Final answer:
The work done by a constant force F₁ = (3 N)I + (4 N)J as the particle moves from coordinate (0, 0) to (5, 6) is calculated using the dot product of force and displacement vectors resulting in 39 Joules.
Step-by-step explanation:
The question asks about the work done by a force ℘1 = (3 N)Ī + (4 N)Ĵĩ on a particle as it moves from one point to another in a Cartesian plane. To calculate the work done, we use the formula W = ℘ · s, where W is work, ℘ is force, and s is displacement. Both the force and the displacement are given in vector components, ℘ = ℘xi + ℘yj and s = sxi + syj respectively. The work done is the dot product of these two vectors, which for a constant force is W = ℘xsx + ℘ysy.
For example, if a particle moves from (0 m, 0 m) to (5 m, 6 m) under the influence of a constant force ℘1 = (3 N)Ī + (4 N)Ĵĩ, the work done by ℘1 can be calculated as follows:
- Calculate the displacement vector: s = (5 m - 0 m)Ī + (6 m - 0 m)Ĵĩ = 5Ī + 6Ĵĩ
- Calculate the work done: W = (3 N × 5 m) + (4 N × 6 m) = 15 J + 24 J = 39 J
The answer is that the work done by the force is 39 Joules.