Concept explainers
Two thin rods are fastened to the inside of a circular ring as shown in Figure P2.42. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide without friction along the rods. (a) If the two beads are released from rest simultaneously from the positions shown, use your intuition and guess which bead reaches the bottom first. (b) Find an expression for the time interval required for the red head to fall from point Ⓐ to point Ⓒ in terms of g and D. (c) Find an expression for the time interval required for the blue bead to slide from point Ⓑ to point Ⓒ in terms of g, L, and θ. (d) Show that the two time intervals found in parts (b) and (c) are equal. Hint: What is the angle between the chords of the circle Ⓐ Ⓑ and Ⓑ Ⓒ? (e) Do these results surprise you? Was your intuitive guess in part (a) correct? This problem was inspired by an article by Thomas B. Greenslade, Jr., “Galileo’s Paradox,” Phys. Teach. 46, 294 (May 2008).
Figure P2.42
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Physics for Scientists and Engineers with Modern Physics
- In a classic clip on Americas Funniest Home Videos, a sleeping cat rolls gently off the top of a warm TV set. Ignoring air resistance, calculate the position and velocity of the cat after (a) 0.100 s, (b) 0.200 s, and (c) 0.300 s.arrow_forwardA skier leaves the ramp of a ski jump with a velocity of v = 10.0 m/s at = 15.0 above the horizontal as shown in Figure P3.52. The slope where she will land is inclined downward at = 50.0, and air resistance is negligible. Find (a) the distance from the end of the ramp to where the jumper lands and (b) her velocity components just before the landing. (c) Explain how you think the results might be affected if air resistance were included.arrow_forwardA bicycle chain is wrapped around a rear sprocket (r = 0.037 m) and a front sprocket (r = 0.06 m). The chain moves with a speed of 1.2 m/s around the sprockets, while the bike moves at a constant velocity. Find the magnitude of the acceleration of a chain link that is in contact with each of the following. a.) the rear sprocket...............m/s2 b.) neither sprocket.................. m/s2 c.) the front sprocket ................ m/s2arrow_forward
- A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a y axis with an acceleration magnitude of 1.27 g, with g = 9.80 m/s2. A 0.599 g coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what are projections of the coin's acceleration relative to the ground on (a)x-axis, (b)y-axis, (c)z-axis and relative to the customer on (d)x-axis, (e)y-axis, (f)z-axis? (g) How long does the coin take to reach the compartment ceiling, 2.4 m above the knee? What are projections of the actual force on the coin on (h)x-axis, (i)y-axis, (j)z-axis and projections of the apparent force according to the customer's measure of the coin's acceleration on (k)x-axis, (l)y-axis, (m)z-axis?arrow_forwardA customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a y axis with an acceleration magnitude of 1.58 g, with g = 9.80 m/s2. A 0.492 g coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what are projections of the coin's acceleration relative to the ground on (a)x-axis, (b)y-axis, (c)z-axis and relative to the customer on (d)x-axis, (e)y-axis, (f)z-axis? (g) How long does the coin take to reach the compartment ceiling, 2.6 m above the knee? What are projections of the actual force on the coin on (h)x-axis, (i)y-axis, (j)z-axis and projections of the apparent force according to the customer's measure of the coin's acceleration on (k)x-axis, (l)y-axis, (m)z-axis? parts g)-m)arrow_forwardA spring gun that is mounted at the edge of a 2.0-m-high table launches a steel ball at an angle of 230 above the horizontal with an initial speed of 7.0 m/s. What is the total time of flight of the steel ball? (Assume that g = 9.81 m/s2.) a. 0.80 s b. 0.60 s c. 0.40 s d. 1.0 s e. 1.2 sarrow_forward
- The tension in a string from which a 4.0-kg object is suspended in an elevator is equal to 44 N. What is the acceleration of the elevator? a. 11 m/s^2 upward b. 1.2 m/s^2 upward c. 1.2 m/s^2 downward d. 10 m/s^2 upward e. 2.4 m/s^2 downwardarrow_forwardWhat is the acceleration of object #2 while it is ascending toward the surface (but before it reaches the surface)? Give your answer in terms of the ratio a/g.arrow_forwardA 82.4 KG person stands on a scale in an elevator. What is the apparent wait when the elevator is (a) accelerating upward with an acceleration of 2.23 m/s^2. (B) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.75 m/s^2?arrow_forward
- You wake up in a strange room, and this time you drop a ball from a height of 1.60 m, and observe that it hits the floor 0.400 s after you drop it. In this case you suspect you are in deep space, far from any planet or star, and that your rocket is accelerating due to the push of its own engines under the floor. In this case, what must the acceleration of your rocket be? (Ignore air resistance). 36.0 m/s^2 36.0 m/s^2 10.0 m/s^2 15.0 m/s^2arrow_forwardA boy kicks a rubber ball at an angle of 200 above level ground toward a 3.0-m high vertical wall that is 12 m from where the boy kicked the ball. With what initial speed must the boy kick the ball so that it barely clears the wall? (Assume that g = 9.81 m/s2.) a. 21 m/s b. 27 m/s c. 18 m/s d. 24 m/s e. 15 m/sarrow_forwardA spring gun launches a heavy steel marble with an initial speed of 19.6 m/s. How long will the steel marble be in the air? a. 6.0 s b. 2.0 s c. 3.0 s d. 5.0 s e. 4.0 sarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning