In the Atwood Machine shown, the pulley is a solid cylinder of mass m. Find the ratio of tensions in the vertical sections of the string.

A solid cylinder with a mass of 15 kg and a radius of 5 cm is mounted on a frictionless horizontal axle over a well as shown in the Figure below. A rope of negligible mass is wrapped around the cylinder and supports a bucket with a mass of 3 kg. Find the bucket’s acceleration as it falls down the well shaft.

Each problem requires a proper FBD and separate kinematic diagram.

With three decimal places

M, R m1 m2 Refer to the figure above for this problem. A wooden bldck of mass m, = 3.2 kg and a hollow block of mass m2 = 8.7 kg are connected by a rope which runs over a friction-less pulley. Assume that the pulley is a solid iron disc with a radius R = 0.3 m and mass M = 5.1 kg. The ramp is wedge- shaped and makes an angle of 0=36°. The coefficient of kinetic friction is 0.29 for both blocks and the wedgeshaped incline. (a) Draw force diagrams of both blocks and of the pulley. (b) Determine the acceleration of the two blocks. (c) Determine the tensions in the string on both sides of the pulley.

A spool of thread consists of a smaller cylinder of radiusR/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 isplaced on a horizontal table, then the end of the thread is pulledin a direction shown in the figure.a) What is the angle α between the thread and the vertical ifthe center of the spool does not move neither to the left nor to theright? (Assume that the spool does not slip.)b) What is the coefficient of static friction between the spool and the table if the spool slipswhen the pulling force reaches a certain value F0?

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'