Three solid, uniform boxes are aligned as in the figure below. Find the x- and y-coordinates (in m) of the center of mass of the three boxes, measured from the bottom left corner of box A. (Consider the three-box system.) HINT Xcm = Y cm Origin 0.300 m m m A 0.700 kg 0.350 m B 1.00 kg 0.150 m с 0.450 kg 0.418 m

The figure shows a three-particle system, with masses m1 = 4.8 kg, m2 = 4.0 kg, and m3 = 6.9 kg. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? y (m) m1 x (m) (a) Number Units (b) Number i Units

The figure shows a three-particle system, with masses m₁ = 4.8 kg, m₂ = 5.0 kg, and m3 = 8.3 kg. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? (a) Number i 1.3 (b) Number i 1.5 y (m) Units Units 1 m m INS 2 №² 3 x (m)

Three beads are placed along a thin rod. The first bead, of mass m1 = 29 g, is placed a distance d1 = 1.5 cm from the left end of the rod. The second bead, of mass m2 = 12 g, is placed a distance d2 = 1.5 cm to the right of the first bead. The third bead, of mass m3 = 46 g, is placed a distance d3 = 4.9 cm to the right of the second bead. Assume an x-axis that points to the right. Find the center of mass, in centimeters, relative to the left end of the rod.

Modeled after the triatomic molecule problem that is let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 7.281 kg, with x coordinate at 6.769 m and y coordinate at 9.989 m. The second atom has a mass of 61.310 kg, with x coordinate at 39.549 m and y coordinate at 25.180 m. The third atom has a mass of 49.316 kg, with x coordinate at 35.553 m and y coordinate at 31.216 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?

A ball weighing 800 grams and having a radius of 2cm moves in the direction of the positive x-axis at a speed of 5m/s. It collides with another stationary ball weighing 500 grams and also having a radius of 2cm. The collision occurs off-center, with the vertical components of the centers of the balls differing by 1cm. Following the collision, the lighter ball attains a speed of 3m/s. Determine the velocity of the heavier ball after the collision and calculate the amount of energy lost during the collision.

1. An inventor patents a "golf machine". It consists of a "golf club" which is really a pendulum of length L = 2 (m), with a massles string and a mass M = 30 (kg) on the end. By pulling back on the pendulum until the string makes an angle 0= 10° from the vertical, and then releasing it from rest, the golf club strikes the "golf ball" exactly horizontally. The golf ball is a mass m = that rests on a platform which is h = 20 (cm) above the horizontal ground. Assume that all collisions are elastic and all masses are point masses. Finally you should ignore air resistance but gravity acts down as usual. M) 0.1 (kg) h А. What is the speed of M just before it strikes m? | After m is struck by M, how long is m in the air before it hits the В. ground?

A merry-go-round at an amusement park consists of an outer ring of horses and an inner ring of elephants. The ring of eight horses has a radius of rh = 8.9 m. Each of the eight horses has a mass mh = 110 kg. The ring of four elephants has a radius of re = 6.5 m and each of the four elephants has a mass me = 195 kg. The platform of the merry-go-round itself has a mass of mp = 1500 kg and a radius of rp = 10.5 m. At it’s operating speed, the merry-go-round makes one revolution every t = 11 s.Enter an expression for the total moment of inertia of the carousel about its axis, in terms of the defined quantities. I =Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared. I =Enter an expression for the angular speed of the carousel, in terms of the defined quantities. ω =  Calculate the carousel’s angular speed, in radians per second.  ω =

Three beads are placed along a thin rod. The first bead, of mass m1 = 25 g, is placed a distance d1 = 0.75 cm from the left end of the rod. The second bead, of mass m2 = 11 g, is placed a distance d2 = 1.8 cm to the right of the first bead. The third bead, of mass m3 = 48 g, is placed a distance d3 = 3.9 cm to the right of the second bead. Assume an x-axis that points to the right. -Find the center of mass, in centimeters, relative to the left end of the rod.  (Xcm = ?)

Objects with a uniform mass distribution and a symmetric shape have a center of mass at the center of the object. For non-uniform objects, the center of mass needs to be determined experimentally. To measure the center of mass of such an object, a pivot is placed in the middle of a board and the top of the non-uniform object is placed to the right of the pivot. When a uniform 10.0 kg mass has its center placed 60.0 cm to the left of the pivot the system balances perfectly (as shown below). The mass of the non-uniform object is measured with an electronic scale in the lab and found to beM = 39.8 kg . Top of non-uniform object 10.0 kg M 60.0 cm Part A Where is the center of mass of the non-uniform object? (report the location from the top of the object, and in cm) ΑΣΦ ? dCM = ст