Final answer:
To calculate the work done upon the backpack as Sam pulls it, the horizontal component of the force should be used. The work done is the product of the force component in the direction of the displacement and the distance the backpack was pulled. The calculated work done is 11292.4 joules.
Step-by-step explanation:
To calculate the work done upon the backpack, we must consider the component of the force that acts in the direction of the displacement which, in this case, is horizontal. As Sam pulls his backpack to the right with a force that has an upward and rightward component, the horizontal component of the force is the only part that does work on the backpack.
The work done by a force is given by the formula W = F × d × cos(θ), where W is work, F is the magnitude of the force, d is the distance over which the force is applied, and θ is the angle between the force and the displacement.
Using the given values:
- Force, F = 43.2 N
- Distance, d = 455.7 m
- Angle, θ = 55°
Therefore, the horizontal component of the force is Fx = F × cos(θ) = 43.2 N × cos(55°). Once we find Fx, we multiply it by the distance to find the work done, W.
We calculate as follows:
Fx = 43.2 N × cos(55°) = 43.2 N × 0.5736 ≈ 24.7805 N
W = Fx × d = 24.7805 N × 455.7 m ≈ 11292.38285 J ≈ 11292.4 J (rounded to one decimal place).
So, the work done upon the backpack by Sam is approximately 11292.4 joules.