the string must exert a force equal to the ball's weight and the circular force that maintains circular motion. 64 When you drive rapidly on a hilly road or ride in a roller coaster you feel lighter as you go over the top of a hill, and heavier when you go through a valley. Sketch the situation, showing the forces that explain this sensation. 62 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock swinging on a rope. To move you in a circular path, there is an added upward force on you. Since you react to external forces, t his makes you feel heavier or lighter 65 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock swinging on a rope, at the top of a vertical circle.

9 66 Two satellites are in circular orbits about Earth, one 150 km above the surface, the other 160 km. (a) Which satellite has the larger orbital period? (b) Which one has the larger velocity? (a) The one at 160 km has the larger period. (b) The one at 150 km has the larger velocity. 71 Using Astronomical Data (a) Calculate the velocity that a satellite shot from Newton's cannon must have in order to orbit Earth, 150 km above its surface. (b) How long would it take for the satellite to return to the cannon in seconds and minutes? (a) 7.8 x 10 3 m/s (b) 84 min 18 sec 67 A satellite is placed in a circular orbit with a radius of 1.0 x 10 7 m a period of 9.9 x 10 3 s. Calculate the mass of Earth. Hint: Gravity supplies the needed centripetal force for such a satellite. Scientists have actually measured the mass of Earth this way. 72 A geosynchronous satellite appears to remain over one spot on Earth. A geosynchronous satellite has an orbital radius of 4.23 x 10 7 m. (a) Calculate its speed in orbit. (b) Calculate its period x kg Find the speed and period of a satellite that would orbit Mars 175 km above its surface. (a) 3.07 x 10 3 m/s (b) 24.0 h V = 3.47 x 10 3 m/s T = 6.45 x 10 3 s or 1.79 h 73 On July 19, 1969, Apollo li's orbit around the moon was adjusted to an average orbit of 111 km. The radius of the moon is 1785 km and the mass of the moon is 7.3 x kg. (a) How many minutes did it take to orbit once? (b) At what velocity did it orbit the moon? 69 The following problem examins some characteristics of the planet Mercury. (a) Find the speed of a satellite in orbit 265 km above Mercury s surface. (b) Find the the period of the satellite orbit 265 km above Mercury s surface. (a) 2.96 x 10 3 m/s (b) 85.9 min 74 (a) 1.2 x 10 2 min (b) 1.6 x 10 3 m/s A 10, 000 kg spaceship is drifting on a long mission toward the outer edge of the solar system. It has put out a small experimental satellite which revolves around it at a distance of 120 meters under their mutual gravitational attraction. (a) What is the period of revolution of the satellite? (b) What is the speed of the satellite? 70 Using Astronomical data. (a) Find the velocity with which Mercury around the sun (b) Also, find the velocity of Saturn. (c) Now, comment on whether or not it mae sense that Mercury is named after a speedy messenger of the gods, while Saturn is named after the father or Jupiter. (a) 1.01 x 10 7 s (b) m/s or 7.5 x 10-5 m/s (a) 4.79 x 10 4 m/s (b) 9.65 x 10 3 m/s (c) about as 1/5 as fast as Mercury

10 75 Assume the earth is perfectly round and has a radius of 6400 km. (a) What is the weight of a 100 kg man at the North Pole? (b) What is the centripetal force of a 100 kg man at the Equator? (c) How much less does a man with a mass of 100 kg apparently weigh at the equator than at the poles because of the rotation of the earth? (d) How fast would the earth have to spin in order that he would exert no force on a scale at the equator? (e) How many times larger is the speed of rotation in d than the actual speed? (a) 980 N (b) 3.37 N (c) N (d) S or 1.4 hours, or m/s (e) 17 times greater A 1200-kg car rounds a curve of radius 67 m banked at an angle of 12º. If the car is traveling at 95 km/h, will a friction force be required? If so, how much and in what direction? N down the plane A curve of radius 67 m is banked for a design speed of 95 km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve? A car goes around a curve on a road that is banked at an angle of Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 24.0 m/s. What is the radius of the curve? 76 A banked circular curve of highway is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a stormy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road? 83 A curve has a radius of 50 meters and a banking angle of 15 o. What is the ideal, or critical, speed (the speed for which no friction is required between the car's tires and the surface) for a car on this curve? 84 A turn of radius 100 m is being designed for a speed of 25 m/s. At what angle should the turn be banked? Identify the force that maintains the circular motion of a bobsled turning a corner on its track 85 Talladega Motor Speedway in Alabama has turns with radius 1,100 ft. that are banked at 33 o. What is the "no friction" speed for a car on these turns? the normal force from the curved side of the track 86 Suppose you want to negotiate a curve with a radius of 50 meters and a bank angle of If the coefficient of friction between your tires and the pavement is 0.50, what is the maximum speed that you can safely use? 78 Why do bicycle riders lean inward when rounding a curve at high speed? 79 the following questions: (a) Why do airplanes bank when they turn? (b) How would you compute the banking angle given its speed and radius of the turn? 87 Talladega Motor Speedway in Alabama has turns with radius 1,100 ft. that are banked at 33 o. In NASCAR race cars actually go through the turns at Talladega Motor Speedway at about 200 mi/hr. If that is the case, what coefficient of friction exists between the car's tires and the pavement?

