The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r h = 0.262 m and mass 5.46 kg , and two thin crossed rods of mass 8.66 kg each. A farmer would like to replace his wheels with uniform disks t d = 0.0525 m thick, made out of a material with a density of 5530 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?

0.136m

Explanation:

Given

rh = 0.262m

m1 = 5.46 kg

m2 = 8.66 kg

td = 0.0525m

density, ρ= 5530 kg/m³

Calculating the moment of inertia of the new disk;

M1 = m1r²

M1 = 5.46 * 0.262²

M1 = 0.375 kg·m²

Calculating the moment of inertia of the rod

M2 = m2r²

M2 = 8.66 * (2 * 0.262)²/12

M2 = 0.198 kg·m²

Moment of inertia of the old wheel;

M3 = M1 * M2

M3 = 0.375 + 2 * 0.198

M3 = 0.771 kg·m²

Calculating Moment of Inertia of the disk

M4 = mr²/2

To get the mass of the disk, W

We'll need to calculate the mass from its volume V and density ρ

m = V * ρ

Where V = Area * Thickness

m = Area * Thickness * ρ

m = πr² * 0.0525 * ρ

m = 0.525ρπr²

So, M4 = 0.525ρπr² * r²/2

M4 = 0.2625ρπr⁴/2

Solving for r

r⁴ = M4/0.2625ρπ

M4 must equal M3 = 0.771

So, r⁴ = 0.771/0.2625ρπ/2

r⁴ = 0.771/(0.2625 * 5530 * 3.14/2)

r⁴ = 0.000338298667044

r = (0.000338298667044)^¼

r = 0.135620415830572

r = 0.136m --- Approximately

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.

a sonic boom is a loud boom that breaks the sound barrier

explanation: