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Native people throughout North and South America used a bola to hunt for birds and animals. A bola can consist of three stones, each with mass m, at the ends of three light cords, each with length ℓ. The other ends of the cords are tied together to form a Y. The hunter holds one stone and swings the other two above his head (Figure P11.41a, page 308). Both these stones move together in a horizontal circle of radius 2ℓ with speed v0. At a moment when the horizontal component of their velocity is directed toward the quarry, the hunter releases the stone in his hand. As the bola flies through the air, the cords quickly take a stable arrangement with constant 120-degree angles between them (Fig. P11.41b). In the vertical direction, the bola is in free fall. Gravitational forces exerted by the Earth make the junction of the cords move with the downward acceleration
Figure P11.41
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Chapter 11 Solutions
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- A child works on a project in art class and uses an outline of her hand on a sheet of construction paper to draw a turkey (Fig. P16.36). The teacher pins the turkey to the bulletin board in the front of the classroom by using a thumbtack. The student notices that if she flicks her finger on the end of the turkey, it oscillates back and forth with a frequency of about 1.65 Hz. If the rotational inertia of the paper turkey is 1.25 105 kgm2 and its mass is 0.005 kg, what is the distance between the thumbtack and the center of mass of the turkey? FIGURE P16.36arrow_forwardChapter 10, Problem 069 In the figure, a small disk of radius r=4.00 cm has been glued to the edge of a larger disk of radius R=7.00 cm so that the disks lie in the same plane. The disks can be rotated around a perpendicular axis through point O at the center of the larger disk. The disks both have a uniform density (mass per unit volume) of 1.40 x 103 kg/m3 and a uniform thickness of 6.00 mm. What is the rotational inertia of the two-disk assembly about the rotation axis through O? Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Workarrow_forwardOne end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.N(b) At this instant, find the tangential and radial components of acceleration. at = m/s2 downward tangent to the circle ac = m/s2 inward (c) At this instant, find the total acceleration.inward and below the cord at °(d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? YesNo (e) Explain your answer to part (d).arrow_forward
- One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…arrow_forwardOne end of a cord is fixed and a small 0.700-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.00 m, as shown in the figure below. When θ = 21.0°, the speed of the object is 8.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string. N(b) At this instant, find the tangential and radial components of acceleration. at = m/s2 downward tangent to the circle ac = m/s2 inward (c) At this instant, find the total acceleration. inward and below the cord at °(d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? YesNo (e) Explain your answer to part (d).arrow_forwardA giant toy car with big wheels has a total mass (including the wheels) of 0.21 kg. The car has 4 wheels and each wheel has radius of 3.3 m and a moment of inertia of 0.22 kg m2. The car is attached to a horizontal spring. The spring is inititally unstretched and the car is given an initial speed of 1.9 m/s away from the spring. The car moves forward 0.38 m before it stops and is pulled back by the spring. The wheels roll without slipping the entire time. What is the spring constant?arrow_forward
- You tie one end of a string to a spring with spring constant 75 N/m and wind the string around a spindle, which rotates freely around an axis that passes through its center. The spindle consists of two cylinders attached together. The lower one has radius 30 cm and mass 6.0 kg. while the upper one has radius 15 cm and mass 4.0 kg. You turn the spindle, winding the string around it, until the spring is stretched a distance of 10 cm beyond its equilibrium length. You then release it from rest. What is the final angular velocity of the spindle, assuming friction is negligible? 15 cm 75 N/m 30 cmarrow_forwardPenny is adjusting the position of a stand up piano of mass mp = 150 kg in her living room. The piano is lp = 1.6 m in length. The piano is currently at an angle of θp = 45 degrees to the wall. Penny wants to rotate the piano across the carpeted floor so that it is flat up against the wall. To move the piano, Penny pushes on it at the point furthest from the wall. This piano does not have wheels, so you can assume that the friction between the piano and the rug acts at the center of mass of the piano.Randomized Variables mp = 150 kglp = 1.6 mθp = 45 degrees a) Write an expression for the minimum magnitude of the force Fs in N Penny needs to exert on the piano to get it moving. Assume the corner of the piano on the wall doesn't slide and the static friction between the rug and the piano is μs. Fs,min = b) The coefficient of kinetic friction between the carpet and the piano is μk = 0.27. Once the piano starts moving, calculate the torque τp in N⋅m that Penny needs to apply to keep…arrow_forwardYou have a cylinder. You don't know what its internal structure looks like, but you plan to roll it down a ramp, as in this week's procedure. The ramp is 1 m long, and is elevated at an angle of 15°. The mass of the cylinder is 450 g and its diameter is 2.1 cm.After you release the cylinder, it rolls down the ramp without slipping, gaining speed. How much total energy (in J)does the block have at the bottom of the ramp?arrow_forward
- A string is wrapped around a disk of mass m = 2.2 kg and radius R = 0.08 m. Starting from rest, you pull the string with a constant force F = 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x = 0.12 m, your hand has moved a distance of d = 0.27 m. m d (a) At this instant, what is the speed of the center of mass of the disk? Vcm = m/s (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? Krot = Additional Materials M eBookarrow_forwardA small ball of mass 740.0 g is placed in a tube that is bent into a circular arc of radius R= 67.5 cm.The friction between the ball and the walls of the tube is negligible. The ball has an iron core. A magnet is used to raise the ball until it makes an angle of 5.00 degrees with the vertical, and then released from rest. Where will the ball be 1.20 seconds after being released? Express your answer in terms of the angle,θ, that the ball makes with the vertical.arrow_forward1. a) Define a holonomic constraint and explain the impact of such constraints on the number of degrees of freedom of a system. Give an example of a non-holonomic constraint. b) Five identical flat circular plates are served on a circular conveyor belt. The plates have mass m, radius 5 cm and moment of inertia Ip about their axis of symmetry. They are free to move under gravity on top of a conveyor belt which has inner radius a, outer radius b and moment of inertia Ic about a vertical axis through its centre. From above, it looks like the diagram below. a The belt is banked at a fixed angle a such that the inner edge is lower than the outer edge. Assuming the conveyor belt rotates freely, how many degrees of freedom does this system have? Find the Lagrangian for the system. Hence find and identify any conserved quanti- ties of the system. 1 1arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning