Three beads are placed on the vertices of an equilateral triangle of side d = 3.9 cm. The first bead of mass m1 = 145 g is placed on the top vertex. The second bead of mass m2= 55 g is placed on the left vertex. The third bead of mass m3 = 75 g is placed on the right vertex.   Part (a)  Write a symbolic equation for the horizontal component of the center of mass relative to the left vertex of the triangle. Part (b)  Find the horizontal component of the center of mass relative to the left vertex, in centimeters. Part (c)  Write a symbolic equation for the vertical component of the center of mass relative to the base of the triangle. Part (d)  Find the vertical component of the center of mass relative to the base of the triangle, in centimeters.

Problem #3: A firework with total mass 5.0 kg is lit and eventually explodes into three main pieces. Two of the pieces were caught on film and later had their masses measured. The first piece with m1 = 2.0 kg travels to the left at an angle of 30° above the -x axis with a speed of 15.0 m/s. The second piece with m2 = 2.0 kg travels downward at an angle of 20° from the -y axis at a speed of 25 m/s. a. With what speed and in which direction did the third piece travel away from the explosion? b. If the firework was placed on a table of height 1.5m above the ground when it exploded, how far from the base of the table did the piece land on the ground?

Four beads, each of mass m = 1 kg, are attached at various locations to a ring, also of mass m = 1 kg, and radius M R = 1 m (see figure). Find the coordinates of the center of mass of the system consisting of the ring and the beads. m, Angle A, located between the first bead and the horizontal, m. is equal to 43°. Angle B, located between the horizontal and the second bead, is equal to 50°. Angle C, located D A between the third bead and the horizontal, is equal to 68°. Angle D, located between the horizontal and the fourth bead, is equal to 31°. Xcm m m, m, Уст — m ||

A tabletop gamer has designed a game that requires three dice to be thrown onto a tray with a measurement grid. To add an extra degree of randomness, the coordinates of the center of mass of the three dice are used as well. The masses of the three dice are 11.10 g, 13.70 g, and 17.30 g, and their respective coordinates after one particular throw are (0.2810 m,−0.2330 m), (−0.1910 m,0.2890 m), and (−0.4790 m,−0.2210 m). What are the resulting coordinates of the center of mass of the dice, ?cm and ?cm?   ?cm = ? m  ?cm = ? m

An overnight rainstorm has caused a major roadblock. Three massive rocks of mass m₁ = 514 kg, m₂ = 7.00 x 10² kg, and m3 = 366 kg have blocked a busy road. The rocks are lined up from left to right in the order m₁, m2, and m3. The city calls a local contractor to use a bulldozer to clear the road. The bulldozer applies a constant force to m₁ in order to slide the rocks off the road. Assuming the road is a flat, frictionless surface and the rocks are all in contact, what force, FA, must be applied to m₁ to slowly accelerate the group of rocks from the road at 0.400 m/s²? Use the value for FA to find the force, F12, exerted by m₁ on m₂. FA = F12 = N N

A billiard ball moving at 5.45 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.90 m/s, at an angle of 26° with respect to the original line of motion. (a) Find the velocity (magnitude and direction) of the second ball after collision. (Enter the direction with respect to the original line of motion. Include the sign of your answer. Consider the sign of the first ball's angle.) m/s (b) Was the collision inelastic or elastic? O inelastic elastic

Two cars are driving in the same direction separated by 220 m. The car in front has a mass of 1500 kg and is moving at 22 m/s. The car in the back has a mass of 1200 kg and is moving in the same direction at 15 m/s. Part A: How far ahead of the trailing car is the center of mass? Part B: What is the velocity of the center of mass? (if the center of mass is moving opposite the direction the cars are moving, indicate with a negative sign) Part C: What is the total momentum of the two-car system? (if the system momentum is opposite the direction that the cars are moving, indicate with a negative sign) 

Masses of m =2 (kg) and m2 =4 (kg), the directions of which are shown in the figure, collide totally elastically with the velocity vi=v2-8 (m/s) at the origin. Find the position vector of the center of mass in (m) 2 seconds after the collision. y 37° m2

The vector position of a 3.40 g particle moving in the xy plane varies in time according to r, = (3î + 3ĵ)t + 2ĵt² where t is in seconds and r is in centimeters. At the same time, the vector position of a 5.90 g particle varies as r, = 3î - 2ît2 - 6ĵt. (a) Determine the vector position (in cm) of the center of mass of the system at t = 2.70 s. cm cm (b) Determine the linear momentum (in g · cm/s) of the system at t = 2.70 s. p = g· cm/s (c) Determine the velocity (in cm/s) of the center of mass at t = 2.70 s. V. cm cm/s (d) Determine the acceleration (in cm/s2) of the center of mass at t = 2.70 s. a cm cm/s2 (е) Determine the net force (in µN) exerted on the two-particle system at t = 2.70 s. net UN

A system of four particles moves along one dimension. The center of mass of the system is at rest, and the particles do not interact with any objects outside of the system. Find the velocity v4 of particle 4 at t₁ = 2.83 s given the details for the motion of particles 1, 2, and 3. U4 = particle 1: m₁ = 1.69 kg, particle 2: particle 3: particle 4: m₂ = 2.69 kg, m3 = 4.85 kg, m4 = 5.03 kg U₁ (t) = (7.41 m/s) + (0.365 m/s²) x t U₂ (t) = (8.27 m/s) + (0.567 m/s²) x t v3 (t) = (6.33 m/s) + (0.447 m/s²) × t m/s