In the swing carousel amusement park ride, riders sit in chairs that are attached by a chain to a large rotating drum as shown in (Figure 1). As the carousel turns, the riders move in a large circle with the chains tilted out from the vertical. In one such carousel, the riders move in a 16.5−m-radius circle and take 8.3 s to complete one revolution. Figure 1 of 1 What is the angle of the chains, as measured from the vertical? Express your answer in degrees. θ = ∘
In this version of the "Giant Swing", the seat is connected to two cables, one of which is horizontal (Figure 1). The seat swings in a horizontal circle at a rate of 26.0 rpm (rev/min). For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of A conical pendulum. Figure 1 of 1 Part A If the seat weighs 305 N and a 825 N person is sitting in it, find the tension Thorizontal in the horizontal cable. Express your answer with the appropriate units. View Available Hint(s) Submit Request Answer Part B If the seat weighs 305 N and a 825 N person is sitting in it, find the tension Tinclined in the inclined cable. Express your answer with the appropriate units. View Available Hint(s) Submit Request Answer
A simple pendulum consists of a 5−kg mass attached to a string of length 2 m. It is released from rest at A, 0.2 m above the lowest point of the swing. The tension in the string at the lowest point B is closest to: Ans. 60 N
A 119 g ball is tied to a string. It is pulled to an angle of 8.0∘ and released to swing as a pendulum. A student with a stopwatch finds that 18 oscillations take 15 s. Part A How long is the string? Express your answer with the appropriate units. L = Units Submit Request Answer
At the low point in its swing, a pendulum bob with a mass of 0.15 kg has a velocity of 3 m/s. What is its potential energy at its high point (assuming its potential at its low point was zero)? 0.23 J 0.68 J 0.46 J 0J
A "swing" ride at a carnival consists of chairs that are swung in a circle by 10.8 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 282 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair. (a) Number Units ◻ (b) Number Units
A 0.30−kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m), as shown. At an instant when q = 50∘, the tension in the string is 8.0 N. What is the magnitude of the resultant force on the mass at this instant? A. 5.6 N B. 6.0 N C. 6.5 N D. 5.1 N E. 2.2 N
A tiny ball is placed on the end of a string, pulled back to a small angle, and released from rest. The ball is then free to swing back and forth. a. At what position in the swing will the magnitude of the angular acceleration of the ball be the largest? b. If the string were lengthened, the time to reach the release position would be. . . EXPLAIN i. Longer than in the original situation ii. The same as in the original situation iii. Shorter than in the original situation c. If the mass of the ball were increased, the time to reach the release position would be. . . EXPLAIN i. Longer than in the original situation ii. The same as in the original situation iii. Shorter than in the original situation
As shown in the figure, a small ball with mass m is attached to a string, which goes over a pulley and makes a small angle swing. The length of the string is L. The gravitational acceleration is g. (10%) Find the period of this simple pendulum. (15%) Find the equation of tension on the string in terms of time.
A mass swings from a cord in uniform circular motion as shown in figure 5 . Report answers in Cartesian coordinates. (a) At what angle in degrees (θ) is the mass swinging at, given that it's time period of rotation (T) is 2 s ? (b) What is the magnitude of the tension in the cord? (c) What is the velocity of the mass, located at point P = (x, 0, 0) ? (d) What is the acceleration of the mass at point P = (x, 0, 0) ? (e) What increase in velocity would be necessary for the mass to raise the plane of rotation's height by 0.2 meters? Figure 5: Mass swinging around a fixed axis, with mass m, cord length R and angle θ.
