Conceptual Physics Projectile and Circular Motion Review Packet Mr. Zimmerman Textbook Reference: pp. 33-42, 122-135 Key Terms (fill in definitions) projectile - any object that moves through the air or through space, acted on only by gravity (and air resistance, if any) component - one of the vectors, often mutually perpendicular, whose sum is a resultant vector. Any resultant vector may be regarded as the combination of two or more vectors. o x-component (horizontal) - the left / right component o y-component (vertical) - the up / down component rotation - the spinning motion that takes place when an object rotates about an axis located within the object revolution - motion of an object moving around an axis outside the object rotational speed - the number of rotations or revolutions per unit of time; often measured in rotations or revolutions per second (Hz) or per minute (r.p.m.) tangential speed - the speed of an object moving along a circular path centripetal force - a center-directed force that causes an object to move in a curved (sometimes circular) path centrifugal "force" - an apparent outward force on a rotating or revolving body. It is fictitious in the sense that it is not part of an interaction but is due to the tendency of a moving body to move in a straight-line path Key Formulas For motion of projectile launched horizontally: vertical component: horizontal component: For circular motion: measured in Hertz (Hz) 1
Key Ideas An object projected horizontally takes the same time to reach the ground as an object that is dropped from the same height. If air resistance can be ignored, the horizontal component of the object's motion has a constant speed. Its horizontal acceleration is zero. If air resistance can be ignored, the vertical component of the object's motion has a constant acceleration of -10 m/s 2. A near-earth satellite also has a vertical acceleration of about -10 m/s 2, but due to its very high horizontal speed, it falls around the Earth rather than into it. A rotation is a spin around your own axis; a revolution is a movement of a whole object around an external axis. "Centripetal" means "center-seeking." Centripetal force is toward the center of the circular path. "Centrifugal" means "center-fleeing." It is not a real force; instead, it is a perception from a curving frame of reference. Example: In a washing machine during the spin cycle, the perceived centrifugal force that seems to push water outward is fictitious; in fact, the centripetal force of the spinning cylinder on the clothes forces them away from the water! The fact that the constraint on an object being forced to move in a circle feels like a force is pushing the object outward allows us to simulate gravity in outer space. A spinning space station could simultaneously simulate different strengths of gravity by having compartments at different distances from the center. The further out, the stronger the perceived force would feel. Circular Motion Concepts 1. Does a child on a merry-go-round revolve or rotate around the merry-go-round's axis? Revolves 2. Distinguish between linear speed and rotational speed. Linear speed is distance traveled per unit of time. Rotational speed is the number of rotations or revolutions per unit of time. 3. What is linear speed called when something moves in a circle? Tangential speed. 4. At a given distance from the axis, how does linear (or tangential) speed change as rotational speed changes? As rotational speed increases, so does the linear speed. They are in direct proportion to each other. 5. At a given rotational speed, how does linear (or tangential) speed change as the distance from the axis changes? As distance from the axis increases, so does the linear speed. They are in direct proportion to each other. 6. When you whirl a can at the end of a string in a circular path, what is the direction of the force that acts on the can? Inward along the string, toward the center of rotation. 2
7. Does the force that holds the riders on the carnival ride in Figure 9.1 act toward or away from the center? Toward the center, same as for any centripetal force. 8. When a car makes a turn, do seat belts provide you with a centripetal force or centrifugal force? Centripetal force (centrifugal "force" is a sensation, not a real force at all) 9. If the string that holds a whirling can in its circular path breaks, what causes the can to move in a straight-line path -- centripetal force, centrifugal force, or lack of force? What law of physics supports your answer? Lack of force. This is an example of the law of inertia (Newton's 1st law) Labs: Marble Launcher Main outcomes: x-component (horizontal) and y-component (vertical) of projectile motion are independent; vertical and horizontal motions use different formulas, because gravity affects only the vertical component knowing the distance from the floor, can calculate the time of fall using (equation 1) once you have the time of fall, you can find the projectile's initial speed (horizontal) using (equation 2) to predict the range from a different height, you used these equations in the reverse order, assuming that the launch speed for a given notch would be consistent Activity: Direction of Acceleration Main outcomes: a weight hanging from a string is a simple accelerometer; the weight hangs straight if there is zero acceleration; if it's not zero, the weight points in the direction opposite the acceleration for circular motion, the weight points radially outward, so the acceleration must be radially inward Turn, Turn, Turn Main outcomes: the coin further out starts sliding first; when this happens, it means that the friction force available from the turntable is less than the centripetal force that is required to keep the coin moving in a circle the further out the coin was, the greater its tangential speed could be before slipping analogy to car going around a curve; can take the turn at a higher speed if the curve is wider CANNONS computer simulation Main outcomes: reinforcement of the ideas of the Marble Launcher lab time to hit the ground is the same for all cannonball speeds, if launched horizontally mass or diameter of the ball has no effect, unless air resistance is added optimum angle to achieve the greatest range is 40.5 from the 5-meter pedestal 3
Sample Test questions if fired from the ground, the optimum angle is 45 ; optimum angle decreases as the pedestal gets higher air resistance shortens the range; the path is no longer an accurate parabola 1. A marble launcher is 1 m above the floor. You fire a marble horizontally. At the same time you drop a second marble from the same height. Which marble hits the ground first? a) launched marble b) the dropped marble c) they reach the ground at the same time 2. Explain why you chose the answer you did in the previous question. Be as thorough as possible. (defend your answer with physics) The x-component (horizontal) and y-component (vertical) of projectile motion are independent. In this case, the vertical motions are identical. 3. Careful! Read all choices! A projectile is fired horizontally in a vacuum (no air). The projectile maintains its horizontal component of speed because: a) The projectile is not acted on by any forces. b) The projectile is not acted on by any horizontal forces. c) The projectile has no vertical component of speed to begin with. d) There is no gravity in a vacuum. 4. During freefall, objects experience constant a) velocity b) speed c) acceleration d) distances fallen each second *5. A projectile with an initial horizontal velocity of 10 m/s and an initial vertical velocity of 20 m/s is fired from ground level. How many seconds after it is launched will it reach the top of its trajectory? a) 10 s b) 4.0 s c) 2.0 s d) 1.0 s *6. The angle with the horizontal at which a projectile must be launched from ground level so that it goes as far downrange as possible is... a) dependent on the initial velocity b) 0o c) 45o d) 90o 7. A marble is fired horizontally out of a marble launcher with a speed of 5 m/s. The launcher is sitting on a 20 m tall building. With what speed is it moving in the vertical direction after 1 second? a) 5 m/s b) 10 m/s c) 10 m/s 2 d) 20 m/s 8. A marble is fired horizontally out of a marble launcher with a speed of 5 m/s. The launcher is sitting on a 20 m tall building. How fast is it moving in the horizontal (x) direction after 1 second? a) 0 m/s b) 5 m/s c) 10 m/s d) 10 m/s 2 9. A marble is fired horizontally out of a marble launcher with a speed of 5 m/s. The launcher is sitting on a 20 m tall building. What is the magnitude of the marble s acceleration after 1 second? a) 0 m/s b) 5 m/s c) 10 m/s d) 10 m/s 2 4
