A thin washer of internal radius 5 cm and external radius of 12 cm carries a load of 15mC distributed evenly on its surface located on the Y axis. A small 7.5g sphere with a load of 3mC is placed exactly in the center. A small push is given along the axis of the washer (the x-axis) to remove it from rest. How fast will the sphere be moving when it is 2m from the center of the washer? (hint, ignore gravity and energy is conserved)

4. A rod is L meters long and the center of mass of the rod is at the point L meters from the left end. If the measure of the linear density at a point is proportional to a power of the measure of the distance of the point from the left end and the linear density at the right end is 20 kg/m, find the linear density at a point x meters from the left end. (Leithold, 1996)

if global warming continues it is likely that some ice from the polar ice caps of the Earth will melt and the water will be distributed closer to the equator. If this occurs , what would happen to the length of the day?

The cylindrical plug A of mass ma-2.9 kg is released from rest at B and slides down the smooth circular guide. The plug strikes the block C of mass me 1.8 kg and becomes embedded in it. Calculate the distances which the block and plug slide before coming to rest. The coefficient of kinetic friction between the block and the horizontal surface is 0.38 and the distance r= 1.62m. Answer: s m

-3. ssm The hammer throw is a track-and-field event in which a 7.3 kg ball (the “hammer"), starting from rest, is whirled around in a circle sev- eral times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 29 m/s. For comparison, a .22 caliber bullet has a mass of 2.6 g and, start- ing from rest, exits the barrel of a gun at a speed of 410 m/s. Determine the work done to launch the motion of (a) the hammer and (b) the bullet.

A block of mass M with a semicircular track of radius R, rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest at the top point A (see fig.). The cylinder slips on the semicircular frictionless track. (a) How far has the block moved when the cylinder reaches the bottom (point B) of the track ? (b) How fast is the block moving when the cylinder reaches the bottom of the track? 105 100 gubwe A А m ck?) I noites R ITIS IS M B A min yd snob

A 250g meter stick extends over the edge of the lab bench as shown below. Find the maximum position from the edge of the bench at which a 250g coin can be placed which maintains the system’s state of equilibrium.

A skateboarder with his board can be modeled as a particle of mass 70.0 kg, located at his center of mass. As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point 4). On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius 5.70 m. (a) Find his speed at the bottom of the half-pipe (point B) m/s (b) Immediately after passing point®, he stands up and raises his arms, lifting his center of mass and essentially "pumping" energy into the system. Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.34 m, reaching point D. As he passes through point, the speed of the skateboarder is 4.60 m/s. How much chemical potential energy in the body of the skateboarder was converted to mechanical energy when he stood up at point Ⓡ? (c) How high above point does he rise? m

The stem of a mushroom is right circular cylinder of diameter 1 and length 2 and its cap is a hemisphere of a radius “a”. If the mushroom is a homogeneous solid with axial symmetry and if its center of mass lies in the plane where the stem joins the cap, find “a”. （let the center of mass be at the origin）

Countries with excellent wind energy sources decide on national projects for the development of wind energy. Ten percent of the land area will be devoted to 1.5 kW wind energy per person, roughly the amount of electricity used by one person in an industrialized country.  2 MW wind turbine with a rotor of 80 m diameter is placed in the average layout space of the figure. Depending on the wind conditions, the average output is 650 kW per turbine. Calculate the maximum density of a single sphere consistent with this business plan. Align geographic information with Germany, Spain, India and Denmark (they all have active wind power programs), and discuss the possibilities for achieving this goal in each of these countries.