A pendulum consisting of a mass of m = 100 g attached to a rigid wire which is L = 28.0 cm from the pivot point. When the pendulum swings, the middle of the mass (the black dot) is h = 3.00 cm higher than when the pendulum is at its lowest point. What is the angle of swing θ ? θ = degrees
A child on a swing has a speed of 7.7 m/s at the low point of the arc (Figure 3.46). How high will the swing be at the high point? Provide your answer in meters
3/46 A "swing ride" is shown in the figure. Calculate the necessary angular velocity ω for the swings to assume an angle θ = 35∘ with the vertical. Neglect the mass of the cables and treat the chair and person as one particle. PROBLEM 3/46
The chain on a child's swing is 1.5 m long. When the swing swings from one side to the other side, the horizontal distance it travels is 2.02 m. What is the size of the angle through which the swing swings? Select one: a. 84.6∘ b. 61.8∘ c. 95.2∘ d. 0.093∘
Mike swings from a vine. At the bottom of the swing, what is the direction of the net force on Mike? 9 zero magnitude 10 more info needed direction: Hint: What would a free-body diagram tell you? What does the momentum principle tell you?
A child weighing 200 N is being held back in a swing by a horizontal force of 125 N, as shown in the image. What is the tension T in the rope that supports the swing? Note: Only type in your numerical answer into the text box below. If you include units (such as "N" for Newtons), you will get the answer wrong. Also, leave your answer in standard notation (not scientific notation).
A 20 kg child is on a swing that hangs from 3.0−m-long chains, as shown in Figure P10.58. What is her speed vi at the bottom of the are if she swings out to a 45∘ angle before reversing direction? FIGURE P10.58
A "swing" ride at a carnival consists of chairs that are swung in a circle by 18.3−m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 168 kg. Find the speed of the chair. (g = 9.80 m/s2)
A father fashions a swing for his children out of a long rope that he fastens to the limb of a tall tree. As one of the children with a mass of 42 kg swings from this rope that is 2.6 m long, his tangential speed at the bottom of the swing is 2.6 m/s. What is the centripetal force of the child at the bottom of the swing?
Tarzan, who weighs 695 N, swings from a cliff at the end of a convenient vine that is 15.0 m/ong (see the figure). From the top of the cliff to the bottom of the swing. he descends by 4.46 m. The vine will break if the force on it exceeds 1440 N. What would the greatest force on the vine be during the swing?
A 20 kg child is swinging on a swing. She is released at a point 1.5 m above the lowest point in the swing's path. If the child is given a push start so she is moving 2.0 m/s at the original 1.5 m starting level, a) how fast shall she be moving at the lowest point? UP b) what is the value of the Tension in the rope in the initial position and at the lowest point.
A common amusement park ride has a circular platform with swings hanging from it. Riders get in and the platform begins to rotate, causing the riders to also begin rotating and swing outward, eventually maintaining a constant angle with respect to the vertical. If a rider is a distance of 12 m from the axis of rotation and moving with a speed of 40 km/hr. a. Drawing Free Body Diagram at the rider b. What is the angle θ that the supporting wires make with the vertical? (46.40∘)
The diagram shows the various positions of a child in motion on a swing. Somewhere in front of the child a stationary whistle is blowing. Reference: Ref 16-2 At which position(s) will the child hear the lowest frequency for the sound from the whistle?
Dr. McBride's wife sets up a small swing for her squirrels. Eddy and Half-tail have a great time riding on the swing and completely enjoy it. How long should Dr. McBride make the string so the squirrels and swing have a period of 1.6 seconds?
Jane, whose mass is 50.0 kg, needs to swing across a river (having width D ) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F→, on a vine having length L and making an angle φ = 29.1∘ with the vertical (see below figure). Take D = 51.0 m, F→ = 108 N, L = 40.0 m, and θ = 52.0∘. (a) With what minimum speed must Jane begin her swing to just make it to the other side? (If Jane can make it across with zero initial velocity, enter 0.) m/s (b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume that Tarzan has a mass of 80.0 kg. m/s
A "swing" ride at a carnival consists of chairs that are swung in a circle by 15.0−m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 152.0 kg. Determine the centripetal force of the total mass of a chair and its occupant. The answer must be rounded to one decimal place. Don't put any unit in the blank. Use g = 9.8 m/s2
An MET student wants to swing from A to B as shown below. The length of the rope is 5 m and its tensile breaking strength is 0.75 kN. If the student is 60 kg, how large should θ be for him to reach point B without breaking the rope?
11 A 2.0 kg ornament tied to the end of a 1.8 m long ribbon swings as a pendulum. At the lowest point of the swing, the speed of the ornament is 6.0 m/s. What is the speed of the ornament at the instant that the ribbon makes an angle of 40∘ with respect to the vertical? 12. A boxcar of a toy train set (m = 600 g) is moving at a rate of 40 cm/s when it collides perfectly elastically with a 900 g caboose initially at rest. What is the velocity (magnitude and direction) of each of the cars after the collision?
The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, L, what combination of g and L must the period be proportional to? Acceleration has dimensions of [L][T−2]. g/L gL gL gL2 L/g
A child of mass 30 kg is playing on a maypole swing in a playground. The length of rope is x = 3.0 m long and at an angle of 60∘ to the horizontal as she swings freely in a circular path. Ignore the mass of the rope in your calculations and find the speed of girl when she swings.
You swing an object around in a horizontal circle with the setup shown below. If the hanging mass is 35 grams and the mass on the end of the string (moving in a circle) is 15 grams and the length of the string (from the pivot point to the mass) is 42 cm, how long does it take to make one revolution?
A simple pendulum is pivoted at O and is free to swing in the vertical plane of the plate. If the plate is given a constant acceleration a = 4.6 m/s2 up the incline θ = 24∘, find the steady angle β assumed by the pendulum after all initial start-up oscillations have ceased. Neglect the mass of the slender supporting rod. Answer: β =
The sphere at A is given a downward velocity v0 of magnitude 5.7 m/s and swings in a vertical plane at the end of a rope of length / = 2 m attached to a support at O. Determine the angle θ at which the rope will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere. The rope will break at an angle of ∘.
A 0.00555−kg bullet traveling horizontally with a speed of 1.00×103 m/s enters a 20.0−kg door, embedding itself 20.0 cm from the side opposite the hinges as in the figure below. The 1.00−m-wide door is free to swing on its hinges. (a) Before it hits the door, does the bullet have angular momentum relative to the door's axis of rotation? Yes No Explain. This answer has not been graded yet. (b) Is mechanical energy conserved in this collision? Answer without doing a calculation. Yes No (c) At what angular speed does the door swing open immediately after the collision? (The door has the same moment of inertia as a rod with axis at one end.) rad/s (d) Calculate the energy of the door-bullet system. (Enter the kinetic energy of the door-bullet system just after collision.) J Determine whether the energy of the door-bullet system is less than or equal to the kinetic energy of the bullet before the collision. less than equal
Bob is sitting on a swing that has a rope hooked up to it. The rope then goes through a pulley attached to a tree above him, and the loose end of the rope is then put in Bob's hand as he sits on the swing. In this way Bob can pull the swing and himself up by pulling down on the rope. The rope is nearly massless, so it has a constant tension throughout - this means that the force with which Bob pulls down on its loose end is equal to the force that the rope exerts on the swing with the tied end. Bob's mass is 100 kg, the swing's mass is 30 kg, and Bob's pulling force is 800 N, which means that the tension in the rope is 800 N. a) Draw a single free body diagram, treating Bob and the swing as a single object, for use in part b. Also draw the free body diagram for Bob alone, which you'll use to solve part c. b) Apply Newton's 2 nd Law to your first diagram, and then solve it for the acceleration a. c) If Bob was sitting on a scale while this was going on, the scale would read the normal force on Bob from the swing, which is called the apparent weight. Find Bob's apparent weight while he's accelerating upward. Hint: this is similar to the turtle in the elevator, except that Bob has both tension and normal force acting upward on him.
A child weighing 200 N is being held back in a swing by a horizontal force of 148 N. Use the component method to determine the tension T in the rope in Newtons. However do not include the unit in your answer. Doing so would count your response as incorrect.
