A physics experiment is set up using two pulleys, a string, and a weight as shown below. The larger pulley has a radius of 14 centimeters, and the smaller pulley has a radius of 8 centimeters. The distance between the centers of the pulleys is 56 centimeters. The string is pulled tightly across both pulleys so that AB is a common tangent of the pulleys. Find the length of string from A to B to the nearest tenth of a centimeter.

The spur gear is subjected to the two forces caused by contact with other gears. Determine the resultant of the two forces and express the result as a Cartesian vector. F₂=180 lb 60° 24 135⁰ 25 F₁ = 50 lb

To study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to rotate freely. The pivot is taken as the origin or your coordinate system. You apply a force of F = Fx i + Fy j + Fz k at a point r = rx i + ry j + rz k on the beam. 1. Enter a vector expression for the resulting torque, in terms of the unit vectors i, j, k and the components of F and r.  2. Calculate the magnitude of the torque, in newton meters, when the components of the position and force vectors have the values rx = 3.03 m, ry = 0.035 m, rz = 0.085 m, Fx = 2.8 N, Fy = 4.8 N, Fz = 5.8 N.  3. If the moment of inertia of the beam with respect to the pivot is I = 71 kg˙m2, calculate the magnitude of the angular acceleration of the beam about the pivot, in radians per second squared.

A block of mass 2 kg slides down an inclined plane at an angle of 45° with a massless tether attached to a pulley with mass 3 kg and radius 0.7 m at the top of the incline (see the following figure). The pulley can be approximated as a disk. The coefficient of kinetic friction on the plane is 0.2. What is the acceleration of the block (in m/s²)? (Enter the magnitude.) 3.59 45° x m/s²