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Zina [86]
3 years ago
10

A stone is dropped at t = 0. A second stone, with 6 times the mass of the first, is dropped from the same point at t = 160 ms. (

a) How far below the release point is the center of mass of the two stones at t = 290 ms? (Neither stone has yet reached the ground.) (b) How fast is the center of mass of the two-stone system moving at that time?
Physics
1 answer:
o-na [289]3 years ago
7 0

Answer with Explanation:

Let mass of one stone=m_1=m

Mass of second stone,m'=6 m

a.t_1=290 ms=290\times 10^{-3} s

1 ms=10^{-3} s

t=160 ms=160\times 10^{-3} s

t'=t-t_1=290\times 10^{-3}-160\times 10^{-3}=130\times 10^{-3} s

Initial velocity=u_1=u'=0

y_1=\frac{1}{2} gt^2_1=\frac{1}{2}(9.8)(290\times 10^{-3})^2=0.412 m

Where g=9.8 m/s^2

y'=\frac{1}{2}gt'^2=\frac{1}{2}(9.8)(130\times 10^{-3})^2=0.0828 m

Center of mass=\frac{m_1y_1+m'y'}{m_1+m'}

Center of mass=\frac{m(0.412)+6m(0.0828)}{m+6m}=\frac{m(0.412+6(0.0828)}{7m}=0.13 m

b.v=u+gt

Using the formula

v_1=9.8(290\times 10^{-3})=2.8m/s

v'=9.8(130\times 10^{-3})=1.27m/s

Velocity of center of mass=\frac{m_1v_1+m'v'}{m_1+m'}

Velocity of center of mass=\frac{m(2.8)+6m(1.27)}{m+6m}=\frac{m(2.8+6(1.27)}{7m}=1.49 m/s

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Answer:

1. The density of the cube is 1.03 g/mL.

2. Dish soap

Explanation:

1. Determination of the density of the cube.

From the question given above, the following data were obtained:

Mass (m) of cube = 21.7 g

Volume (V) of cube = 21 mL

Density (D) of cube =?

The density of a substance is simply defined as the mass of the substance per unit volume of the substance. Thus, density can be expressed mathematically as:

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

D = m / V

With the above formula, we can obtain the density of the cube as follow:

Mass (m) of cube = 21.7 g

Volume (V) of cube = 21 mL

Density (D) of cube =?

D = m / V

D = 21.7 / 21

D = 1.03 g/mL

Thus, the density of the cube is 1.03 g/mL.

2. Determination of the layer of density the cube will settle in.

From the question given above,

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Comparing the density of the cube (i.e 1.03 g/mL) with those in the table able, we can conclude that the cube will settle in the DISH SOAP layer since they both have the same density.

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