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vredina [299]
3 years ago
11

An object travels 20 m in 10s What is its speed?

Physics
1 answer:
ella [17]3 years ago
3 0

speed=distance/time

distance=20m

time=10s

speed=?

speed=20×10

speed=200m/s

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Illustrates an Atwood's machine. Let the masses of blocks A and B be 7.00 kg and 3.00 kg , respectively, the moment of inertia o
Harman [31]

Answer:  

A) 1.55  

B) 1.55

C) 12.92

D) 34.08

E)  57.82

Explanation:  

The free body diagram attached, R is the radius of the wheel  

Block B is lighter than block A so block A will move upward while A downward with the same acceleration. Since no snipping will occur, the wheel rotates in clockwise direction.  

At the centre of the whee, torque due to B is given by  

{\tau _2} = - {T_{\rm{B}}}R  

Similarly, torque due to A is given by  

{\tau _1} = {T_{\rm{A}}}R  

The sum of torque at the pivot is given by  

\tau = {\tau _1} + {\tau _2}  

Replacing {\tau _1} and {\tau _2} by {T_{\rm{A}}}R and - {T_{\rm{B}}}R respectively yields  

\begin{array}{c}\\\tau = {T_{\rm{A}}}R - {T_{\rm{B}}}R\\\\ = \left( {{T_{\rm{A}}} - {T_{\rm{B}}}} \right)R\\\end{array}  

Substituting I\alpha for \tau in the equation \tau = \left( {{T_{\rm{A}}} - {T_{\rm{B}}}} \right)R  

I\alpha=\left( {{T_{\rm{A}}} - {T_{\rm{B}}}} \right)R  

\frac{I\alpha}{R} =\left {{T_{\rm{A}}} - {T_{\rm{B}}}} \right  

The angular acceleration of the wheel is given by \alpha = \frac{a}{R}  

where a is the linear acceleration  

Substituting \frac{a}{R} for \alpha into equation  

\frac{I\alpha}{R} =\left {{T_{\rm{A}}} - {T_{\rm{B}}}} \right we obtain  

\frac{Ia}{R^2} =\left {{T_{\rm{A}}} - {T_{\rm{B}}}} \right  

Net force on block A is  

{F_{\rm{A}}} = {m_{\rm{A}}}g - {T_{\rm{A}}}  

Net force on block B is  

{F_{\rm{B}}} = {T_{\rm{B}}} - {m_{\rm{B}}}g  

Where g is acceleration due to gravity  

Substituting {m_{\rm{B}}}a and {m_{\rm{A}}}a for {F_{\rm{B}}} and {F_{\rm{A}}} respectively into equation \frac{Ia}{R^2} =\left {{T_{\rm{A}}} - {T_{\rm{B}}}} \right and making a the subject we obtain  

\begin{array}{c}\\{m_{\rm{A}}}g - {m_{\rm{A}}}a - \left( {{m_{\rm{B}}}g + {m_{\rm{B}}}a} \right) = \frac{{Ia}}{{{R^2}}}\\\\\left( {{m_{\rm{A}}} - {m_{\rm{B}}}} \right)g - \left( {{m_{\rm{A}}} + {m_{\rm{B}}}} \right)a = \frac{{Ia}}{{{R^2}}}\\\\\left( {{m_{\rm{A}}} + {m_{\rm{B}}} + \frac{I}{{{R^2}}}} \right)a = \left( {{m_{\rm{A}}} - {m_{\rm{B}}}} \right)g\\\\a = \frac{{\left( {{m_{\rm{A}}} - {m_{\rm{B}}}} \right)g}}{{\left( {{m_{\rm{A}}} + {m_{\rm{B}}} + \frac{I}{{{R^2}}}} \right)}}\\\end{array}  

