a) A 128 g textbook slides up a 20.5° incline that is 4.50 m long. Using conserv

Question

a) A 128 g textbook slides up a 20.5° incline that is 4.50 m long. Using conservation of energy and assuming the incline is frictionless, what minimum initial speed is needed to accomplish this?

b)A 27100 kg train is reaching the end of the line. In order to slow down, the front of the train snags a cable that is attached to a spring. If the spring has a spring constant of 75100 N/m and the train's initial speed is 65.0 m/s, how much will the spring stretch to stop the train?

c)A billiard table in a bar is set up so that the numbered balls are heavier than the cue ball. A 150 g cue ball is shot at a speed of 5.85 m/s at a 300 g numbered ball at rest, resulting in a perfect elastic collision. What is the final velocity of the cue ball after the collision?

Explanation / Answer

(A) PEi + KEi = PEf + KEf

0 + m v^2 / 2 = m g h + 0

v = sqrt(2 x 9.81 x 4.50sin20.5)

{ h = L sin20.5}

v = 5.56 m/s

(B) energy conservation,

k x^2 / 2 = m v^2 / 2

75100 x^2 = (27100) (65^2)

x = 39 m

(c) for elastic collision,

5.85 = V + v

V = 5.85 - v

momentum conservation,

150 x 5.85 + 0 = - 150 v + 300 V

150 x 5.8 = - 150 x 5.850 + 150 v + 300 v

v = 3.9 m/s

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