11 88 Civil engineers generally bank curves on roads in such a manner that a car going around the curve at the recommended speed does not have to rely on friction between its tires and the road surface in order to round the curve. Suppose that the radius of curvature of a given curve is r = 60 m and that the recommended speed is v = 40 km/h. At what angle theta should the curve be banked? 91 A car travels 22 m/s around curve of radius 75 m so it does not need friction to complete the curve. (a) What is the angle of the bank on the curve? (b) How many g's are felt by the rider on the curve? 89 A curve of radius 163 m is banked at an angle of 9. An 762-kg car negotiates the curve at 76 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following. (a) the normal force exerted by the pavement on the tires (b) the frictional force exerted by the pavement on the tires (c) the minimum coefficient of static friction between the pavement and the tires 92 Design a banked curve where the passenger feels 3.5 g's while traveling at 52 m/s. 93 the following questions about rollercoaster design. (a) What must the curve s angle be for a roller coaster car to travel around a curve of radius 30 m at 20 m/s? (b) How many g s are felt by a rider as he travels around the banked curve in the previous problem? 90 At what angle should a curve of 200 m radius be banked so that no friction is required when a car travels at 60 kilometers per hour around the curve?

12 94 A car is to make it around a banked curve. The radius is m and the car will travel at 30 m/s. What is the optimum banking angle of the curve? 99 the following questions. (a) What are the dimensions of period? (b) What are the dimensions of frequency? sec/cyc cyc/sec 100 A vibrating reed in a harmonica makes 200 vib/sec. What is the period? 95 A car is to make it around a banked curve. The radius is m and the car will travel at 30 m/s. This roller coaster is on the moon where the acceleration due to gravity is 1.67 m/s 2. What is the optimum banking angle of the curve? sec What is the time required for 2400 vibrations of a loaded spring if the frequency is 4 vib/sec? 96 A rider is to make it around a curve of radius of m so that the rider will feel 2.50 g s. What is the angle of the banked curve? 600 sec. 102 If the force constant of a spring is 8 N/m, what suspended mass will give a period of 1 sec? 0.2 kg 97 A rider is to make it around a curve of radius of m so that the rider will feel 1.64 g s. How fast must the rider be traveling? 103 A point on a horizontal vibrating piano string is moving up and down in SHM with a frequency of 200 vib/sec. The maximum displacement of the point below its normal position is 0.5 mm. (a) What is the maximum velocity of the particle, and where is this velocity reached? (b) What is the maximum acceleration of the particle? (a) m/sec (b) 789 m/sec 2 98 A rider is to make it around a curve of radius of m so that the rider will feel 4.52 g s. How fast must the rider be traveling?

13 104 A 30 g load hangs from a long, light spring. When pulled down 20 cm below its equilibrium position and released, it vibrates with a period of 2 sec. (a) What is its velocity as it passes through the equilibrium position? (b) By how much will the spring shorten if the load is removed? 108 A small electronic computer placed on board a satellite must withstand a maximum acceleration of 10 G's. To test this, the computer is attached to a horizontal table which is driven from side to side in SHM at 20 vib/s. What must be the amplitude of vibration of this shake-test apparatus in order to give a maximum acceleration of 10 G's? 105 (a) 62.8 cm/sec (b) 0.99 m With what acceleration must be given to a 20 kg mass suspended from a spring so that it will oscillate in SHM with a period of 0.5 sec and an amplitude of 2 cm m Describe a method of using a simple pendulum to find the value of g at a given location m/sec 2 Use the equation 2π (l/g) or g = (4π2l)/T 2 measure the length of the pendulum and its period, and calculate g. 106 A raft of weight 4000 N is floating in a pond. When a 1000 N man climbs on board, the raft sinks 0.04 m deeper into the water to a new equilibrium position. If the man rolls off, how many vertical vibrations does the empty raft make in 5 seconds? 110 What is the length of a simple pendulum whose period is l.00 s? Assume normal g m 6.25 vib when the mans rolls off boat 111 Compute the length of a clock pendulum that ticks once each second. (Hint: It ticks twice during each complete vibration.) 107 A light rubber band is hanging loosely from the ceiling. A load is attached to the free end of the rubber band, and it is observed that the load, when released, moves downward a distance of 40 cm before starting to rise again. What is the period of this SHM? (Hint: The mass is not given. Assign to it the value of m, on the chance that it will cancel out of your final equation for the period? m What would be the period of a pendulum suspended from the top of a tall building with a light string 353 m long? sec 37.7 sec. 113 The value of the acceleration due to gravity on the moon is about 1/6 that on the earth. What would be the period on the moon of a simple pendulum whose period on the earth is 2.0 sec? 4.90 sec

