A 3.00kg object undergoes an acceleration given by acceleration is equal to (2.00i hat + 5.00j hat). Find (a) the resultant force acting on the object and (b) the magnitude of the resultant force.
To find the resultant force acting on the object given its acceleration, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
(a) To find the resultant force, we multiply the object's mass by its acceleration. Given the acceleration vector (2.00i hat + 5.00j hat) and the mass of the object as 3.00kg, we can calculate the resultant force vector:
Force = mass x acceleration
Force = 3.00kg x (2.00i hat + 5.00j hat)
Multiplying each component separately, we get:
Force = (6.00kg * i hat) + (15.00kg * j hat)
So, the resultant force acting on the object is (6.00i hat + 15.00j hat).
(b) To find the magnitude of the resultant force, we can use the Pythagorean theorem. The magnitude (or the length) of a vector is given by the square root of the sum of the squares of its components.
Magnitude of force = √[(6.00^2) + (15.00^2)]
Simplifying the calculation, we have:
Magnitude of force = √[36.00 + 225.00]
Magnitude of force = √261.00
Magnitude of force ≈ 16.13 N
Therefore, the magnitude of the resultant force acting on the object is approximately 16.13 Newtons.