Exam Review Tuesday, September 17, :00 PM

Transcription

1 ExamReview Page 1 Exam Review Tuesday, September 17, :00 PM Chapter 2, Problem 65 A juggler throws a ball straight up with an initial speed of 10 m/s. With what speed would she need to throw a second ball, half a second later, starting from the same position as the first ball, so that the second ball hits the first ball at the top of the first ball's trajectory? Solution:

2 ExamReview Page 2 Chapter 2, Problem 67 A car starts from rest at a stop sign. It accelerates at 2.0 m/s 2 for 6.0 s, then coasts for 2.0 s, then slows down at a rate of 1.5 m/s 2 until the next stop sign is reached. Determine the distance between the stop signs. Solution: Chapter 3, Problem 17 A car travelling at 30 m/s runs out of gas while travelling up a 5.0 degree slope. How far will it coast before starting to roll back down?

3 ExamReview Page 3 Chapter 3, Problem 33 On the Apollo 14 mission to the Moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the surface of the Moon is 1/6th that of the Earth. Suppose he hit the ball with an initial speed of 25 m/s at an angle of 30 degrees above the horizontal. a. Determine how long the ball was in flight. b. Determine how far the ball travelled (horizontally). c. Ignoring air resistance, how much farther would the ball travel on the Moon than on the Earth? c. Repeat the calculation for Earth data, and you'll find that both the time of flight and the horizontal distance are 6 times greater on the Moon. Chapter 3, Problem 67 A spring-loaded gun, fired vertically, shoots a marble 6.0 m straight up. Determine the marble's range if it is fired horizontally from 1.5 m above the ground. Solution: First determine the initial velocity of the marble. Next, determine the time of flight for the second motion.

4 ExamReview Page 4 Next, determine the time of flight for the second motion. Therefore, the range is a. b. Chapter 3, Problem 77 A car moves around a circular road that has radius 110 m. Determine the car's acceleration if the car moves through the curve at a constant speed of 40 m/s. At what speed would the car's acceleration be double the value calculated in Part a? Solution: Chapter 5, Problem 41 A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob's rope pulls to the left, 15 degrees below the horizontal, with 500 N of tension. Ellen's rope pulls to the right, 25 degrees below the horizontal. a. Determine the tension in Ellen's rope if the piano descends vertically at a constant speed. b. Determine the tension in the main cable supporting the piano. Solution:

5 ExamReview Page 5 Chapter 5, Problem 49 Bob, who has a mass of 75 kg, can throw a 500 g rock with a speed of 30 m/s. The distance through which his hand moves as he accelerates the rock forward from rest until he releases it is 1.0 m. a. Determine the constant force Bob exerts on the rock. b. If Bob is standing on frictionless ice, what is his recoil speed after releasing the rock? Solution: Bob clearly has a "rifle-arm."

6 ExamReview Page 6 Chapter 5, Problem 60 A person with compromised pinch strength in his fingers can only exert a normal force of 6.0 N to either side of a pinch-held object, such as a book. Determine the heaviest book he can hold if the coefficient of static friction between his fingers and the surface of the book is Solution: Chapter 5, Problem 67 A wood block is sliding up a wood ramp. If the ramp is very steep, the block will reverse direction at its highest point and slide back down. If the ramp is shallow, the block will stop when it reaches its highest point. Determine the smallest ramp angle, measured from the horizontal, for which the block will slide back down. (Note that the coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.2.) Solution: Once the block reaches its highest point, the forces acting on it along the slope are a component of its weight and the frictional force. If the slope is not large enough, then static friction will be able to balance the component of weight along the slope. When the static friction force is maximum,

7 ExamReview Page 7 For larger angles, the block will slide back down, as the static friction force will not be large enough to balance the component of the weight directed down the slope. Chapter 5 test problem Chapter 6, Problem 53 A car drives over the top of a hill that has a radius of 50 m. Determine the car's maximum speed so that it does not fly off the road at the top of the hill.

8 ExamReview Page 8 Chapter 6, Problem 54 A 100 g ball on a 60-cm-long string is swung in a vertical circle whose centre is 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The ball reaches a height 600 cm above the floor. Determine the tension in the string an instant before it broke.

9 ExamReview Page 9 Chapter 6, Problem 59 A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is m/s 2 less than at sea level. Determine the observatory's altitude. Chapter 6, Problem 60 Suppose we could shrink the Earth without changing its mass. At what fraction of its current radius would the free-fall acceleration at the surface be three times its current value?

10 ExamReview Page 10 the surface be three times its current value? Chapter 6, Problem 62 Determine the speed and altitude of a geostationary satellite orbiting Mars. Mars rotates on its axis once every 24.8 h, has a mass of kg, and has a radius of 3370 km.

11 ExamReview Page 11 Chapter 7, Problem 36 The 2.5 kg object shown in the figure has a moment of inertia about the rotation axis of 0.085kg m 2. The rotation axis is horizontal. When released, what will be the object's initial angular acceleration?

12 ExamReview Page 12 Chapter 7, Problem 46 A computer disk is 8.0 cm in diameter. A reference dot on the edge of the disk is initially located at an angle of 45 degrees. The disk accelerates steadily for 0.50 s, reaching 2000 rpm, then coasts at a steady angular velocity for another 0.50 s. a. Determine the tangential acceleration of the reference dot after 0.25 s. b. Determine the centripetal acceleration of the reference dot after 0.25 s. c. Determine the angular position of the reference dot after 1.0 s. d. Determine the speed of the reference dot after 1.0 s.

13 ExamReview Page 13 Chapter 7, Problem 49 The 20-cm disk in the figure can rotate on an axle through its centre. Determine the net torque about the axle. Chapter 7, Problem 59 The ropes in the figure are each wrapped around a cylinder, and the cylinders are fastened together. The smaller cylinder has a

14 diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. Determine the angular acceleration of the cylinders assuming they turn on a frictionless axle. ExamReview Page 14

15 ExamReview Page 15 Chapter 9, Problem 29 A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 20 m/s. The third piece has twice the mass as the other two. Determine the speed and direction of the third piece.

16 ExamReview Page 16 Chapter 9, Problem 59 A 10 g bullet is fired into a 10 kg wood block that is at rest on a wood table. The block, with the bullet embedded, slides 5.0 cm across the table. Determine the speed of the bullet. (Assume that the coefficient of friction is 0.20.)

17 Chapter 9, Problem 61 A 1500 kg weather rocket accelerates upward at 10.0 m/s 2. It explodes 2.00 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m. What were the speed and direction of the heavier fragment just after the explosion? ExamReview Page 17

18 ExamReview Page 18 Chapter 9, Problem 67 The figure shows a collision between three balls of clay. The three hit simultaneously and stick together. Determine the speed and direction of the resulting blob of clay.

19 ExamReview Page 19 Chapter 10, Problem 19 How far must you stretch a spring with stiffness constant 1000 N/m to store 200 J of energy? Chapter 10, Problem 31 A 10 kg runaway grocery cart runs into a spring with stiffness constant 250 N/m and compresses it by 60 cm. What was the speed of the cart just before it hit the spring? Chapter 10, Problem 65 A 20 g ball is fired horizontally toward a 100 g ball that

20 is hanging motionless from a 1.0-m-long string. The balls undergo a head-on, elastic collision, after which the 100 g ball swings out to a maximum angle of 50 degrees. Determine the initial speed of the 20 g ball. ExamReview Page 20

21 Some conceptual questions ExamReview Page 21

22 ExamReview Page 22 When a ball is thrown vertically upward, the force acting on the ball in a vertically upward direction gradually decreases as the ball's speed decreases. When a ball is thrown vertically upward it gradually slows down, momentarily stops, and then falls down again. When it momentarily stops, the net force acting on the ball is zero. A cargo plane flies West at 900 km/h. When the plane is directly over the Brock tower, it drops a package of physics textbooks. The package lands to the West of the tower.

23 ExamReview Page 23 When a heavy truck collides with a light car, the force that the truck exerts on the car is greater than the force that the car exerts on the truck. An elevator is lifted up at a constant speed by a steel cable. The force that the cable exerts on the elevator cabin is greater than the force that gravity exerts on the elevator cabin. A passenger in a car moving very fast around a circular curve feels that he or she is "thrown" towards the outside of the curve because of a force that pushes objects away from the centre of the circular curve.

24 ExamReview Page 24 If we assume no air resistance, then for a projectile motion the net force in the horizontal direction is constant but the net force in the vertical direction is not constant. A horse is hitched to a cart. The driver says, "Giddyup!", but the horse doesn't move. He argues (yes, he's a talking horse) that there is no point in exerting any effort, because no motion is possible, because of Newton's third law. "After all," says the horse, "when I exert a force on the cart, by Newton's third law the cart exerts an equal and opposite force on me. The net force is therefore zero, and nothing moves." Explain.

25 ExamReview Page 25 A 250-pound linebacker collides with a 150-pound wide receiver. The receiver is thrown to the ground violently. Obviously the force that the linebacker exerts on the wide receiver is greater than the force that the wide receiver exerts on the linebacker. When you fire a rifle, you should hold the butt of the rifle tightly against your shoulder. Why? (a) Explain how a propeller (boat or airplane) works. (b) How do rockets work?