1) While the irrate student (of mass 70kg) is throwing eggs on campus, campus se

Question

1) While the irrate student (of mass 70kg) is throwing eggs on campus, campus security creeps up behind them. A security officer with a mass of 94kg dives with an initial speed of 3.4m/s towards the student (who is initially at rest). How fast is the officer+student moving after the tackle? Assume the collision is completely inelastic.

2)A 6.2kg block of wood is initially at rest on a table. A 10g bullet, fired horizontally at a speed of 440m/s, goes completely through the block, emerging at a speed of 243m/s. What is the speed of the block immediately after the bullet exits?

3)A 11,386kg coal car (a type of train car) coasts under a coal storage bin at a speed of 1.9m/s. As it goes under the bin, 297kg of coal is dropped into the car. What is the final speed of the loaded car?

4)Ice skaters often end their performances with spin turns, where they spin very fast about their center of mass with their arms folded in and legs together. Upon ending, their arms extend outward, proclaiming their finish. Not quite as noticeably, one leg goes out as well. Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.4kg*m^2 and for arms and legs in is 0.80kg*m^2. If the skater starts out spinning at 273rpm, what is their final speed (in rpm) when their arms and one leg open outward?

Explanation / Answer

2.

Use Conservation of Momentum. The formula is m1v1 + m2v2 = m1vi + m2v2. m is the mass while v is the velocity. The left side are the initial values while the right side are the final values. Now just plug in the number, and before you do that just make sure all the masses have kilograms units and all the velocities have m/s units. This is what it will look like after you plug in the numbers:
(.01 kg)(440 m/s) + (6.2 kg)(0 m/s) = (.01 kg)(243 m/s) + (6.2 kg)(v)
4.4=2.43 + 6.2v
v=(4.4-2.43)/6.2
v= 0.318 m/s

1. The formula is m1v1 + m2v2 = ( m1+ m2) v
   70*0 + 94*3.4 = (70+94) v
   v = 94*3.4/164
   = 0.195 m/s

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