Knightro is learning a new trick called the Spring Launch, where he stands on a

Question

Knightro  is  learning  a  new  trick  called  the  Spring  Launch,  where  he  stands  on  a  skateboard  and  is  launched  up  a  ramp  by  a  giant  spring.  In  the  first  test  run,  the  spring  is  compressed  a  distance  ?x,  Knightro  moves  across  the  horizontal  portion  of  the  ramp  with  speed  v  and  reaches  a  maximum  height  H  at  the  end  of  the  ramp.  For  the  next  trial,  Knightro  plans  to  compress  the  spring  a  distance  2?x.  

1. For  the  second  trial,  will  the  Knightros  speed  on  the  horizontal  portion  of  the  ramp  be:

(circle  one)      greater  than  2v    less  than  2v    equal  to  2v

Explain  your  reasoning.  

  2. Will  the  height  reached  by  Knightro  for  the  second  trial  be:

(circle  one)      greater  than  2H    less  than  2H    equal  to  2H  

Explain  your  reasoning

Explanation / Answer

1)

PE = Ke
First trial

1/2 k x^2 = 1/2 mv^2

second trial

1/2 k (2x)^2 = 1/2 m v2^2

4 1/2 k x^2 = 1/2 m v2^2

4 1/2 m v^2 = 1/2 m v2^2

4 v^2 = v2^2

v2 = 2 v

so equal to 2v

2)

now first trial

1/2 k x^2 = m g H

second trial

1/2 k (2x)^2 = m g H2

4 1/2 k x^2 = m g H2

plug in first trial

4 m g H = m g H2

H2 = 4 H

so greater than 2H

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