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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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3 years ago
An arrow is shot vertically upward at a rate of 250ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in
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Answer:

The arrow is at a height of 500 feet at time t = 2.35 seconds.

Explanation:

It is given that,

An arrow is shot vertically upward at a rate of 250 ft/s, v₀ = 250 ft/s

The projectile formula is given by :

h=-16t^2+v_ot

We need to find the time(s), in seconds, the arrow is at a height of 500 ft. So,

-16t^2+250t=500

On solving the above quadratic equation, we get the value of t as, t = 2.35 seconds

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6 0
4 years ago
Read 2 more answers
Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a sheer granite cliff of height 910 m in Yosemite
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Answer:

The jumper is in freefall for 12.447 seconds.

Explanation:

Let's start by calculating how far the jumper falls.

Initial height (on cliff) = 910 m

Final height after freefall = 150 m

Distance the jumper falls in freefall = 910 - 150 = 760 m

We can now use the equation of motion below to solve for the time:

s=u*t+\frac{1}{2} (a*t^2)

here. acceleration = 9.81 m/s   (due to gravity)

initial speed (u) = 0 m/s    (because vertical speed is 0 at the start)

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3 years ago
You have a string with a mass of 0.0127 kg. You stretch the string with a force of 9.33 N, giving it a length of 1.93 m. Then, y
melomori [17]

Answer:

wavelength = 0.968 m

frequency = 39.02 Hz

Explanation:

given data

mass = 0.0127 kg

force = 9.33 N

length = 1.93 m

to find out

wavelength and Frequency

solution

we know here linear density that is

linear density = \frac{mass}{length}   .........1

linear density = \frac{0.0127}{1.93}

linear density = 6.5803 × 10^{-3} kg/m

so

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wavelength = \frac{2L}{n}   ..............2

here n = 4 for forth harmonic

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and

frequency will be for 4th normal mode of vibration is

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frequency = \frac{4}{2*1.93} \sqrt{\frac{9.33}{6.5803*10^{-3}} }

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