Aplastic sphere floats in water with 50.0% of its volume submerged. this same sphere floats in glycerin with 40.0% of its volume submerged. determine the densities of: a. the glycerin b. the sphere.

Explanation:

weight of water displaced=weight of sphere,

Since,  plastic sphere floats in water with 50.0% of its volume submerged

so, water=2 sphere,

so sphere's density = 1/2 of water's  density

Now,  weight of glycerin displaced=weight of sphere,

Also given This same sphere floats in glycerin with 40.0% of its volume submerged.

so glycerin =2.5 sphere,

so sphere's density = .4 of glycerin's = 1/2 of water's.

So glycerin = 1.25 water

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft