A particle is displaced from (3, 4, −5) to (4, 6, −2)under a con-stantforce ~F = (2ˆi+4ˆj +2ˆk) N . Find the work done by the constant force on the particle
Question
A particle is displaced from (3, 4, −5) to (4, 6, −2)under a con-stantforce ~F = (2ˆi+4ˆj +2ˆk) N . Find the work done by the constant force on the particle
Solution
The work done by a force on a particle is given by the dot product of the force vector and the displacement vector.
Step 1: Find the displacement vector. The displacement vector is the final position minus the initial position.
Δr = r_final - r_initial
= (4, 6, -2) - (3, 4, -5)
= (4-3, 6-4, -2-(-5))
= (1, 2, 3)
So, the displacement vector Δr = (1, 2, 3).
Step 2: Find the dot product of the force vector and the displacement vector. The dot product of two vectors A = (a1, a2, a3) and B = (b1, b2, b3) is given by:
A.B = a1*b1 + a2*b2 + a3*b3
So, the work done W = F.Δr = (2, 4, 2).(1, 2, 3) = 21 + 42 + 2*3 = 2 + 8 + 6 = 16 Joules
So, the work done by the constant force on the particle is 16 Joules.
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