Francois places a ring made of an unknown metal into a graduated cylinder. the water level in the graduated cylinder rises from 10.0 cm to 11.5 cm. he has already found that the mass of the ring is 16.5 g. what is the density of the ring? o a. 1.7 g/cm o b. 0.09 g/cm3 o c. 11.0 g/cm o d. 1.4 g/cm3

Explanation:

Density is a physical characteristic property of matter that establishes a relationship between the mass   of a body or substance and the volume  it occupies. Mathematically is expressed as:

   (1)

We already know the mass of the ring, which is  and the volume we can find it by the Archimedes' Principle, which states the following:

A body totally or partially immersed in a fluid at rest, experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.

In this case, we are told Francois places the ring into a graduated cylinder (in ), where the water level initially was in and then rose to .

So, if we calculate the difference we will find the volume displaced by the ring:

  (2)

Now we can find the density of the ring, with (1):

   (3)

Finally:

By Newton's second law, the car has acceleration a such that

2000 N = (1500 kg) a

a = (2000 N) / (1500 kg)

a = 4/3 m/s² ≈ 1.33 m/s²

After 15 s, the car will attain a speed of

(4/3 m/s²) (15 s) = 20 m/s

It will have traveled a distance ∆x such that

(20 m/s)² - 0² = 2 (4/3 m/s²) ∆x

∆x = (20 m/s)² / (8/3 m/s²)

∆x = 150 m