Does 200 Foot-Pounds of Work Require More Work?

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Lifting a 50 lb weight over a distance of 4 feet results in 200 foot-pounds of work. However, walking horizontally while holding the weight does not require an additional 200 foot-pounds of work. This is because the force exerted by the hand is perpendicular to the direction of motion. According to the definition of work, which involves a dot product, the work done in this case is zero for perpendicular vectors. Therefore, no additional work is required while walking with the weight.
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You lift a 50 lb weight by a distance of 4 ft so you do 200 foot-pounds of work. You then hold the weight and walk a horizontal distance of 4 feet, does this require an additional 200 foot-pounds of work? Please excuse the units, this question came from a calculus book.
 
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The simple answer would be ; no. This is because the force your hand applies perpendicular to the direction of motion of the weight. The definition of work involves a dot product, which is zero for 2 perpendicular vectors.
 

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