A father builds a swing for his children. The swing consists of a board attached to two ropes, as shown in Figure 3.17. The swing is mounted on a tree branch, with the board 3.5 m below the branch. The diameter of the branch is 8.2 cm and the kinetic coefficient of friction between the ropes and the branch is 0.1. After the swing is installed and his child is seated, the father pulls the swing back 10 and releases. What is the decrease in angle of each swing and how many swings will the child receive before Dad needs to give another push?

A father builds a swing for his children. The swing consists of a board attached to two ropes, as shown in Figure 3.17. The swing is mounted on a tree branch, with the board 3.5 m below the branch. The diameter of the branch is 8.2 cm and the kinetic coefficient of friction between the ropes and the branch is 0.1. After the swing is installed and his child is seated, the father pulls the swing back 10 and releases. What is the decrease in angle of each swing and how many swings will the child receive before Dad needs to give another push?

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter7: Dry Friction

Section: Chapter Questions

Problem 7.78P: The figure shows a steel bar being processed by a rolling mill. Given that P=80kN and r =0.016,...

See similar textbooks

Similar questions

A block weighing 2.50 kg begins its motion from a stationary position at point A, located at the highest point of a frictionless ramp. The ramp is inclined at an angle of 40° relative to the horizontal and has a length of 1.50 m. As the block slides down the ramp, it reaches a region between point B and point C, which is a rough horizontal surface with a kinetic friction coefficient of 0.30. After covering a distance of 1.00 m on the horizontal surface, the block encounters a lightweight spring with a spring constant of 900 N/m. A. Find the total energy for point A and point B? B. Find the speed of the block at point B? C. What is the cumulative work performed on the block as it moves along the rough horizontal surface? D. By employing the work-energy theorem, determine the velocity of the block at point C just before it collides with the spring?
consider the mass and pulley system in the attached file. mass m1 = 29 kg and mass m2 = 12kg. the angle of the inclined plane is given and the coefficient of kinetic friction between mass m2 and the inclined plane is uk = 0.12. assume the pulleys are massless and frictionless when mass m2 moves a distance 4.94 m up the ramp, how far downward does mass m1 move? d= ?
1) Jonny pulls his sister Jane (weight 28 lbs), who is sitting in a wagon, up an incline ramp (θ = 17°) with a steady speed. If the coefficient of kinetic friction is 0.18, the wagon has a mass of 14 kg, and the length of the ramp is 2.4 m, find: the work done by the frictional force. the work done by the gravitational force.
A pulley system uses a flat belt of cross sectional area 500 mm2 and density 1300 kg/m3. The angle of lap is 165O on the smaller wheel. The coefficient of friction is 0.35. The maximum force allowed in the belt is 600 N. If the the diameter of the smaller wheel is 50 cm and rotates at 3850 rpm , determine Initial tension in the belts and Power transmitted.
Two blocks with masses M1 and M2 are connected by a massless string that passes over a pulley as shown. M1 is on an incline of 49.5° with coefficient of kinetic friction μ1 = 0.205. M2 has a mass of 4.84 kg and is on an incline of 35.5° with coefficient of kinetic friction μ2 = 0.105. The pulley can be modeled as a disk with a mass of 305 g and radius of 15 cm. When the system is released, Block M2 accelerates down the incline at rate of 0.52 m/s2. (a) Determine mass of block 1 and the tension forces in the string connecting the blocks and the pulley. Draw accurate free body diagrams of both blocks and pulley, label each force correctly and show the steps in derivation of equations. (b) How much energy will be dissipated by friction 2 second after the blocks are released?
