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- To get up on the roof, a person (mass 70.0 kg) places 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to frictionless. The center of ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.Look for the center of mass of a uniform solid right circular cone using M as mass, R as radius and H as Height.Two particles of mass 5 kg and10 kg respectively are attached to the two ends of a rigid rod of length Im with negligible mass. The center of mass of the system from the 5kg particle is nearly at a distance of:
- Check Your Understanding Suppose you have a macroscopic salt crystal (that is, a crystal that is large enough to be visible with your unaided eye). It is made up of a huge number of unit cells. Is the center of mass of this crystal necessarily at the geometric center of the crystal?The tennis racket of the previous question is modified by adding a point mass m, = m/2 to the part of the rim furthest from the shaft. Find the new posi- tion of the center of mass.A system is made up of point masses P1 at position (1, -6, 5) m, P2 at position (-5, 4, 2) mand P3 at position (7, 5, 3) m. Calculate the center of mass of the system if each of the pointmasses have the same mass
- Four objects are situated along the y axis as follows: a 1.98-kg object is at +2.94 m, a 3.08-kg object is at +2.49 m, a 2.43-kg object is at the origin, and a 3.99-kg obgect is at -0.496m where is the center of mas of these objects? Need Help? Read It Watch t A rod of length 34.50 cm has linear density (mass per length) given by 1= 50.0 + 22.Dx where x is the distance from one end, and i is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass?A teenager is standing at the rim of a large horizontal uniformwooden disk that can rotate freely about a vertical axis at itscenter. The mass of the disk (in kg) is M and its radius (in m) is R. Themass of the teenager (in kg) is m. The disk and teenager are initially atrest. The teenager then throws a large rock that has a mass (in kg) ofmrock. As it leaves the thrower’s hands, the rock is traveling horizontallywith speed v (in m/s) relative to the earth in a direction tangent tothe rim of the disk. The teenager remains at rest relative to the disk andso rotates with it after throwing the rock. In terms of M, R, m, mrock,and v, what is the angular speed of the disk? Treat the teenager as apoint massThe 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）
- 4.30P ) a) A piece of gum of mass ml is thrown at a bar of mass m2 and length of d, pivoted about its center and initially at rest as shown in figure. The gum sticks to the end of bar and the final angular speed of the bar is measured to be w. What is the vi initial speed of the gum? b) Calculate the moment of inertias of systems in figures. Each of mass is m and distance between them is 2d. Rotation axes are shown in figure.9-2 find the center of mass of a uniformly solid cone of base diameter 2a and height h.A bowling ball rolls up a ramp 0.5 m high without slipping to storage. It has an initial velocity of its center of mass of 3.0 m/s. (a) What is its velocity at the top of the ramp? (b) If the ramp is 1 m high does it make it to the top?