To find the acceleration of the object, we need to determine the net force acting on it. Since forces are vectors, we can break them down into their horizontal and vertical components and then find the resultant.
Given: Mass of the object (m) = 27 kg Force 1 (F₁) = 12 N (points due south) Force 2 (F₂) = 17 N (points due west)
Let's find the horizontal and vertical components of the forces:
Horizontal component of F₁ = F₁ * cos(90°) = 12 N * cos(90°) = 0 N Vertical component of F₁ = F₁ * sin(90°) = 12 N * sin(90°) = 12 N
Horizontal component of F₂ = F₂ * cos(180°) = 17 N * cos(180°) = -17 N Vertical component of F₂ = F₂ * sin(180°) = 17 N * sin(180°) = 0 N
The horizontal components of both forces cancel each other out, resulting in a net horizontal force of 0 N. The vertical components of both forces add up to a net vertical force of 12 N.
The net force acting on the object can be calculated using the Pythagorean theorem:
Net force (F_net) = √((net horizontal force)² + (net vertical force)²) = √((0 N)² + (12 N)²) = √(0 + 144 N²) = √144 N² = 12 N
Now, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
F_net = m * a
Rearranging the formula, we get:
a = F_net / m = 12 N / 27 kg ≈ 0.444 m/s² (rounded to three decimal places)
Therefore, the acceleration of the object is approximately 0.444 m/s².