A blob of mass m = 0.50 kg is moving at a constant speed in uniform circular motion within a conically-shaped, banked curve as shown. The angle of the bank is 0 = 45° and the radius is R=0.50 m. The blob m is attached via a horizontal, light string which goes through a cylinder in the middle to a hanging block of mass M = 2.0 kg. There is no friction between the blob and the surface, nor is there any friction between the string and the cylinder. What speed, v, does the block m need to have to remain in uniform circular motion?

A blob of mass m = 0.50 kg is moving at a constant speed in uniform circular motion within a conically-shaped, banked curve as shown. The angle of the bank is 0 = 45° and the radius is R=0.50 m. The blob m is attached via a horizontal, light string which goes through a cylinder in the middle to a hanging block of mass M = 2.0 kg. There is no friction between the blob and the surface, nor is there any friction between the string and the cylinder. What speed, v, does the block m need to have to remain in uniform circular motion?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

Problem 59P: A single bead can slide with negligible friction on a stiff wire that has been bent into a circular...

See similar textbooks

Similar questions

A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.0 cm as shown in Figure P5.59. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle θ that the radial line, from the center of the loop to the bead, makes with the vertical. (a) At what angle up from the bottom of the circle can the bead stay motionless relative to the turning circle? (b) What If ? Repeat the problem, this time taking the period of the circle’s rotation as 0.850 s. (c) Describe how the solution to part (b) is different from the solution to part (a). (d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? (e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem. Figure P5.59
The block B of mass 7.1 kg and cylinder A of mass 14.2 kg are connected to a light cord that passes through a hole in the center of the smooth table. If the block is given a speed v = 9.1 m/s, determine the radius r of the circular path along which it travels.
A skateboarder is attempting to make a circular arc of radius r = 14 m in a parking lot. The total mass of the skateboard and skateboarder is m = 89 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.59 . What is the maximum speed, in meters per second, he can travel through the arc without slipping?
A skateboarder is attempting to make a circular arc of radius r = 11 m in a parking lot. The total mass of the skateboard and skateboarder is m = 86 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.59 . He speeds up very slightly and begins to slide. The coefficient of kinetic friction is μk = 0.21. What is the new magnitude of his radial acceleration in m/s2?
A small block with mass 0.0500 kg slides in a vertical circle of radius 0.475 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 3.80 N . In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.665 N . How much work was done on the block by friction during the motion of the block from point A to point B?
A 5 kg mass is attached to a massless string and is being rotated in a horizontal circle. The length of the string is 0.5 m and the mass has a tangential velocity of 10 m/s. Find the tension in the string.
One end of a string of length 0.64 m is attached to a bucket containing water and the bucket is rotated about the other end in a vertical circle. Find the minimum speed with which it can be rotated without spilling the water at the highest point. How many revolutions per minute it is making?
On the International Space Station an object with mass m = 440 g is attached to a massless string of length L = 0.61 m. The string can handle a tension of T = 5.8 N before breaking. The object undergoes uniform circular motion, being spun around by the string horizontally.What is the maximum speed v the mass can have before the string breaks? Give your answer in units of m/s.
a 0.25 kg stone tied to a rope is swung to make a circular motion in a vertical plane . If the circle is of radius 300cm, what is the minimum uniform speed of the stone that will keep the rope taut
A small object with mass of 0.5kg is attached to the lower end of a long string and moves in a horizontal circle of radius 0.7 m with a constant speed of 3 m/s. What angle does the string make with the vertical?
An 80 kg person riding a Ferris wheel moves in a vertical circular trajectory of radius 6 m. As the person reaches the lowest point, a scale that the person is sitting on reads 920 N. There is nothing else in contact with the person. The person's speed is ____ m/s.
A skateboarder is attempting to make a circular arc of radius r = 19 m in a parking lot. The total mass of the skateboard and skateboarder is m = 98 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.66. The maximum speed he can go without slipping is 11.09 m/s. He speeds up very slightly and begins to slide. The coefficient of kinetic friction is μk = 0.11. What is the new magnitude of his radial acceleration in m/s2?