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Luda [366]
3 years ago
13

Two objects each moving with speed v travel in opposite directions along a straight line passing through both their centers. The

objects stick together when they collide and move together with speed v/4 after the collision.
(a) What is the ratio of the final kinetic energy to the initial kinetic energy? (answer: Kf/Ki = 1/16)
(b) What is the ratio of the mass of the more massive object to the mass of the less massive object? (answer: mmore massive/mless massive = 5/3)
Physics
1 answer:
Tpy6a [65]3 years ago
6 0

Answer:

\dfrac{1}{16}

\dfrac{5}{3}

Explanation:

m_1 = Mass of first object

m_2 = Mass of second object

v = Speed of both objects

\dfrac{v}{4} = Combined velocity

The ratio of final kinetic energy to initial kinetic energy will be

\dfrac{K_f}{K_i}=\dfrac{\dfrac{1}{2}(m_1+m_2)(\dfrac{v}{4})^2}{\dfrac{1}{2}(m_1v^2+m_2v^2)} \\\Rightarrow \dfrac{K_f}{K_i}=\dfrac{(m_1+m_2)\dfrac{v^2}{16}}{m_1v^2+m_2v^2}\\\Rightarrow \dfrac{K_f}{K_i}=\dfrac{(m_1+m_2)\dfrac{1}{16}}{m_1+m_2}\\\Rightarrow \dfrac{K_f}{K_i}=\dfrac{1}{16}

The ratio is \dfrac{1}{16}

As the linear momentum is conserved

m_1v-m_2v=(m_1+m_2)\dfrac{v}{4}\\\Rightarrow m_1-m_2=(m_1+m_2)\dfrac{1}{4}

Divide by m_2 on both sides

\dfrac{m_1}{m_2}-1=\dfrac{m_1}{4m_2}+\dfrac{1}{4}\\\Rightarrow \dfrac{m_1}{m_2}-\dfrac{m_1}{4m_2}=\dfrac{1}{4}+1\\\Rightarrow \dfrac{3m_1}{4m_2}=\dfrac{5}{4}\\\Rightarrow \dfrac{m_1}{m_2}=\dfrac{5\times 4}{3\times 4}\\\Rightarrow \dfrac{m_1}{m_2}=\dfrac{5}{3}

The ratio of mass is \dfrac{5}{3}

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Answer:

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4 years ago
C is correct just an FYI
belka [17]

Answer:

Huh?

Explanation:

3 0
3 years ago
Four copper wires of equal length are connected in series. Their cross-sectional areas are 1.6 cm2 , 1.2 cm2 , 4.4 cm2 , and 7 c
EleoNora [17]

Answer:

63.8 V

Explanation:

We are given that

A_1=1.6 cm^2=1.6\times 10^{-4} m^2

1 cm^2=10^{-4} m^2

A_2=1.2 cm^2=1.2\times 10^{-4} m^2

A_3=4.4 cm^2=4.4\times 10^{-4} m^2

A_4=7 cm^2=7\times 10^{-4} m^2

Potential difference,V=140 V

We know that

R=\frac{\rho l}{A}

According to question

l_1=l_2=l_3=l_4=l

In series

R=R_1+R_2+R_3+R_4

R=\rho l(\frac{1}{A_1}+\frac{1}{A_2}+\frac{1}{A_3}+\frac{1}{A_4})

R=\rho l(\frac{1}{1.6\times 10^{-4}}+\frac{1}{1.2\times 10^{-4}}+\frac{1}{4.4\times 10^{-4}}+\frac{1}{7\times 10^{-4}})

R=\rho l(18284.6)

I=\frac{V}{R}=\frac{140}{\rho l\times 18284.6}

Potential across 1.2 square cm=V_1=IR_1=\frac{140}{\rho l\times 18284.6}\times \rho l(\frac{1}{1.2\times 10^{-4}}=63.8 V

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3 years ago
Distance Between Two Cars A car leaves an intersection traveling west. Its position 4 sec later is 19 ft from the intersection.
faltersainse [42]

Answer:

The answer to the question is;

The rate at which the distance between the two cars is changing is equal to 14.4 ft/sec.

Explanation:

We note that the distance  traveled by each car after 4 seconds is

Car A = 19 ft in the west direction.

Car B = 26 ft in the north direction

The distance between the two cars is given by the length of the hypotenuse side of a right angled triangle with the north being the y coordinate and the  west being the x coordinate.

Therefore, let the distance between the two cars be s

we have

s² = x² + y²

= (19 ft)² + (26 ft)² = 1037 ft²

s = \sqrt{1037 ft^2} = 32.202 ft.

The rate of change of the distance from their location 4 seconds after they commenced their journeys is given by;

Since s² = x² + y² we have

\frac{ds^{2} }{dt} = \frac{dx^{2} }{dt}  + \frac{dy^{2} }{dt}

→ 2s\frac{ds }{dt} = 2x\frac{dx}{dt}  + 2y\frac{dy }{dt} which gives

s\frac{ds }{dt} = x\frac{dx}{dt}  + y\frac{dy }{dt}

We note that the speeds of the cars were given as

Car B moving north = 12 ft/sec, which is the y direction and

Car A moving west = 8 ft/sec which is the x direction.

Therefore

\frac{dy }{dt} =  12 ft/sec and

\frac{dx}{dt} = 8 ft/sec

s\frac{ds }{dt} = x\frac{dx}{dt}  + y\frac{dy }{dt} becomes

32.202 ft.\frac{ds }{dt} = 19 ft \times 8 \frac{ft}{sec}  + 26ft\times 12\frac{ft}{sec}  = 464 ft²/sec

\frac{ds }{dt} = \frac{464\frac{ft^{2} }{sec} }{32.202 ft.} = 14.409 ft/sec ≈ 14.4 ft/sec to one place of decimal.

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goblinko [34]

Answer:

1. Somewhat 2.Yes

Explanation:

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