A 50-kg sack is lifted 2 meters from the ground and a 25-kg sack is lifted 4 meters simultaneously by two different people who has all the variables the same. The power expended in raising the 50-kg sack is Group of answer choicesthe same.half as much as the 25-kg sack.twice as much as the 25-kg sack.triple as much as the 25-kg sack.
Question
A 50-kg sack is lifted 2 meters from the ground and a 25-kg sack is lifted 4 meters simultaneously by two different people who has all the variables the same. The power expended in raising the 50-kg sack is Group of answer choicesthe same.half as much as the 25-kg sack.twice as much as the 25-kg sack.triple as much as the 25-kg sack.
Solution
The power expended in lifting an object is given by the formula:
Power = Work / Time
And the work done in lifting an object is given by the formula:
Work = Force x Distance
In this case, the force is the weight of the sack, which is mass x gravity. Assuming the gravity is 9.8 m/s^2, the force required to lift the 50-kg sack is 50kg x 9.8m/s^2 = 490N, and the force required to lift the 25-kg sack is 25kg x 9.8m/s^2 = 245N.
The work done in lifting the 50-kg sack is 490N x 2m = 980J, and the work done in lifting the 25-kg sack is 245N x 4m = 980J.
Since the work done is the same and the time taken is the same (as given in the question), the power expended in lifting both sacks is the same.
So, the answer is "the same".
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