A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g Ping Pong ball move so that the two balls have the same kinetic energy?

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Latisha Oneil · Accepted Answer

Mass of first ball (M)=7.00kg It&#039;s speed (v)=3.00m/s Mass of second ball (m)=2.45−g Let it&#039;s speed be &quot; V &quot; Since, both balls have the same kinetic energy So, 12Mv2=12mV2 or, V=160m/s

Nick Camelot · Accepted Answer

Step 1:We can use the formula for kinetic energy:{Kinetic&amp;nbsp;Energy}=12mv2where m represents the mass of the object and v represents its velocity.Step 2:Let&#039;s calculate the kinetic energy of the bowling ball first. Given that the mass of the bowling ball is 7.00 kg and its velocity is 3.00 m/s, we have:{Kinetic&amp;nbsp;Energy&amp;nbsp;of&amp;nbsp;the&amp;nbsp;bowling&amp;nbsp;ball}=12×7.00{kg}×(3.00{m/s})2Now, we need to find the velocity of the Ping Pong ball that will give it the same kinetic energy as the bowling ball. Let&#039;s assume the velocity of the Ping Pong ball is vp (in m/s).We can set up an equation to find vp:12×2.45{g}×(vp{m/s})2={Kinetic&amp;nbsp;Energy&amp;nbsp;of&amp;nbsp;the&amp;nbsp;bowling&amp;nbsp;ball}Step 3:Now, let&#039;s solve for vp.12×0.00245{kg}×(vp{m/s})2=12×7.00{kg}×(3.00{m/s})2Simplifying the equation:vp2=7.00×(3.00)20.00245Finally, taking the square root of both sides, we find:vp=7.00×(3.00)20.00245Evaluating this expression gives the final answer:vp≈160{m/s}Therefore, the Ping Pong ball must move at approximately 160m/s to have the same kinetic energy as the bowling ball.

Mr Solver · Accepted Answer

The kinetic energy of an object can be calculated using the formula:Kinetic&amp;nbsp;energy=12×mass×velocity2Given that the bowling ball has a mass of 7.00 kg and moves at 3.00 m/s, its kinetic energy is:K1=12×7.00kg×(3.00m/s)2The Ping Pong ball has a mass of 2.45 g, which is equal to 0.00245 kg. We need to find the velocity v of the Ping Pong ball such that its kinetic energy matches the kinetic energy of the bowling ball. So, the kinetic energy of the Ping Pong ball is:K2=12×0.00245kg×v2Since we want K1=K2, we can set up the equation:12×7.00kg×(3.00m/s)2=12×0.00245kg×v2Now we can solve for v:12×7.00kg×3.002m/s2=12×0.00245kg×v2Simplifying further:v2=7.00kg×3.002m/s20.00245kgFinally, solving for v:v=7.00kg×3.002m/s20.00245kgCalculating the value of v will give us the required velocity of the Ping Pong ball.

Eliza Beth13 · Accepted Answer

Answer:vPing&amp;nbsp;Pong≈159.877m/sExplanation:Given:K=12mv2where:K is the kinetic energy,m is the mass of the object, andv is the velocity of the object.Let&#039;s first calculate the kinetic energy of the bowling ball:Kbowling&amp;nbsp;ball=12·7.00kg·(3.00m/s)2Now, we want to find the velocity of the Ping Pong ball that will result in the same kinetic energy. Let&#039;s denote this velocity as vPing&amp;nbsp;Pong.Kbowling&amp;nbsp;ball=12·2.45g·(vPing&amp;nbsp;Pong)2Since the units are different, we need to convert the mass of the Ping Pong ball to kilograms:2.45g=2.45×10−3kgNow we can set up an equation to solve for vPing&amp;nbsp;Pong:12·7.00kg·(3.00m/s)2=12·2.45×10−3kg·(vPing&amp;nbsp;Pong)2To solve for vPing&amp;nbsp;Pong, we can simplify the equation:7.00kg·(3.00m/s)2=2.45×10−3kg·(vPing&amp;nbsp;Pong)2(vPing&amp;nbsp;Pong)2=7.00kg·(3.00m/s)22.45×10−3kgvPing&amp;nbsp;Pong=7.00kg·(3.00m/s)22.45×10−3kgvPing&amp;nbsp;Pong=7.00×9.002.45×10−3Now we can calculate the value of vPing&amp;nbsp;Pong:vPing&amp;nbsp;Pong=25530.6122449m/sTherefore, the Ping Pong ball must move at approximately vPing&amp;nbsp;Pong≈159.877m/s to have the same kinetic energy as the bowling ball.

A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g Ping Pong ball move so that the two balls have the same kinetic energy?

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