Final answer:
To determine the magnitude of acceleration of a speck of clay, one needs to use Newton's second law, consider the forces acting including gravity, and calculate the net forces in both the vertical and horizontal directions, combining them to find the overall magnitude and direction using the Pythagorean theorem.
Step-by-step explanation:
To find the magnitude of acceleration of a speck of clay or any object with a given mass subject to forces, we use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object times its acceleration (F=ma). Therefore, the acceleration (a) can be found by rearranging the formula: a = F/m.
In the provided problem, we are given that the force exerted by the flea (which stands in for our speck of clay) is 1.20 × 10-5 N, and the mass of the flea is 6.00 × 10-7 kg. Additionally, a breeze exerts a force of 0.500 × 10-6 N parallel to the ground.
We also need to consider the force due to gravity, which is the mass times the acceleration due to gravity (Fg = mg). For a mass of 6.00 × 10-7 kg, and using 9.8 m/s2 for the acceleration due to gravity, the gravitational force (Fg) can be calculated. We can then find the net forces in both the vertical and horizontal directions, and use these to calculate the overall magnitude of acceleration using the Pythagorean theorem, as the forces are perpendicular to each other.
In this scenario, we would consider each force component, calculate the separate accelerations, and then combine them to find the overall magnitude and direction of the acceleration.
It's important to remember that in such calculations, the direction of the force and the orientation of the axes being used play a critical role in determining the overall acceleration vector in terms of both magnitude and direction.