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1. A 1.0 ft × 5.0 ft sheet of aluminum foil has a mass of 16 g. What is the thickness of the sheet? (Density of aluminum = 2,700 kg/m3 ) 2. A 420 g soccer ball travelling at 23 m/s hits the goal post and rebounds at 18 m/s. If the ball is in contact with the post for 3.3 ms, what is the average acceleration of the ball during this time interval? 3. An object is shot vertically upward and has a speed of 12 m/s when it reaches one fifth of its maximum height. a. What is the initial speed of the object? b. What is the maximum height of the object? 4. The velocity of an object moving along the x axis is given by vx = (2.0 t − t 2 ) m/s. Initially, at t = 0, the object was at the origin. a. What is the object’s acceleration at t = 3.0 s? b. What is the object’s position at t = 3.0 s? c. Calculate the object’s maximum positive displacement from the origin? d. Draw a position-time graph for the object between t = 0 and t = 4.0 s. 2 5. A Canada goose flies horizontally at a speed of 54 km/h at an elevation h = 110 m above an initially level ground. However, at t = 0 the goose begins to fly over ground sloping upward at an angle θ = 5.7°. If it does not change its heading, at what time does the bird strike the ground? 6. Calculate the corresponding polar coordinates of the points a. (1.0, 2.0) b. (3.0, 5.0) c. (3.0, −5.0) 7. A dolphin swims near the sea surface 350 m west, then 200 m northwest, and then dives below the surface and swims an additional distance in an unknown direction. The final position of the dolphin is 80 m directly below a fishing boat located 400 m north of the starting point. Calculate the dolphin’s displacement during the dive. 8. A cannon located 42 m from the base of a vertical 30 m high cliff has its muzzle pointing towards the cliff at an angle 48° above the horizontal. A shell is fired such that it barely clears the edge of the cliff. Determine: a. the initial speed of the shell as it leaves the cannon’s muzzle b. how far the shell lands past the edge of the cliff 3 9. You are to throw a ball with a speed of 13 m/s at a target that is 4.5 m above the level at which you release the ball. You want the ball’s velocity to be horizontal at the instant it reaches the target. a. At what angle above the horizontal must you throw the ball? b. What is the horizontal distance that separates you from the target? c. What is the speed of the ball just as it reaches the target? 10. A block of ice starts from rest on an apartment building’s roof, which slopes at 41° below the horizontal. The block slides down the icy frictionless roof for 5.0 m and then leaves the edge, which is 12 m above the ground. a. How far from the building does the block strike the ground? b. If a 1.8 m fence stands 6.0 m from the building, show whether or not the ice block will hit the fence. 1 1. The system below is released from rest and moves 90 cm in 1.5 s, without friction. What is the mass m of the hanging object? 2. When the two boxes shown below are released from rest the system accelerates with 2.8 m/s2 . Calculate the coefficient of kinetic friction, assuming that it is the same for both boxes. 3. You tie a rope to a pail of water and you swing the pail in a vertical circle of radius 80.0 cm. What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it? 2 4. Consider the two blocks in the diagram below, where block A is two times heavier than block B. Also, the coefficient of kinetic friction (µk) between the two blocks is the same as between block B and the inclined surface. Knowing that block B slides down the incline at a constant speed, calculate µk. 5. An airplane travels at 500 km/h as it makes a horizontal circular turn of radius 1.6 km. What is the magnitude of the net force on the 78-kg pilot? 6. A bead can slide along a frictionless metal o-ring of radius 20.0 cm. The ring is in a vertical plane and rotates about a vertical axis through its centre at a constant angular speed ω, as shown. a. If ω = 3.0 rev/s, what is the angle θ at which the bead is in vertical equilibrium? b. What will happen when ω reduces to 1.0 rev/s? c. Is it possible for θ to become 90°? Explain. 3 7. A race car starts from rest on a circular track of radius 400 m. Its speed increases at the constant rate of 0.440 m/s2 . At the point where the radial and tangential accelerations are equal, determine: a. the speed of the race car b. the distance traveled c. the elapsed time 8. A force F =5.0 – c x + x 2 acts on a particle as it moves along the x axis, with F in newtons, x in metres and c a constant. At x = 2.0 s, the particles kinetic energy is 15.0 J; at x = 3.0 s, it is 18.0 J. What is the value of c? 9. Consider the system shown below. The 5.0 kg block is given an initial downward speed of 1.0 m/s (pulling the other block to the right). The blocks come to rest after moving 1.5 m. Use the work-kinetic energy theorem to calculate the coefficient of kinetic friction between the 7.0 kg block and the table top. 10. A cart is confined to slide along a horizontal frictionless surface. A cord is attached to the cart and is pulled over a pulley of negligible mass and friction, as shown. If a 30.0 N tension is maintained in the cord, calculate the change in the kinetic energy as the cart slides between points P1 and P2 on the horizontal surface. 1. A pump draws 750 kg of water per minute from a well 15.0 m deep and ejects it with a speed of 25.0 m/s, making a vertical fountain. a. What is the power output of the pump? b. How high is the fountain? Ignore air resistance. 