A train car of mass mị rolls down a hill, starting from rest from a height h; above the valley floor. At the bottom of the valley, car m1 bumps into a second car of mass m2 that has been standing there. The two cars lock to each other and jointly start climbing up the hill on the other side of valley, until they momentarily come to rest at a height hf above the valley floor. Assuming you can neglect friction, what is the ratio between m2 and m1 if hf = h;/9? Check: For hf = hi/16 you should find m2 = 3m1. Hint: Analyze this problem in three stages. The middle (second) stage will be the collision of the two train cars; from right before to right after they collide.

A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 99.5 kg. The mass of the rock is 0.277 kg. Initially the wagon is rolling forward at a speed of 0.488 m/s. Then the person throws the rock with a speed of 16.6 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown (a) directly forward in one case and (b) directly backward in another. (a) vi (b) v-

Two bowling balls are at rest on top of a uniform wooden plank with their centers of mass located as in the figure below. The plank has a mass of 4.90 kg and is 1.00 m long. Find the horizontal distance (in m) from the left end of the plank to the center of mass of the plank-bowling balls system. HINT K 0.240 m A m 0.810 m 4.05 kg 1.00 m B ► I I 1 1 5.60 kg 4.90 kg

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 M1 remains parallel to the top of the table. The blocks have masses M1 = 1.2 kg and M2 = 2.7 kg. Block 1 is a distance r = 0.55 m from the center of the frictionless surface. Block 2 hangs vertically underneath. 1) If we Assume that block two, M2, does not move relative to the table and that block one, M1, is rotating around the table. What is the speed of block one, M1, in meters per second?

A uniform rod of length 0.8 m and mass 2.2 kg, has two point masses at each end. The point mass on the left end has a mass 1.5 kg, and the one on the right end has a mass 2.5 kg. Calculate the location of the center of mass of this system in terms of the distance from the left end.

A rod of length 30.50 cm has linear density (mass per length) given by A = 50.0 + 25.0x where x is the distance from one end, and A is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass? m

in the figure, four point mases are placed as shown. assume that all the numbers in the figure are accurate to two significant figures, What are the x and y cirrdunates if the center of mass (or center of gravity) of this arrangement?

During the filming of a certain movie scene, the director wants a small car (whose mass is m1) traveling due east at speed v1 to collide with a small truck (whose mass is m2) traveling north. The director also wants the collision to be arranged so that just afterward, the interlocked vehicles travel straight toward the camera. If the line between the camera and collision makes an angle of theta with respect to north, at what speed v2 should the trucker drive?