Since {m_{\rm{B}}} = 3kg and {m_{\rm{B}}} = 7kg  

g=9.81 and R=0.12m, I=0.22{\rm{ kg}} \cdot {{\rm{m}}^2}  

Substituting these we obtain  

a = \frac{{\left( {{m_{\rm{A}}} - {m_{\rm{B}}}} \right)g}}{{\left( {{m_{\rm{A}}} + {m_{\rm{B}}} + \frac{I}{{{R^2}}}} \right)}}  

\begin{array}{c}\\a = \frac{{\left( {7{\rm{ kg}} - 3{\rm{ kg}}} \right)\left( {9.81{\rm{ m/}}{{\rm{s}}^2}} \right)}}{{\left( {7{\rm{ kg}} + 3{\rm{ kg}} + \frac{{0.22{\rm{ kg/}}{{\rm{m}}^2}}}{{{{\left( {0.120{\rm{ m}}} \right)}^2}}}} \right)}}\\\\ = 1.55235{\rm{ m/}}{{\rm{s}}^2}\\\end{array}

Therefore, the linear acceleration of block A is 1.55 {\rm{ m/}}{{\rm{s}}^2}

(B)

For block B

{a_{\rm{B}}} = {a_{\rm{A}}}

Therefore, the acceleration of both blocks A and B are same

1.55 {\rm{ m/}}{{\rm{s}}^2}

(C)

The angular acceleration is \alpha = \frac{a}{R}

\begin{array}{c}\\\alpha = \frac{{1.55{\rm{ m/}}{{\rm{s}}^2}}}{{0.120{\rm{ m}}}}\\\\ = 12.92{\rm{ rad/}}{{\rm{s}}^2}\\\end{array}

(D)

Tension on left side of cord is calculated using

\begin{array}{c}\\{T_{\rm{B}}} = {m_{\rm{B}}}g + {m_{\rm{B}}}a\\\\ = {m_{\rm{B}}}\left( {g + a} \right)\\\end{array}

\begin{array}{c}\\{T_{\rm{B}}} = \left( {3{\rm{ kg}}} \right)\left( {9.81{\rm{ m/}}{{\rm{s}}^2} + 1.55{\rm{ m/}}{{\rm{s}}^2}} \right)\\\\ = 34.08{\rm{ N}}\\\end{array}

(E)

Tension on right side of cord is calculated using

\begin{array}{c}\\{T_{\rm{A}}} = {m_{\rm{A}}}g - {m_{\rm{A}}}a\\\\ = {m_{\rm{A}}}\left( {g - a} \right)\\\end{array}

\begin{array}{c}\\{T_{\rm{A}}} = \left( {7{\rm{ kg}}} \right)\left( {9.81{\rm{ m/}}{{\rm{s}}^2} – 1.55{\rm{ m/}}{{\rm{s}}^2}} \right)\\\\ = 57.82{\rm{ N}}\\\end{array}

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Write a balanced equation for the decomposition of ammonium nitrate to form molecular nitrogen, molecular oxygen, and water. Exp
VARVARA [1.3K]

The unbalanced reaction is

<em>a</em> NH₄NO₃   ⇒   <em>b</em> N₂ + <em>c</em> O₂ + <em>d</em> H₂O

where <em>a</em>, <em>b</em>, <em>c</em>, and <em>d</em> are unknown constants.

Count how many times each element appears on either side of the reaction.

• reactants:

N = 2<em>a</em>, H = 4<em>a</em>, O = 3<em>a</em>

• products

N = 2<em>b</em>, O = 2<em>c</em> + <em>d</em>, H = 2<em>d</em>

<em />

Now we solve the system of equations,

2<em>a</em> = 2<em>b</em> … … … [1]

4<em>a</em> = 2<em>d</em> … … … [2]

3<em>a</em> = 2<em>c</em> + <em>d</em> … … … [3]

<em />

From [1] we immediately have

<em>a</em> = <em>b</em>

In [2], we get

2<em>a</em> = <em>d</em>

and substituting for <em>d</em> in [3] gives

3<em>a</em> = 2<em>c</em> + 2<em>a</em>

<em>a</em> = 2<em>c</em>

<em />

Let <em>c</em> = 1; then

• <em>a</em> = 2×1 = 2

• <em>b</em> = 2

• <em>d</em> = 2×2 = 4

So, the balanced reaction is

2 NH₄NO₃   ⇒   2 N₂ + O₂ + 4 H₂O

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so to be exact galixes do make up most of the volume of space because galaxies are what make up space!

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