Collisions
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Calculate the energy loss in an inelastic head-on collision between two spheres of masses m1 and m2 that move in the same direction with speeds v1 and v2.

A bullet of mass 15 g collides with a wooden block of mass 2.985 kg, suspended horizontally by two wires, and the bullet lodges in the block, and the whole system rises 5 cm relative to the initial position, assuming that the wires remain parallel. This system is known as a ballistic pendulum. Determine:
a) The speed of the bullet when it hits the block;
b) The speed acquired by the bullet-block system;
c) The energy lost in the collision.

A nail of mass 5 g is driven into a wall using a hammer of mass 495 g. The speed of the hammer just before striking the nail is 4 m/s, and the collision is perfectly inelastic. Determine:
a) The speed of the nail-hammer system immediately after the impact;
b) The energy dissipated in the collision;
c) Assuming that the nail penetrates the wall 0.5 cm at each strike, calculate the magnitude of the force, suppose constant, opposed by the wall to the penetration.

Two elastic balls, with masses m1 and m2 and speeds v1 and v2 respectively, collide head-on, their speeds are in the direction of the line joining their centers. Determine the speeds of the balls after the collision in the following cases:
a) The speed of the second ball before the impact is equal to zero;
b) The masses of the balls are equal.
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