2. The spring shown below has a spring constant equal to 1,500 N/m. It is compressed 18.0 cm, then launches a 400 g block. The horizontal surface is frictionless and the coefficient of kinetic friction with the incline is 0.15. What horizontal distance d does the block cover while in the air after it takes off at the top of the incline? 3. A locomotive with power capability of 1.5 MW accelerates a train steadily from a speed of 20 km/h to 50 km/h in 5.0 min. Calculate: a. the distance travelled by the train during this time interval b. the mass of the train 4. A uniform chain with a mass of 5.0 kg and a length of 2.0 m lies on a table with 50 cm hanging over the edge. What is the minimum energy required to get all of the chain back on the table? 1 5. A 12 g bullet moving with upward speed of 960 m/s strikes and passes through a 2.0 kg block initially at rest, as shown. The bullet emerges from the block with a speed of 240 m/s. To what maximum height will the block rise above its initial position? 6. A 3.0 kg object moving at 5.0 m/s strikes a 2.0 kg object initially at rest. Immediately after the collision, the heavier object has a velocity of 3.5 m/s directed 33°◦ from its initial direction of motion. a. What is the speed of the other object? b. Is this collision elastic or inelastic? 7. Two identical spheres, labeled A and B, collide. The velocities before the collision A ˆ ˆ (10 i 15 j) m/s i v = −  and B ˆ ˆ (12 i 18 j) m/s i v = −  . After the collision A ˆ ˆ (8.0 i 11 j) m/s f v = −  . What is the final velocity of sphere B? 8. A 7.0 kg block is connected, as shown, by a light cord to a 3.0 kg mass, which slides on a rough surface with the coefficient of kinetic friction equal to 0.35. The pulley is a uniform disk of mass 1.0 kg and rotates about a frictionless axis. The cord does not slip on the pulley. Calculate: a. the linear acceleration of the system b. the tension in the two sections of the cord 2 9. A 2.5 kg solid block has the dimensions a = 12 cm, b = 20 cm and c = 2.0 cm. Calculate its moment of inertia about an axis through one corner and perpendicular to the large faces, as shown. 10. Calculate the moment of inertia of a solid cone about an axis through its centre. The cone has a mass M and height h, and the radius of its circular base is R. 3 1 1. A particle whose mass is 4.0 kg moves in the xy plane with a constant speed of 9.0 m/s along the direction of the vector ( ) ˆ ˆ i j − . When it is at the position (4.0 m, 0) calculate the angular momentum of the particle relative to the point (2.0 m, 0). 2. A 10 kg disk of radius 50 cm rotates while experiencing a variable torque given by τ = − (3.0 2.0) N m t . At time t = 2.0 s, its angular momentum is 2 6.0 kg m / s. At t = 5.0 s calculate the disk’s a. angular momentum b. angular speed 3. A small 60 g block slides down a frictionless surface through a height h = 25 cm and then sticks to the lower end of a vertical rod of mass 150 g and length 50 cm. The rod pivots about a point near its upper end through an angle θ before momentarily stopping. Find θ. 2 4. A 32.0 kg child sits near the edge of a rotating merry-go-round that has the shape of a uniform disk of mass 60.0 kg and diameter 2.00 m. When the rotational speed is ω = 1.00 rad/s, the child catches a ball of mass 0.500 kg thrown by her mom. Just before the ball is caught, it has a horizontal velocity of magnitude v = 16.0 m/s at an angle θ = 30.0° with a line tangent to the outer edge of the merry-go-round, as shown. Calculate the angular speed of the merry-goround just after the ball is caught. 5. A horizontal beam of length 9.0 m and mass 30 kg is hinged at the wall, with the far end supported by a cable that makes an angle of 60° with the horizontal. A 20 kg sign hangs from the beam by two cables as shown. The cable can sustain a maximum tension of 900 N. A 76 kg man starts at the hinge and walks on the beam towards the sign. Calculate: a. the maximum distance the man can walk safely b. the reaction forces at the hinge just before the cable breaks 3 6. Two ladders, 4.0 m and 3.0 m long, are hinged at point A and tied together by a horizontal rope 75 cm above a frictionless surface, as shown. The mass of the longer ladder is 30 kg and that of the shorter one is 20 kg. a. Calculate the upward reaction forces at the bottom of each ladder. b. Calculate the tension in the rope. c. If a 78 kg painter stands at point B, what is the tension in the rope? 7. A square ceramic tile of side width 50 cm is prepared to fit around an edge. A square section of side length 25 cm is cut from one corner of the tile, as shown. As a result, the centre-ofmass of the tile shifts from point A to point B. Find the distance between these two points. 8. A satellite has a circular orbit with a period of 62 hours and a radius of 4 5.2 10 × km around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 2 6.8m/s , calculate the planet’s radius. 4 9. A particle of mass m is placed at a point along the axis of a ring at a distance d from its centre, as shown. The ring has a mass M and radius a. a. Calculate the gravitational potential energy of the system. b. Show that when a d  , the gravitational potential energy reduces to that between two point particles. 10. A weightlifter can lift 120 kg on the earth. What mass could the same person lift on a. the moon? b. the sun? (See Table 13.2 in the textbook for planetary data.)

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