A system consists of three masses mA= 0.4 kg, mB= 0.5 kg, and mC= 0.8 kg. The system is positioned in the xy plane with positions A (1,2) , B (4,4) , and C (2,5) in meters and initially at rest. Determine: a.  Center of mass of the system . b. If objects B and C act on external forces of 10i + 20j N and 16i N, respectively, evaluate the center of mass acceleration of the system after 2 s. c.  The center of mass of the system is 2 s after the force acts on B and C.

Two rail cars roll without friction on a track.  The rail cars have different masses.   The heavier car is at rest.  The lighter car is moving with speed v, hits the heavier car, and sticks to it.  The combined two-car system then moves with speed v/5.   What is the ratio of masses of the two cars?  Ratio = mass of heavier car / mass of lighter car.

Problem 7: Two blocks, which can be modeled as point masses, are connected by a massless string which passes through a hole in a frictionless table. A tube extends out of the hole in the table so that the portion of the string between the hole and M¡ remains parallel to the top of the table. The blocks have masses M1 = 1.5 kg and M, = 2.7 kg. Block 1 is a distance r = 0.35 m from the center of the frictionless surface. Block 2 hangs vertically underneath. M, V M,

James (mass 90.0 kg) and Ramon (mass 60.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. When James has moved 6.0 m toward the mug, how far and in what direction has Ramon moved?

A woman weighing 61.5 kg stands at one end of a 120-kg raft that is 6.00 m long. The other end of the raft is 0.500 m from a pier. So, before the woman moves, she is at a total distance of 6.50 m away from the pier. The woman walks toward the pier until she gets to the other end of the uniform raft and stops there. What is the distance between the uniform raft and the pier?

Two steel blocks glide without friction on a surface horizontal with the speeds shown in the figure. If it is observed that after impact the velocity of block B is 10.5 ft / s toward on the right, determine the coefficient of restitution between the two blocks.

Two rolling carts are moving toward each other at the same constant speed of 10m/s. Cart 1 travels to the right with a mass m1 = 0.2kg and while Cart 2 travels to the left with a mass m2 = 0.4kg. Draw a velocity vector v→ for each cart.

Sphere m1 with a mass of 1.0 kg collides with m2, which also has a mass of 1.0 kg, in an elastic collision.  If v2f= 15 m/s and θ2= 40°, determine v1i.  (Hint:  An elastic collision requires that the after-collision angle between the two velocities must be 90°.)

3. Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 1.50 x 105 kg and a velocity of (0.35 m/s)î , and the second having a mass of 1.10 x 105 kg and a velocity of –(0.10 m/s)î . What is their final velocity? V = (0.30 m/s)î V21 = -(0.12 m/s)î

A rod of length 23.00 cm has linear density (mass per length) given by 1 = 50.0 + 17.5x where x is the distance from one end, and 2 is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass? m