14 114 Sue is swinging her yo-yo as if it was a pendulum. At what point in the swing does the yo-yo have the greatest force acting on it? 118 the following questions. (a) What are the dimensions of Hooke's constant (b) What are the dimensions of the spring constant (c) What are the dimensions of the force constant? At the bottom of the swing 115 A future astronaut lands on a planet with an unknown value of g. She finds that the period of a pendulum 0.65 m long is 2.8 s. What is g for the surface of this planet? (a) N/cm (b) N/cm (c) N/cm m/s 2 A pendulum has a length of 0.67 m. (a) Find its period. (b) How long would the pendulum have to be to double the period? (c) Why is your answer to part b not just double the length? 119 A spring is 6 cm long. When it is suspended vertically and a 200 g mass is hung from its lower end, its length increases to 7.5 cm. (a) What is the constant of the spring? (b) What is the tension in the spring if it is stretched to 8.7 cm? (a) 1.34 N/cm (a) 1.6 s (b) 2.7 m (c) T= l 120 A spring which obeys Hooke's law is stretched 4 cm by a force of 6 N. (a) What is the value of k, the spring constant? (b) How much will the spring be stretched by a force of 1.5 N? 117 A piece cut from a bicycle inner tube is stretched to a total length of 0.7 m long when it carries a load of 25 N. The force constant k is 300 N/m. (a) How far did the rubber tube stretch when 75 Newtons of force were added? (b) What was the original length of the tube when no load was present. (Hint: You need to find the change in x (draw all three pictures) 121 (a) 1.5 N/cm (b) 1 cm A 250 g block is placed on top of a vertical spring with a spring constant k = 2.5 N/cm. How much is the spring compressed? (a).25 (b).616 m.980 c,

15 122 A block is placed on a spring whose spring constant is 2.0 N/cm and compresses the spring 10 cm. (a) What is the weight of the block? (b) What is the mass of the block? (a) 20 N (b) 2.04 kg 126 In a Rotor-ride at a carnival, people are rotated in a cylindrically walled room. The room radius is 4.6 m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. (a) What is the minimum coefficient of static friction so that the people will not slip down? (b) People on this ride say they were pressed against the wall. Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides scary )? [Hint: First draw the free-body diagram for a person.] 123 The piston of an engine moves a total distance of 0.2 m from one extreme point to the other. (a) Draw the piston at the top, middle and bottom of its cycle. (b) What is the amplitude? (c) What is the displacement when the piston is 0.1 m from one end of its stroke? A girl is whirling a ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string? 124 (a) (b) 0.1 m (c) 0.0 The piston in problem 5 makes 2 vib/sec. How fast is it moving when passing through the midpoint of its path? 128 In an amusement-park ride, riders stand against the wall of a spinning cylinder. The floor falls away and the riders are held up by friction. If the radius of the cylinder is 4 m, find the minimum number of revolutions per minute necessary when the coefficient of friction between a rider and the wall is m/sec 23.6 rev/min 125 Compute the time for one vibration of a spring whose force constant is 16 N/m, if the load has a mass of l kg sec 129 Show with a force diagram how a motorcycle can travel in a circle on the inside vertical wall of a hollow cylinder. Assume reasonable parameters (coefficient of friction, radius of the circle, mass of the motorcycle, or whatever is required), and calculate the minimum speed needed. V min = 14.0 m/s = 31.3 mi/h

16 130 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock stuck by friction against the Inside wall of a drum rotating about Its vertical axis at constant speed. 132 The figure below shows the path taken by an automobile. It consists of straight lines and arcs of circles. The automobile starts from rest at point A and accelerates until it reaches point B. It then proceeds at constant speed until it reaches point E. From point E on it slows down, coming to rest at point F. What is the direction of the net force, if there is any, on the automobile at the midpoint of each section of the path? 131 A boy whirls a stone in a horizontal circle 2.0 m above the ground by means of a rope 1.5 meters long. The string breaks and the stone flies off horizontally striking the ground 10 meters away from the release point. (a) How long was the stone in the air after it was released? (b) What was the centripetal acceleration of the stone while it was in circular motion. AB, force vertically upward; BC, force radial toward center of circular arc; CD, no force; DE, force is toward center of circular arc; EF, force acts vertically upward. (a).64 sec (b) m/s m/s 133 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock resting against the frictionless inside wall of a cone rotating about its vertical axis at constant speed. Not accelerating vertically.

17 134 In a popular amusement-park ride, a cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s, as shown in the figure below. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall of the cylinder is needed to keep the rider from slipping? 136 In a Rotor-ride at a carnival, people are rotated in a cylindrically walled room. The room radius is 5.6 m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. (a) What is the minimum coefficient of static friction so that the people will not slip down? (b) People on this ride say they were pressed against the wall. Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides scary )? [ Hint: First draw the free-body diagram for a person.] In a Rotor-ride at a carnival, people are rotated in a cylindrically walled room. The room radius is 7.6 m, and the rotation frequency is 0.25 revolutions per second when the floor drops out. (a) What is the minimum coefficient of static friction so that the people will not slip down? (b) People on this ride say they were pressed against the wall. Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides scary )? [Hint: First draw the free-body diagram for a person.]