Grains of fine california beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.6 × 103 kg/m3. what mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 1.1 m on an edge?

The average radius(r) of each grain is r = 50 nanometers = 50*10^-6 meters

Since it is spherical, so

 Volume=(4/3)*pi*r^3

V= (4/3)*pi*(50*10^-6)^3

V=5.23599*10^-13 m^3

We are given the Density(ρ) =2600kg/m^3

We know that:

Density(p) = mass(m)/volume(V)

m = ρV

So the mass of a single grain is:

m = 5.23599*10^-13 * 2600 = 1.361357*10^-9 kg

The surface area of a grain is:

a = 4*pi*r^2

a = 4*pi*(50*10^-6)^2

a = 3.14*10^-8 m^2

Since we know the surface area and mass of a grain, the conversion factor is:

1.361357*10^-9 kg / 3.14*10^-8 m^2

Find the Surface area of the cube:

cube = 6a^2

cube = 6*1.1^2  = 7.26m^2

multiply this by the converions ratio to get:

total mass of sand grains = (7.26 m^2 * 1.361357*10^-9 kg) / (3.14*10^-8 m^2)

total mass of sand grains = 0.3148 kg = 314.80 g

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.