11. Momentum & Impulse

A fake hockey puck of mass 4m has been rigged to explode. Initially the puck is at rest on a frictionless ice rink. Then it bursts into three pieces. One chunk, of mass m, slides across the ice at velocity vî . Another chunk, of mass 2m, slides across the ice at velocity 2v ĵ . Determine the velocity of the third chunk.

A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then released and the spring pushes them off in opposite directions. Find the speeds of the two blocks when they detach from the spring.

(III) A 195-kg projectile, fired with a speed of 116 m/s at a 60.0° angle, breaks into three pieces of equal mass at the highest point of its arc (where its velocity is horizontal). Two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion; one of these moves vertically downward and the other horizontally. Determine

(a) the velocity of the third fragment immediately after the explosion and

(b) the energy released in the explosion.

(II) An atomic nucleus initially moving at 320 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 280 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?

(II) An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°.

(a) At what angle does the target particle move after the collision?

(II) An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°.

(b) What are the final speeds of the two particles?

(II) An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90°.

(c) What fraction of the initial kinetic energy is transferred to the target particle?

(III) A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hooke’s law and has spring constant k = 850 N/m , is attached to the second block in such a way that it will be compressed when struck by the moving block, Fig. 9–43.

(c) Is the collision elastic? Ignore the mass of the spring.

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