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3 years ago

8

A ball took 0.45s to hit the ground 0.72m from the table. What was the horizontal velocity of the ball as it rolled off the tabl

e?

1 answer:

dusya [7]3 years ago

8 0

the ball hits the ground a very high velocity

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Object A has 27 J of kinetic energy. Object B has one-quarter the mass of object A.

andreev551 [17]

Answer:

the final speed of object A changed by a factor of $\frac{1}{\sqrt{3} }$ = 0.58

the final speed of object B changed by a factor of $\sqrt{\frac{5}{3} }$ = 1.29

Explanation:

Given;

kinetic energy of object A, = 27 J

let the mass of object A = $m_A$

then, the mass of object B = $m_B = \frac{m_A}{4}$

work done on object A = -18 J

work done on object B = -18 J

let $v_i$ be the initial speed

let $v_f$ be the final speed

For object A;

$K.E_A = 27\\\\\frac{1}{2} m_A v_i^2 = 27\\\\m_A v_i^2 = 54\\\\m_A = \frac{54}{v_i^2} ----Equation \ (1)\\\\Apply \ work-energy \ theorem;\\\\\delta K.E_A = -18\\\\\frac{1}{2} m_A v_f^2 - \frac{1}{2} m_A v_i^2 = -18\\\\\frac{1}{2} m_A ( v_f^2 \ - v_i^2 )\ =- 18\\\\v_f^2 \ - v_i^2 = -\frac{36}{m_A} ---Equation \ (2)\\\\v_f^2 \ - v_i^2 = -\frac{36v_i^2}{54}\\\\ v_f^2 \ =v_i^2 - \frac{36v_i^2}{54}\\\\ v_f^2 = \frac{54v_i^2 -36v_i^2 }{54} \\\\v_f^2 = \frac{18v_i^2}{54} \\\\v_f^2 = \frac{v_i^2}{3} \\\\$

$v_f = \sqrt{\frac{v_i^2}{3} }\\\\v_f = \frac{1}{\sqrt{3} } \ v_i\\\\$

Thus, the final speed of object A changed by a factor of $\frac{1}{\sqrt{3} }$ = 0.58

To obtain the change in the final speed of object B, apply the following equations.

$K.E_B_i = \frac{1}{2} m_Bv_i^2\\\\m_B = \frac{m_A}{4} \\\\K.E_B_i = \frac{1}{2}(\frac{m_A}{4} )v_i^2\\\\K.E_B_i = \frac{m_Av_i^2}{8} \\\\But, \ m_Av_i^2 = 54 \\\\K.E_B_i = \frac{54}{8} \\\\Apply \ work-energy \ theorem ;\\\\\delta K.E = -18\\\\K.E_f -K.E_i = -18\\\\\frac{1}{2}m_Bv_f^2 - \frac{1}{2} m_Bv_i^2 = -18\\\\Recall \ m_B = \frac{m_A}{4} \\\\\frac{1}{2}(\frac{m_A}{4} )v_f^2 - \frac{1}{2}(\frac{m_A}{4} )v_i^2 = -18\\\\\frac{1}{2}\times \frac{m_A}{4} (v_i^2 -v_f^2) = 18\\\\$

$\frac{1}{2}\times \frac{m_A}{4} (v_i^2 -v_f^2) = 18\\\\v_i^2 -v_f^2 = \frac{8}{m_A} \times 18\\\\v_i^2 -v_f^2 =\frac{144}{m_A} \\\\But , m_A = \frac{54}{v_i^2} \\\\v_i^2 -v_f^2 =\frac{144v_i^2}{54} \\\\v_f^2 = v_i^2 - \frac{144v_i^2}{54}\\\\v_f^2 = \frac{54v_i^2-144v_i^2}{54}\\\\ v_f^2 = \frac{-90v_i^2}{54} \\\\v_f^2 = \frac{-5v_i^2}{3} \\\\|v_f| = \sqrt{\frac{5v_i^2}{3}} \\\\|v_f| = \sqrt{\frac{5}{3}} \ v_i$

Thus, the final speed of object B changed by a factor of $\sqrt{\frac{5}{3} }$ = 1.29

3 0

2 years ago

Help meee please fill in the blanks !!

Ratling [72]

The atomic number is the simply the number of protons in the atom. So in the first row with atomic number 2, the number of protons is 2.

If the atom has no charge, which I think you can assume for all of these, the number of electrons is equal to the number of protons. So the number of electrons is also 2.

The number of neutrons (which are the particles with no charge in the nucleus) is simply the mass number minus the atomic number i.e. 4 - 2 = 2.

The isotopic symbol is the symbol which is found on the periodic table of elements. There are 2 numbers associated which each element on the table. The larger is the mass number and the smaller is the atomic number. The atomic number or number of protons is what identifies the element. Looking at the periodic table ( https://sciencenotes.org/wp-content/uploads/2015/01/PeriodicTableOfTheElementsBW.pdf or https://simple.wikipedia.org/wiki/Periodic_table_(big) ), it can be seen that the element on the first row above with an atomic number of 2 is Helium with a symbol He. The number that is included with the name is simply the mass number which is 4 in this case, which tells us that this type of helium has 2 neutrons.

Another type (or isotope) of helium is Helium-3 which has one neutron.

Try the next row and post back if you have trouble with it

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2 years ago

Where is the magnet that causes Earth’s magnetic field? What is this magnet made of?

Y_Kistochka [10]

Answer:

The magnetic field of Earth is created by currents of electricity that flow in the molten center.

Explanation:

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2 years ago

I need help ASAP. This is for 15 points

kramer

Answer:

Latitude :

runs: east to west

measures : distances north and south of the equator

Longitude :

runs : north to south

measures : the distance east or west of the Prime Meridian

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2 years ago

Select all that apply.

ikadub [295]

All are true except the first two.

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2 years ago

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