A 8.80 kg bowling ball moves at 1.80 m/s. How fast must a 2.45 g Ping- Pong ball move so that the two balls have the same kinetic energy
To find the speed at which the Ping-Pong ball must move in order to have the same kinetic energy as the bowling ball, we can use the formula for kinetic energy:
KE = 1/2 * m * v^2,
where KE is the kinetic energy, m is the mass, and v is the velocity.
Let's calculate the kinetic energy of the bowling ball:
m_bowling = 8.80 kg (mass of the bowling ball)
v_bowling = 1.80 m/s (velocity of the bowling ball)
KE_bowling = 1/2 * m_bowling * v_bowling^2
= 1/2 * 8.80 kg * (1.80 m/s)^2
= 1/2 * 8.80 kg * 3.24 m^2/s^2
= 14.112 J (joules)
Now, let's find the velocity of the Ping-Pong ball:
m_pingpong = 2.45 g (mass of the Ping-Pong ball)
v_pingpong (velocity of the Ping-Pong ball)
Since we want the kinetic energy to be the same for both balls:
KE_bowling = KE_pingpong
14.112 J = 1/2 * m_pingpong * v_pingpong^2
Let's convert the mass of the Ping-Pong ball into kilograms:
m_pingpong = 2.45 g / 1000
= 0.00245 kg
Now, we can solve for v_pingpong:
14.112 J = 1/2 * 0.00245 kg * v_pingpong^2
14.112 J = 0.001225 kg * v_pingpong^2
Dividing both sides by 0.001225 kg:
v_pingpong^2 = 14.112 J / 0.001225 kg
v_pingpong^2 = 11508.98 m^2/s^2
Finally, taking the square root of both sides:
v_pingpong = √(11508.98 m^2/s^2)
v_pingpong ≈ 107.30 m/s
Therefore, the Ping-Pong ball must move at approximately 107.30 m/s to have the same kinetic energy as the bowling ball.