a force of 150N does 3.40kj of work over a displacement of 25.0m. what is the angle between the force vector and the displacement vector?
To find the angle between the force vector and the displacement vector, we can use the formula for work done:
Work = Force * Displacement * cos(θ)
Where:
- Work is given as 3.40 kJ (kilojoules), which is equivalent to 3400 J (joules).
- Force is given as 150 N (newtons).
- Displacement is given as 25.0 m (meters).
- θ is the angle between the force vector and the displacement vector.
Rearranging the formula, we can solve for cos(θ):
cos(θ) = Work / (Force * Displacement)
cos(θ) = 3400 J / (150 N * 25.0 m)
cos(θ) = 9.0667
To find the angle θ, we can take the inverse cosine (cos⁻¹) of 9.0667:
θ = cos⁻¹(9.0667)
θ ≈ 1.503 degrees (rounded to three decimal places)
Therefore, the angle between the force vector and the displacement vector is approximately 1.503 degrees.