Work energy exercise

# Work energy exercise - W T = T Â d Note The acceleration is...

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m 2 g m 1 Work Cart Exercise Not a Full Laboratory Use the work energy theorem to determine the final velocity of the cart after it travels some distance x in terms of m 1 and m 2 and the distance d traveled and compare to the final velocity derived from kinematics and stop watch. Equipment (5 – 8 sets) 2 and 1 meter stick; cart; track; string; weight sets so cart moves slowly; stop watch; pulley

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(1) ΣF x = T = m 1 a Consider pulley to be frictionless and string of negligible mass (2) ΣF y = T – m 2 g = - m 2 a Lab weight Subtracting (2) from (1) and algebra yields the acceleration : a = g [m 2 /(m 1 + m 2 )] (1) T = m 1 a ( 2) T – m 2 g = - m 2 a Equations of motion m 2 g m 1 Work Cart Lab
Tension in string is : a = g [m 2 /(m 1 + m 2 )] (1) ΣF x = T = m 1 a 2 1 2 1 m m m m g T + = Substituting a into this last equation yields: We see from the above equation that the tension is a constant force acting on car. Tension is the only force causing the car to move. Hence the work done on the car is:

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Unformatted text preview: W T = T Â· d Note: The acceleration is constant and so we use kinematics. This relationship is equivalent to: 2 2 1 2 1 2 1 f T mv d m m m m g W WorkEnergy = + = = 2 / 1 2 1 2 2 + = m m d gm v f d m m m m g W 2 1 2 1 + = But from the work energy theorem, work is equal to the change of kinetic energy of the car. Hence, if car starts from rest then: 1) Show that at a given distance d, with masses m 1 and m 2 , the final velocity v y matches that determined by kinematics: v f = at = [gm 2 /(m 1 + m 2 )]t + = + = 2 1 2 2 / 1 2 1 2 2 m m t gm m m d gm v f m 2 g m 1 x y Graph v f vs. d 1/2 d 1/2 v f 2 / 1 2 1 2 2 + = m m gm Slope Show: a = g [m 2 /(m 1 + m 2 )] Hence show: 2) Show for the v vs. d 1/2 graph the slope is given by: [ 2gm 2 d/(m 1 + m 2 )] 1/2...
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## This note was uploaded on 10/05/2011 for the course PHYS 4A taught by Professor Ernest during the Summer '10 term at Irvine Valley College.

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Work energy exercise - W T = T Â d Note The acceleration is...

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