A spool of thread consists of a smaller cylinder of radius R/2 in the middle and two discs of radius R fixed to its two ends. The thread is wound on the cylinder. The spool of mass m is placed on a horizontal table, then the end of the thread is pulled in a direction shown in the figure. a) What is the angle α between the thread and the vertical if the center of the spool does not move neither to the left nor to the right? (Assume that the spool does not slip.) b) What is the coefficient of static friction between the spool and the table if the spool slips when the pulling force reaches a certain value F0?

A spool of thread consists of a smaller cylinder of radius R/2 in the middle and two discs of radius R fixed to its two ends. The thread is wound on the cylinder. The spool of mass m is placed on a horizontal table, then the end of the thread is pulled in a direction shown in the figure. a) What is the angle α between the thread and the vertical if the center of the spool does not move neither to the left nor to the right? (Assume that the spool does not slip.) b) What is the coefficient of static friction between the spool and the table if the spool slips when the pulling force reaches a certain value F0?

Similar questions

A 1Zero Suit Samuskg object is located at a distance of 6.4 x106 m from the center of a larger object whose mass is 6.0 x 1024 kg. What is the size of the force acting on the smaller object?
A solid disk of radius, R = 0.063 m, and mass, M= 0.500 kg, has a small hole drilled through it halfway between its center and outer edge and the disk is pinned to the wall through the hole so that it may rotate freely on the pin. a) Using a free-body diagram, with the weight of the disk acting at its centre of mass, determine the torque on the system about the axis and determine, using similar arguments as were used for a pendulum for the class notes, the constant k for the linear restoring torque in this case. b)The effective mass of the system will be the moment of inertia about the axis which you have already calculated above. Your work above should establish that the system executes SHM with the angle theta as the variable rather than the displacement, x, as was the case for the spring motion we studied in class. Use the similarity of this analogous system to follow the same steps as were used in class to get the angular frequency of a pendulum and determine the period that the…
In the figure, a nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown in the figure here. One cord makes the angle 8 = 34.4 with the vertical; the other makes the angle o = 55.6 with the vertical. If the length L of the bar is 3.4 m, compute the distancex from the left end of the bar to its center of mass. com
A 7-kg mass (m1) hangs from a cord that runs through a pulley and back down to attach to a 6-kg mass (m2) that is hanging from the other side. The pulley has a mass of 5.00-kg and a diameter of 20-cm. Find: A) the tension in the cord supporting m1 and the tension in the cord supporting m2; B) the tension in the cord supporting the pulley. C) Why is the answer to B) not equal to the sum of tensions in A)? Why is it not equal to the sum of the three weights?
A square trap door, of length and width 2m and mass 20kg, is heldopen at an angle of 65° with respect to the floor. A rope is attached to theraised edge of the door and fastened to the wall behind the door in such aposition that the rope pulls perpendicularly to the trap door. (a) What is thetorque exerted on the trap door by the rope? (b) What is the moment of inertiaof the door rotating on its hinge? (c) Suppose the rope is cut, causing the doorto slam shut, what angular acceleration would the door have right after therope was cut?
The drawing below shows two forces acting on a rigid beam. The blue dot is the center of mass of the beam. The forces (red arrows) are equal in magnitude. Consider the net force on the beam and net torque about its center. Which of the following statements are true? Check ALL that apply. The net force is zero. The net force is not zero. The net torque is zero. O The net torque is not zero.
Three blocks - A, B, and C-are connected by massless ropes that move over frictionless pulleys without slipping as shown in the figure; the mass of block A is 1 kg, the mass of block B is 2 kg, and the mass of block Cis 4 kg. Each pulley can be modeled as a uniformly dense solid cylinder with a radius of 4 cm and a mass of 3 kg. The coefficient of kinetic friction between block B and the horizontal surface is 0.30. What is the magnitude of the tension (in N) in the rope between block A and the pulley nearest it? C 2.352
A solid disk of radius, R = 0.063 m, and mass, M= 0.500 kg, has a small hole drilled through it halfway between its center and outer edge and the disk is pinned to the wall through the hole so that it may rotate freely on the pin. a) Using a free-body diagram, with the weight of the disk acting at its centre of mass, determine the torque on the system about the axis and determine, using similar arguments as were used for a pendulum for the class notes, the constant k for the linear restoring torque in this case. b)The effective mass of the system will be the moment of inertia about the axis which you have already calculated above. Your work above should establish that the system executes SHM with the angle theta as the variable rather than the displacement, x, as was the case for the spring motion we studied in class. Use the similarity of this analogous system to follow the same steps as were used in class to get the angular frequency of a pendulum and determine the period that the…
The center of mass of the arm shown in the figure is at point A. Find the magnitudes (in N) of the tension force F and the force F which hold the arm in equilibrium. (Let 8 = 24.0°.) Assume the weight of the arm is 48.3 N. IF 8.00 cm 29.0 cm 1₂ 354 X Draw a diagram showing the forces and distances. Find the sum of the torques about point O, and set this equal to zero. Solve your equation for F₁. N 340.30 X Apply Newton's second law in the x and y directions, and solve for F Sx Pythagorean theorem to calculate F. . N and F You will need your value of F. Then use the sy'