Question

Determine the amount of work done by a force F = -4.0i – 6.0j N acting on a particle that movers through a displacement r = -3.0i + 2.0jm.

Answer 1

The work done by a force of F = -4.0i - 6.0j N on a particle moving through a displacement of Δr = -3.0i + 2.0j m is 0 joules, as calculated by the dot product of force and displacement.

Step-by-step explanation:

The student asked to determine the amount of work done by a force F = -4.0i – 6.0j N on a particle that moves through a displacement Δr = -3.0i + 2.0j m. To calculate the work done, we apply the concept of a dot product to multiply the force vector by the displacement vector. The work done W can be calculated using the formula W = F · Δr, which results in:

W = (-4.0i - 6.0j) · (-3.0i + 2.0j)
= (-4.0)(-3.0) + (-6.0)(2.0)
= 12.0 - 12.0
= 0 J

Therefore, the work done by the force on the particle is 0 joules.