A 7.0 kg bowling ball moves at 2.40 m/s. How fast must a 2.60 g Ping-Pong ball move so that the two balls have the same kinetic energy?
(1/2)( 7) (2.4)^2 = (1/2) (.0026) v^2
v^2 = 7*2.4^2/.0026
Well, well, well, looks like we have a physics problem on our hands! Let's dive right in, shall we?
So, we have a bowling ball weighing 7.0 kg and moving at 2.40 m/s. The task is to find the speed at which a Ping-Pong ball weighing 2.60 g must move to have the same kinetic energy as the bowling ball.
First things first, let's convert the Ping-Pong ball's mass to kilograms, because we need to be consistent here. 2.60 grams is equivalent to 0.0026 kg. Don't worry, I double-checked my math!
Now, the formula for kinetic energy is KE = 0.5 * mass * velocity squared. Since we want the Ping-Pong ball's kinetic energy to be the same as the bowling ball's, we can set up an equation:
0.5 * 7.0 kg * (2.40 m/s)^2 = 0.5 * 0.0026 kg * (Ping-Pong ball's velocity)^2
Simplifying that puppy, we get:
17.64 joules = 0.0013 * (Ping-Pong ball's velocity)^2
Now, let's solve for the Ping-Pong ball's velocity. Taking the square root of both sides gives us:
Ping-Pong ball's velocity = √(17.64 joules / 0.0013)
Calculating that, we get:
Ping-Pong ball's velocity ≈ 48.1 m/s
So, the Ping-Pong ball must move at approximately 48.1 m/s to have the same kinetic energy as the bowling ball. Just make sure you don't blink, or you might miss it!
Hope that put a smile on your face!
To determine the speed of the Ping-Pong ball, we need to set up an equation based on the principle of conservation of kinetic energy. The kinetic energy (KE) of an object is given by the equation:
KE = (1/2) * mass * velocity^2
Let's denote the mass of the bowling ball as Mb and the mass of the Ping-Pong ball as Mp. Given the information in the problem:
Mb = 7.0 kg (mass of the bowling ball)
Vb = 2.40 m/s (velocity of the bowling ball)
Mp = 2.60 g = 0.00260 kg (mass of the Ping-Pong ball)
Vp = ? (velocity of the Ping-Pong ball)
Now we can set up the equation for the kinetic energy of the bowling ball and the Ping-Pong ball:
KEb = KEp
(1/2) * Mb * Vb^2 = (1/2) * Mp * Vp^2
Substituting the given values:
(1/2) * 7.0 kg * (2.40 m/s)^2 = (1/2) * 0.00260 kg * Vp^2
Simplifying the equation:
(1/2) * 7.0 * (2.40)^2 = (1/2) * 0.00260 * Vp^2
167.76 = 0.0013 * Vp^2
Dividing both sides by 0.0013:
Vp^2 = 129200
Taking the square root of both sides:
Vp ≈ √129200
Vp ≈ 359.56 m/s
Therefore, the Ping-Pong ball must move at approximately 359.56 m/s in order to have the same kinetic energy as the 7.0 kg bowling ball.