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Stells [14]
3 years ago
14

A(n) 7.7-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting th

e object into two equal chunks and adding 17 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume that the one of the chunks after explosion moves in the positive x direction. The x component of the average acceleration of this chunk during the explosion is afrontx, the x component fo the average acceleration of the other chunk during the explosion is arearx.
What are the x-components of the average accelerations of the two chunks during the explosion?
Physics
1 answer:
-BARSIC- [3]3 years ago
5 0

Answer:

Average acceleration on first part of the chunk is given as

a_1 = 13.125 m/s^2

Average acceleration on second part of the chunk is given as

a_2 = -13.125 m/s^2

Explanation:

By momentum conservation along x direction we will have

mv_i = \frac{m}{2}v_1 + \frac{m}{2}v_2

so we have

v_1 + v_2 = 2v

v_1 + v_2 = 4.68

also by energy conservation

\frac{1}{2}(\frac{m}{2})v_1^2 + \frac{1}{2}(\frac{m}{2})v_2^2 - \frac{1}{2}mv^2 = 17 J

\frac{1}{4}m(v_1^2 + v_2^2) - \frac{1}{2}mv^2 = 17

(v_1^2 + v_2^2) - 2v^2 = \frac{4}{7.7}(17)

(4.68 - v_2)^2 + v_2^2 - 2v^2 = 8.83

21.9 + 2v_2^2 - 9.36 v_2 - 10.95 = 8.83

2v_2^2 - 9.36v_2 + 2.12 = 0

by solving above equation we will have

v_1 = 4.44 m/s

v_2 = 0.24 m/s

Average acceleration on first part of the chunk is given as

a_1 = \frac{4.44 - 2.34}{0.16}

a_1 = 13.125 m/s^2

Average acceleration on second part of the chunk is given as

a_2 = \frac{0.24 - 2.34}{0.16}

a_2 = -13.125 m/s^2

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5 0
3 years ago
A book is sitting on a table. Which of the following is true about the table? O A. It is pushing up on the book. O B. It exerts
777dan777 [17]

Answer:

yes it does exert a force, it pushes it up

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this is called normal force

if it didn't exert a force the book would keep going down

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so the book exerts a force on the table and vice versa

hope this helped

5 0
2 years ago
A person of mass 55 kg swings on a rope length 4 m from rest (when the rope makes an angle of 30 degrees with the vertical) and
vovangra [49]

Answer:

θ = 19.66°

Explanation:

To determine the angle that the rope makes with the vertical for the two people, you first take into account the potential energy of the first person before he swings on the rope:

U=mgh

h: distance to the ground

g: gravitational acceleration = 9.8m/s^2

m: mass of the first person = 55 kg

In the image attache below you can notice that the height h is:

h=4-4cos(30\°)=0.53m

Then, the potential energy is:

U=(55kg)(9.8m/s^2)(0.53m)=285.67J

When the first person picks up the second person (when the rope is exactly vertical), all the potential energy becomes kinetic energy. Next, when both people reaches the maximum height h' the energy must be equal to the initial potential energy of the first person:

U'=(m_1+m_2)gh'=285.67\ J

From the previous equation you can get h':

h'=\frac{285.67J}{(55kg+70kg)(9.8m/s^2)}=0.2332m

Finally, you obtain the angle between the rope at the height h,' and the vertical, by calculating the following:

h'=4-4cos(\theta)\\\\\theta=cos^{-1}(\frac{4-h'}{4})=cos^{-1}(\frac{4-0.2332}{4})=19.66\°

hence, the angle between the rope and the vertical, when the two people are in the rope is 19.66°

8 0
3 years ago
A paperweight consists of a 8.55-cm-thick plastic cube. Within the plastic a thin sheet of paper is embedded, parallel to opposi
ella [17]

Answer:

\mu=1.5322

Explanation:

Given:

Thickness of the paperweight cube, x=8.55\ cm

apparent depth from one side of the inbuilt paper in the plastic cube, i=4.02\ cm

apparent depth from the other side of the inbuilt paper in the plastic cube, i'=1.56\ cm

Now as we know that refractive index is given as:

\rm \mu=\frac{real\ depth}{apparent\ depth}

  • Let the real depth form first side of the slab be, d
  • Then the depth from the second side of the slab will be, d'=x-d=8.55-d

Since refractive index for an amorphous solid is an isotropic quantity so it remains same in all the direction for this plastic.

\mu=\mu'

\frac{d}{i} =\frac{d'}{i'}

\frac{d}{4.02}=\frac{8.55-d}{1.56}

d=6.1597\ cm

Now the refractive index:

\mu=\frac{d}{i}

\mu=\frac{6.1596}{4.02}

\mu=1.5322

7 0
3 years ago
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