The static coefficient of friction μs applies to an object of mass m placed on a platter that revolves about a vertical axis at frequency f. Derive an expression for the maximum distance r from the center of the platter at which the object can remain without sliding off the platter
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- %3D A 3.7-kg sphere is suspended by a cord that passes over a 1.7-kg pulley of radius 3.4 cm. The cord is attached to a spring whose force constant is k = 86 N/m as in the figure below. Assume the pulley is a solid disk. www- (a) If the sphere is released from rest with the spring unstfetched, what distance does the sphere fall through before stopping? 0.3079 Your response differs from the correct answer by more than 10%. Double check your calculations. m (b) Find the speed of the sphere after it has fallen 25 cm. 1.67 m/sMultiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius = 0.168 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.57 s. Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. μs = Number Type your answer here Units Choose your answer hereM.G.r 302 Chapter 10 Rotation of a Rigid Object About a Fixed Axis 25. A war-wolf or trebuchet is a device used during the Mid- dle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A sim- ple trebuchet is shown in Figure P10.25. Model it as a stiff rod of negligible mass, 3.00 m long, joining particles of mass 60.0 kg and 0.120 kg at its ends. It can turn on a fric- tionless, horizontal axle perpendicular to the rod and 14.0 cm from the large-mass particle. The rod is reteased from rest in a horizontal orientation. (a) Find the maxi- mum speed that the 0.120-kg object attains. (b) While the 9420-kg object is gaining speed, does it move with con- stant acceleration? Does it move with constant tangential acceleration? Does the trebuchet move with constant angular acceleration? Does it have constant momentum? Does the trebuchet-Earth system have constant mechani- cal energy? tread wal 20.0 cm. A 1.10 x 10 axis throu 28. • A unif 0.870…
- A 3.00-kg stone is tied to a thin, light wire wrapped around the outer edge of the uniform 8.00-kg cylindrical pulley. The inner diameter of the pulley is 55.0 cm, while the outer diameter is 1.00 m. The system is released from rest, and there is no friction at the axle of the pulley. a) Find the acceleration of the stone and the tension of the wire. b) Find the angular acceleration of the pulley.Current Attempt in Progress The figure shows particles 1 and 2, each of mass m, attached to the ends of a rigid massless rod of length L₁ + L2, with L₁ = 2.0 m and L₂ = 3.0 m. The rod is held horizontally on the fulcrum and then released. What are the magnitudes of the initial accelerations of (a) particle 1 and (b) particle 2? (a) Number (b) Number Units Units 1 L > >A constant horizontal force of 10 N is applied to a wheel of mass = 10 kg and radius of 0.3 m. The center of mass of the wheel has an acceleration of 0.48 m/s/s. a) Determine the magnitude of the friction force acting on the wheel. b) Determine the magnitude of the rotational inertia if the linear acceleration were 0.48 m/s/s. You will have to recalculate the friction force.
- In the figure, a uniform sphere of mass m = 0.551 kg and radius r = 0.139 m is held in place by a massless rope attached to a frictionless wall a distance L = 2.31 m above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall.4. A homogeneous, rigid cylinder of mass M and radius R is placed on a М,R small rectangular plate of mass m. There is sufficient static friction between the cylinder and the plate. The plate itself is placed on a flat, frictionless table. A constant force of magnitude F is applied to the plate in direction parallel to the table as shown on the diagram. Once the force F is applied, the cylinder goes immediately into pure rolling F т (no slipping or skidding). Find: a. The translational (linear) acceleration of the block, ap. b. The angular acceleration of the cylinder, a. c. The translational (linear) acceleration of the cylinder ac. Given variables: M, R, m, FIn the figure, a uniform sphere of mass m = 0.783 kg and radius r = 0.394 m is held in place by a massless rope attached to a frictionless wall a distance L = 1.58 m above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall. L. (a) Number i Units (b) Number i Units
- Multiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius = 0.168 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.57 s. Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. μs = Number Type your answer here Units Choose your answer hereAm1= 19.0-kg object and a m 2 = 9.0-kg object are suspended, joined by a cord that passes over a pulley with a radius of R = 30.0 cm and a mass of M = 3.00 kg as seen in the Figure. The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest d = 5.00 m apart. Treat the pulley as a uniform disk, and determine the speeds of the two objects as they pass each other. (Your result must be in units of m /s and include 2 digit after the decimal point. Maximum of 4% of error is accepted in your answer. Take g = 9.80 m/s 2.) Hint: For solid cylinder of disk the moment of inertia about an axis through center of mass is IcOM = MR %3D d.