A 4.6 "kilo" bag of sugar is on a counter. How much work is required to put the bag on a shelf a distance of 0.45 m above the counter?
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To calculate the work required to lift the bag of sugar to the shelf, we need to use the formula:
Work = Force x Distance x cosθ
Here, we'll assume that the force required to lift the bag straight up is equal to the weight of the bag. The weight of an object can be calculated using the formula:
Force = mass x gravitational acceleration
Let's break down the steps to find the work:
1. Determine the weight of the bag:
From the problem, we are given that the mass of the bag is 4.6 kilograms. The standard acceleration due to gravity is approximately 9.8 m/s².
Weight = mass x gravitational acceleration
Weight = 4.6 kg x 9.8 m/s²
2. Calculate the work needed to lift the bag:
Now, we need to calculate the work required to raise the bag a distance of 0.45 meters above the counter.
Work = Force x Distance x cosθ
Work = Weight x distance x cosθ
Work = (4.6 kg x 9.8 m/s²) x 0.45 m x cosθ
Note: The θ in the formula represents the angle between the force applied and the direction of motion. Since the bag is being raised straight up, θ = 0°, and the cosθ term becomes 1.
Work = (4.6 kg x 9.8 m/s²) x 0.45 m x 1
Now, let's calculate the work:
Work = 4.6 kg x 9.8 m/s² x 0.45 m
By plugging in the values:
Work = 20.574 J
Therefore, it would require approximately 20.574 Joules of work to put the 4.6-kilogram bag of sugar on the shelf 0.45 meters above the counter.