Final answer:
To achieve an acceleration of 15 m/s² with perpendicular forces of 3.0 N and 4.0 N, the mass of the block should be 0.33 kg, calculated using the resultant force and Newton's second law.
Step-by-step explanation:
To find the mass of the block that allows for an acceleration of 15 m/s² given forces of 3.0 N and 4.0 N acting at right angles, we must first determine the resultant force acting on the block using Pythagoras' theorem. The force can be found by the equation F = √(F_x^2 + F_y^2), where F_x and F_y are the components of the forces acting along the x-axis and y-axis, respectively.
In this case, F = √(3.0^2 + 4.0^2) = √(9 + 16) = √25 = 5.0 N. Using Newton's second law, F = ma, where F is the total force, m is the mass, and a is the acceleration, we can rearrange the formula to solve for mass: m = F / a.
Given F = 5.0 N and a = 15 m/s², we get m = 5.0 N / 15 m/s² = 0.33 kg. Therefore, the mass of the block should be 0.33 kg to achieve 15 m/s² acceleration when the forces of 3.0 N and 4.0 N are acting at right angles on it.