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Alex777 [14]
3 years ago
6

Three small balls of the same size but different masses are hung side-by-side in parallel on the strings of same length. They to

uch each other. The first ball of mass m1 is pulled to the height h and released from rest. The first ball collides elastically with the second ball of mass m2, and the second ball collides elastically with the third ball of mass m3 afterwards. After these two collisions, three balls will have the same momentum. What is the value of m3?
(a) m1
(b) 2m1/3
(c) m1/6
(d) m1/2
(e) m1/3
Physics
1 answer:
andrey2020 [161]3 years ago
8 0

Answer:

m1/6 ( c )

Explanation:

since all the balls starts having the same momentum after the two collisions we will apply the principal of conservation of energy

After first collision

m1v = m1v1 + m2v2 --- ( 1 )

After second collision

m2v2 = m2v2 + m3v3   ---- ( 2 )

combining equations 1 and 2

m1v = m1v1 + m2v2 + m3v3  ----- ( 3 )

All balls moving at the same momentum ( p ) = m1v1 = m2v2 = m3v3

note ; 3p = m1v ∴ m3 = \frac{m1v}{3v3}  -----  ( 4 )

applying conservation of energy

3v = v1 + v2 + v3 ------- ( 5 )

also 3m1v1 = m1v = v1 = v/3 =

v2 + v3 = 8/3 v ----- ( 6 )

next eliminate V3 for equation 6 by applying conservation of energy and momentum

m1 =  2m2 ------ ( 7 )

now using p1 = p2 = m1v1 = 1/2 m1v1  hence v2 = 2v1  where v1 = 1/3 v

hence ; v2 = 2/3 v ------- ( 8 )

solving with equation 6 and 8

v3 = 2v ------ ( 9 ) ∴  v/v3 = 1/2 ---- ( 10 )

solving with equation 9 and 10

m3 = m1/3 * 1/2 = m1/6

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mario62 [17]

Answer:

GE = ME - \frac{1}{2} m\,v^2,  which agrees with option C in your list.

Explanation:

The definition of Mechanical Energy (ME) of a system is the addition of the gravitational potential energy (GE) plus the kinetic energy (KE) of the system:

ME = GE + KE

Given that the KE is: \frac{1}{2} m\,v^2,

solving for GE in the formula above gives:

GE = ME - KE = ME - \frac{1}{2} m\,v^2,  which agrees with option C

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3 years ago
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NeX [460]

Answer:

The transverse displacement is   y(1.51 , 0.150) = 0.055 m    

Explanation:

 From the question we are told that

     The generally equation for the mechanical wave is

                    y(x,t) = Acos (kx -wt)

     The speed of the transverse wave is v = 8.25 \ m/s

     The amplitude of the transverse wave is A = 5.50 *10^{-2} m

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      At t= 0.150s , x = 1.51 m

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          w = vk

Substituting values  

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The propagation constant k is mathematically represented as

                  k = \frac{2 \pi}{\lambda}

Substituting values

                  k = \frac{2 * 3.142}{0. 540}

                   k =11.64 m^{-1}

Substituting values into the equation for mechanical waves

      y(1.51 , 0.150) = (5.50*10^{-2} ) cos ((11.64 * 1.151 ) - (96.03  * 0.150))

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nekit [7.7K]

Answer:

1)0.325

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<u>Given:</u>

The angle that falling raindrops make with the vertical=18^\circ

Let V_R be the velocity of the raindrops and V_B be the velocity of the bus.

1)

\dfrac{V_R}{V_B}=\tan 18^\circ\\\dfrac{V_R}{V_B}=0.315\\

2)Speed of the raindrops=0.315\times 19

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