To climb a 400 meter high mountain, you have two options, a straight line route with a 40 ° slope or a route composed of 5 equal sections (same length) each with a 20 ° slope. If traveling in a car with a mass of 1280 kg and a maximum power of 88 kW, Determine (assume the whole car as a particle): a) Is the friction enough to prevent the car from sliding? The coefficient of static friction of the tires with the ground is 0.95. b) What is the power required to climb the 40 ° slope at a constant speed of 40 km / h? Does the car have enough power to go up at that speed? c) What is the constant speed at which the 40 ° slope can be climbed with a 60 kW power? d) What is the power required to climb a 20 ° slope at 40 km/h? Does the car has enough power to go up at that speed? e) In which of the two trajectories does the car do more work? Ignore the resistance of the air and rolling resistance and radius of curves between sections of the compound route. Please add the free body diagram.
A 50.0 kg grindstone is a solid disk 0.530 m in diameter. You press an ax down on the rim with a normal force of F = 160 N. The coefficient of kinetic friction between the blade and the stone is 0.60, and there is a constant friction torque of 6.50 N⋅m between the axle of the stone and its bearings. a) How much force must be applied tangentially at the end of a crank handle 0.500 m long to bring the stone from rest to 120 rev/min in 7.00 s? b) After the grindstone attains an angular speed of 120 rev/min, what tangential force at the end of the handle is needed to maintain a constant angular speed of 120 rev/min? c) How much time does it take the grindstone to come from 120 rev/min to rest if it is acted on by the axle friction alone?
Fred pushes a 55 kg refrigerator with a force P = 100 N inclined at 30° from the horizontal at 1.60 m from the floor as shown in the diagram. The coefficient of static friction between the floor and the refrigerator is 0.40.1. Which among the choices shows the limiting value of the frictional force between the refrigerator and the floor?A) 90.9 NB) 195.8 NC) 108.8 ND) 490 N2. Is the refrigerator not moving, moving, or on the verge of moving? Prove this through calculations.3) Write the correct moment equilibrium equation about A for the refrigerator. (Just use P, don't use P =100)
If there is no friction between shaft AB and the collar, what angular velocity Ö must the mechanism have to keep the collar at r= 660 mm from the vertical axis? Consider the same mechanism again, with m = 3.3 kg, d = 275 mm, k = 180 N/m, only now, instead of being smooth, the collar and shaft have a maximumcoefficient of friction of 0.74. What is the minimum angular velocity required to keep the collar at a constant distance r= 660 mm from the axis of rotation?
Box A weighs 1000N and has a height of H1=3m and width W1=2m. Box B weighs 800N. the static friction coefficient between the boxes is uA=0.7 and the static friction coefficient between box B and the ramp is uB=0.5. Find the max allowable angle for the following instances where no motion occurs, box A and B remain stationary. 1) Box A slides, Box B remains stationary 2) Box A tips, Box B remains stationary 3) Box B slides, Box A remains stationary on block B
A slowly moving conveyor belt passes through a small opening in a wall which is high enough to accommodate a single package, but a reckless worker stacks two packages on the belt. The one at the bottom, package 1 which has mass m1m1, continues, without slipping against the belt, through the opening. (The belt continues without slowing.) The one on the the top, package 2 with mass m2m2, presses firmly against the wall and slips across the lower package. The same coefficients of friction, μsμs and μkμk, apply between the pair of packages and between the package and the belt. Weights, if required, will be denoted with the corresponding subscript of the package as F⃗ g,iF→g,i, for i=1,2i=1,2. The normal force exerted by object aa on object bb, if required, will be denoted as F⃗ n,a→bF→n,a→b for a,b∈{1,2,belt,wall}a,b∈{1,2,belt,wall}, but a≠ba≠b. The force of kinetic friction exerted by object aa on object bb, if required, will be denoted as F⃗ k,a→bF→k,a→b for…
Consider the following arrangement of masses: Mass 1 is connected to mass 2 by a very light string and moves over a frictionless pulley so that both masses move with the same speed and move the same distances (?2 to the right a distance ? and ?1 down a distance ?).Assume ?1 = 15 ??, ?2 = 15 ??, and the coefficient of kinetic friction between ?2 and the table is ?? = 0.73. Let the masses start with an initial speed of 1.00 m/s. What is their speed after moving 1.00 cm (? = 0.0100 ?)?