Part 1) The clock in the image above has a pendulum of mass m = 1.19 kg that swings on the end of a rod that is l = 0.590 m long. The angular amplitude of the swing is α = 6.07 (which can be considered small). Assume the rod has a negligible mass. Determine the period of the pendulum in seconds. T = s Part 2) What is the maximum speed that the mass on the end of the pendulum has during its swing? v = m/s Part 3) The clock is powered by a 1.83 kg weight that falls slowly, taking one day to drop by 3.00 m. The falling weight supplies the energy to compensate for the energy lost through friction in the pendulum, ensuring the amplitude stays constant. Suppose that the weight reaches the floor and no-longer supplies energy to the clock. Estimate how long (in seconds) the pendulum will continue to swing (assuming the energy loss is constant with time). Tf = s
A 65 kg girl is coasting back and forth on a swing as shown in the figure to the right. The ropes holding up the swing have length L and are very light but the seat of the swing is 5 kg. The girl is swinging back and forth such that it takes her 1.2 seconds to go from the backmost part of her swing (position A) to the frontmost part of her swing (position C). In this time she travels a total distance of 3 meters. 1) a) What is the length L of each rope of the swing? b) Some time later, the girl lets go of the swing at point C and the swing continues to oscillate back and forth without the girl. What is the period, T, of the swing after the girl lets go?
Tarzan, who weighs 592 N, swings from a cliff at the end of a convenient vine that is 20 m long (see the figure). From the top of the cliff to the bottom of the swing, he descends by 4.5 m. The vine will break if the force on it exceeds 1060 N. What would the greatest force on the vine be during the swing? Number Units
A swing is made from a rope that will tolerate maximum tension of T = 1295 N without breaking. Initially, the swing hangs vertically. The swing is then pulled at an angle of 40.0∘ with respect to the vertical and released from rest. What is the mass of the heaviest person who can ride the swing?
The two ropes supporting the hammock shown in the illustration below are both tied to the trees at the same height. At what angle, θ, will the tension T in each rope be equal to the person's weight? In other words, at what angle θ does Tension = mg? 30 60 45 20
Tarzan swings on a rope from rest at point A past the lowest point B to the other side. a) By considering his velocities (changes) along the circular arc, sketch below to indicate the direction of his acceleration vector at both point A and B. b) At the lowest point B, is the tension in the rope greater than, less than, or equal to Tarzan's weight?
A 20 kg child is on a swing that hangs from 2.6−m long chains. For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Car rolling down a hill. Part A What is her maximum speed if she swings out to a 49∘ angle? Express your answer with the appropriate units.
A ball of mass m1 = 1.00 kg swings downward with an initial speed of v0 = 7.40 m/s at a height h = 32.0 cm and strikes a ball of mass m2 = 3.70 kg that is at rest as shown in the figure. (a) Calculate the speed of the m1 just before the impact. 4.0m/s (b) Assuming the collision is perfectly inelastic, determine the height the balls reach after the collision. 4.0cm (c) Calculate the magnitude of the energy lost during the collision. 4.00 J
[10] (2) A "swing" ride at a carnival consists of chairs that are swung in a circle by 3.0 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 50.0 kg. [2] (2.a) Plot the free body diagram of the chair and its occupant. [8] (2.b) Determine the tension T in the cable attached to the chair when its velocity is 3.46 m/s. [Hint: You may need to solve a quadratic equation to find θ.]
A pendulum, comprised of a light string of length L and a small sphere (its radius is much smaller than L or d ), swings in the vertical plane. The pendulum is released from rest at the horizontal position (θ = 90∘). During the swing, the string bends around a peg located a distance d below the point of suspension, and the pendulum swings a full circle around the peg. We choose d to be the smallest distance that allows this to happen. a) At this value of d, what is the kinetic energy of the pendulum at the top of the circular swing? b) What is d in terms of L ? c) Discuss how the results for (a) and (b) would change if the pendulum moves against air resistance throughout its path. No calculations are required but you should answer in terms of work and energy.
