CP Two uniform solid spheres, each with mass M = 0.800 kg and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant k = 160 N/m has one end attached to the wall and the other end attached to a frictionless ring that passes over the rod at the center of mass of the spheres, which is midway between the centers of the two spheres. The spheres are each pulled the same distance from the wall, stretching the spring, and released. There is sufficient friction between the tabletop and the spheres for the spheres to roll without slipping as they move back and forth on the end of the spring. Show that the motion of the center of mass of the spheres is simple harmonic and calculate the period.
CP Two uniform solid spheres, each with mass M = 0.800 kg and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant k = 160 N/m has one end attached to the wall and the other end attached to a frictionless ring that passes over the rod at the center of mass of the spheres, which is midway between the centers of the two spheres. The spheres are each pulled the same distance from the wall, stretching the spring, and released. There is sufficient friction between the tabletop and the spheres for the spheres to roll without slipping as they move back and forth on the end of the spring. Show that the motion of the center of mass of the spheres is simple harmonic and calculate the period.
CP Two uniform solid spheres, each with mass M = 0.800 kg and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant k = 160 N/m has one end attached to the wall and the other end attached to a frictionless ring that passes over the rod at the center of mass of the spheres, which is midway between the centers of the two spheres. The spheres are each pulled the same distance from the wall, stretching the spring, and released. There is sufficient friction between the tabletop and the spheres for the spheres to roll without slipping as they move back and forth on the end of the spring. Show that the motion of the center of mass of the spheres is simple harmonic and calculate the period.
Pete Zaria works on weekends at Barnaby's Pizza Parlor. His primary responsibility is to fill drink orders for
customers. He fills a pitcher full of Cola, places it on the counter top and gives the 2.6-kg pitcher a 7.8 N
forward push over a distance of 36 cm (0.36 m) to send it to a customer at the end of the counter. The
coefficient of friction between the pitcher and the counter top is 0,25.
a. Determine the work done by Pete on the pitcher during the 36 cm push.
b. Determine the work done by friction upon the pitcher.
c. Determine the total work done upon the pitcher.
d. Determine the kinetic energy of the pitcher when Pete is done pushing it.
e. Determine the speed of the pitcher when Pete is done pushing it.
A thin wire has mass m and length L. It is bent into a semicircular shape. The wire is placed in the x-y plane such that it is symmetrical across the x-axis, and the two end points of the wire are placed at x = 0.
Write an expression for the center of mass XCM of the wire about the x-axis.
The mass of the wire is 69 g and the length of the wire is 0.65 m. Determine the x-coordinate for the center of mass in meters.
A arrow of mass 0.01 kg moving horizontal suddenly strikes a block of wood of mass 8.6 kg that is suspended by a light string, like a pendulum. The arrow passes through the wood, then the wood swings upward and momentarily stops when the string is horizontal. The length of the string is 2.0 cm. How long did it take the arrow to go through the wood if the friction force between the bullies and the wood is 100 N?
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