10. A rock is thrown upward at an angle of 50. As it rises, its vertical component of velocity A. increases B. remains unchanged C. decreases 11. A rock is thrown upward at an angle of 50. As it rises, its horizontal component of velocity A. increases B. remains unchanged C. decreases 12. A bullet that is fired horizontally hits the ground in 0.5 seconds. If it had been fired with twice the speed but in the same direction and from the same height, it would have hit the ground in A. less than 0.5 s B. 0.5 s C. more than 0.5 s 13. An object is dropped and freely falls to the ground with an acceleration of -10 m/s 2. If it is thrown upward at an angle instead, its vertical acceleration would be A. zero B. -10 m/s 2 C. more than -10 m/s 2 D. none of these 14. A stone is thrown with an initial x-velocity of 3 m/s and an initial y-velocity of 4 m/s. What will the velocity of the stone be when it is at the peak of its trajectory? At the peak, the y-velocity (vertical component) is zero. At that time, the total velocity is 3 m/s, horizontally. *15. A marble is launched horizontally from a table that is 2 m tall. It lands 20 m away. a) How much time did it take to fall? (show equation(s) used and all steps) Look at the vertical component of the motion: b) What was its initial velocity (speed and direction)? (show equation(s) used and all steps) Look at the horizontal component of the motion: 16. Harry jumps horizontally from the top of a building that is 30 m tall. He hopes to reach a swimming pool that is at ground level, 10 m from the edge of the building. If he is to reach the pool, what must his jumping speed be? First, find the time it takes to fall 30 meters 5
Second, find the horizontal speed that will move the required distance in that 2.4 s *17. A diver steps off the edge of a vertical cliff and reaches the water below 2.0 s later. How high was the cliff? The only motion to consider here is vertical: 18. An expert with a bow can shoot an arrow with an initial speed of 50 m/s. A. If the arrow is shot horizontally, what horizontal distance will it travel in 2 seconds? B. What will its horizontal speed be at the end of those 2 seconds? still 50 m/s (no horizontal force, so no change in the horizontal speed C. What will its vertical speed be at the end of those 2 seconds? 20 m/s (starts with zero vertical speed, gains 10 m/s downward every second) 18. A marble is shot from a marble launcher set horizontally (angle = 0). The mouth of the launcher is 1.8 m off the ground. The horizontal distance the marble travels before it hits the ground is 3.0 m. a. Find the time the marble takes to hit the ground. Look at the vertical component of the motion: b. Find the initial speed of the marble. Look at the horizontal component of the motion: 6
Circular Motion questions 1. A penny is placed on a rotating platform. You rotate the platform, and the penny moves in a circle. Draw a force diagram showing all three forces acting on the coin as it turns. Label the forces with their correct names! 2. What is the name for a force that keeps an object moving in a circle? _Centripetal force 3. Is this an inwardly or outwardly directed force? 4. In this case (penny on platform), what force produces this c word force? (choose from tension, friction, support force, gravitational force, or no force) 5. The penny is placed 0.02 m from the center of a rotating platform and makes 60 revolutions in 30 seconds. Show all of your work. a) What is the penny s frequency? b) What is the period of the penny s spin? c) What is the tangential speed of the penny? 6. Sue owns a super deluxe macho edition Jeep with no doors and VERY slippery seat covers. She is driving Rob home from school. Sue is wearing her seatbelt. Rob refuses to wear his. The paths that Sue and Rob follow when the jeep turns a sharp corner have been drawn and labeled. Sue Rob a) What force keeps the car moving in the circular path? _Friction_ (the centripetal force) What two objects are involved in that interaction? the car's tires and the road's surface material b) What force (or lack of force) keeps Sue moving in a circular path? (choose from tension, friction, support force, gravitational force, or lack of force) 7
c) What object (if any) most directly produces this force? _the seat belt d) What force (or lack of force) keeps Rob moving in a straight line path? (choose from tension, friction, support force, gravitational force, or lack of force) e) What object (if any) most directly produces this force? n/a f) Using Newton s First law in your answer, explain why Rob takes the path that he takes? Rob is moving with constant velocity (straight line, steady speed) as Newton's law predicts in the absence of an outside force, which Rob unfortunately does not have available. 7. Centrifugal forces are an apparent reality to observers in a reference frame that is. a) moving at a constant velocity b) an inertial frame of reference c) at rest d) rotating 8