Your young sibling is on a swing set, hanging vertically initially at rest. The combined mass of the swing and your sibling is 49 kg, and the light ropes are 2.51 m long. You push your sibling with an applied external force that is always tangent to the circular path, but that varies in magnitude as a function of angle θ in radians measured from the vertical as Ft(θ) = 364⋅(1 − θ) Newtons. Use g = 9.81 m/s2. In moving the swing from θ1 = 0 to θ2 = 0.49 radians = 28.07 degrees with the vertical, what is. . . a) [2]. . . the work done by you? WF = J b) [2]. . . the work done by gravity? Wgrav = J c) [2]. . . your sibling's speed? v = m/s
Derive the equation of motion of the spring mass pendulum system shown below (assume small swing angles, no deflection in vertical direction and negligible mass of the pendulum rod) a. Using Newton's 2 nd law (show free-body diagrams clearly) b. Using the energy method c. Using Lagrange's method
Suzy is swinging at the park. Her height above the ground is modeled by the function h(t) = 3 cos(π 1.9 t)+5 Where h(t) is measured in feet, and t is measured in seconds What is her maximum height above the ground? : feet What is her minimum height above the ground? : feet How long does it take her to make one complete swing? : seconds Given that the period (T) and length (L) of pendulum are related as: L = 32.2(T 2π)2, What is the length of the chain on Suzy's swing? feet
Logan is standing on a dock holding onto a rope swing that is L = 3.50 m long and suspended from a tree branch above. The rope is taut and makes a 30.0∘ angle with the vertical. Logan swings in a circular arc, passing through the bottom of the arc then releasing the rope when it makes an angle of θ = 11.9∘ with the perpendicular. If Logan's mass is 79.0 kg, how much work Wgrav does gravity do on him up to the point where he releases the rope? Wgrav = J
A mass m2 is attached at a fixed length to a swinging pendulum. The distance from the pendulum to mass m2 is x. Attached to the end of mass m2 by a spring of stiffness k is another mass m1. Two external foces of F1 and F2 are acting on the two masses in the horizontal direction. The length from the hinge of the pendulum to mass m1 is L. The spring's unstretched length is L0. Find the equations of motion using the Lagrange method.
Problem 9: A uniform rod of mass mrod and length L is free to rotate about an axis at one end. A small sphere with mass msphere is attached to the other end of the rod. The rod makes an angle ϕ with vertical and is released from rest. Part (a) Determine an expression for the difference in potential energy of the system before the rod is released and the system when the sphere is at its lowest point. Your answer will be in terms of msphere , mrod , L and g. Part (b) As the system swings through the point where the rod is vertical, its angular speed is ω. Determine an expression for the rotational kinetic energy of the system as it moves through this point. Your answer will be in terms of msphere , mrod , L and ω. Part (c) Determine an expression for the angular speed at the bottom of the swing. ω =
A child is on a swing. An adult tied a rope to the seat of the swing and pulled the swing forward. That rope is now horizontal, and the ropes attached to the swing structure make an angle θ with the vertical, as shown. (Note: There are two ropes tied to the chair that go to the top of the swing structure, one on each side of the child. We just see one in the in the image since we are looking at a side view. ) The child has a mass m. The adult uses the rope to hold the child at rest. What is the tension in the horizontal rope, and what are the tensions in each of the ropes connecting the seat to the top of the swing structure? [Use the following values. θ = 50.0∘, m = 25.0 kg ]
The slender rod is subjected to a couple moment M and a constant horizontal force P. What is the work done by the force P when the rod swing from its vertical position (θ = 0∘) to the position shown? −P/sinθ −P/tanθ P/sinθ P/cosθ P/cosθ
Figure 6 shows a boy sitting on a swing and being pumped (pushed) by a harmonic force Fosinωt where Fo is the force amplitude and ω is the angular frequency of pumping in the horizontal direction. This forced oscillation can be modelled by a simple pendulum which consists of a lumped mass m swinging at a distance L from the pivot. (i) Write the equation of motion for this pendulum under forced vibration. (ii) Find the amplitude of angular swing based on the assumption of a small angle. (7 marks) Figure 6