Physics, 04.04.2020 10:23 jaccamoboy

A billiard ball of mass m moving with speed v1=1 m/s collides head-on with a second ball of mass 2m which is at rest. What is the velocity of the ball of mass 2m after the collision?

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Answer from: joslynndiggs

The velocity of mass 2m is v_B = 0.67 m/s

Explanation:

From the question w are told that

The mass of the billiard ball A is =m

The initial speed of the billiard ball A = v_1 =1 m/s

The mass of the billiard ball B is = 2 m

The initial speed of the billiard ball B = 0

Let the final speed of the billiard ball A = v_A

Let The finial speed of the billiard ball B = v_B

According to the law of conservation of Energy

$\frac{1}{2} m (v_1)^2 + \frac{1}{2} 2m (0) ^ 2 = \frac{1}{2} m (v_A)^2 + \frac{1}{2} 2m (v_B)^2$

Substituting values

$\frac{1}{2} m (1)^2 = \frac{1}{2} m (v_A)^2 + \frac{1}{2} 2m (v_B)^2$

Multiplying through by $\frac{1}{2}m$

1 =v_A^2 + 2 v_B ^2 ---(1)

According to the law of conservation of Momentum

mv_1 + 2m(0) = mv_A + 2m v_B

Substituting values

m(1) = mv_A + 2mv_B

Multiplying through by

1 = v_A + 2v_B ---(2)

making v_A subject of the equation 2

v_A = 1 - 2v_B

Substituting this into equation 1

(1 -2v_B)^2 + 2v_B^2 = 1

1 - 4v_B + 4v_B^2 + 2v_B^2 =1

6v_B^2 -4v_B +1 =1

6v_B^2 -4v_B =0

Multiplying through by $\frac{1}{v_B}$

6v_B -4 = 0

$v_B = \frac{4}{6}$

v_B = 0.67 m/s

Answer from: Quest

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas

Answer from: Quest

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

so, refractive index of medium = 300000/200000 = 1.5

1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

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A billiard ball of mass m moving with speed v1=1 m/s collides head-on with a second ball of mass 2m...

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