A solid sphere of mass 0.750 kg and radius 5.00 cm is spun up to an angular velocity 10.0 rad/s, spinning clockwise. The sphere is held just barely above a flat platform of mass 5.00 kg, then released onto the platform. The sphere begins to skid and moves along the platform until it rolls without slipping. The coefficient of kinetic friction between the sphere and the platform is 0.70. The coefficient of friction between the platform and the ground is 0.05, and the platform begins to slide across the ground. Find an expression for the horizontal position of the center of mass of the sphere as a function of time (hint—it’s piecewise!), and note the times at which the sphere’s motion changes.

f=ma newton's second law 7x8=56n

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .