Final answer:
The energy to slide a crate on the floor is calculated using the force applied and the distance moved, resulting in 2000 J. Lifting the crate into a truck involves calculating the work done against gravity, totaling 1960 J. The total energy expenditure is 3960 J, with the sliding and lifting contributing roughly equal fractions to this total.
Step-by-step explanation:
When calculating the energy required to move a crate on the floor and then lift it into a truck, we consider both kinetic and potential energy aspects of work. To slide a 50 kg crate for 10 m along a concrete floor with a force of 200 N, the work done is the product of the force and displacement, so:
Work (sliding) = Force × Distance = 200 N × 10 m = 2000 J (joules)
The same concept is applied when we lift the crate vertically 2 m into the truck. Here we use the gravitational force multiplied by the height:
Work (lifting) = Weight × Height = (50 kg × 9.8 m/s2) × 2 m = 980 N × 2 m = 1960 J
The total energy used is the sum of both actions:
Total energy expenditure = Work (sliding) + Work (lifting) = 2000 J + 1960 J = 3960 J
Each portion of the work done can be expressed as a fraction of the total:
Fraction for sliding = Work (sliding) / Total energy = 2000 J / 3960 J = 0.505
Fraction for lifting = Work (lifting) / Total energy = 1960 J / 3960 J = 0.495