Question

How fast must a 2.70-g ping-pong ball move in order to have the same kinetic energy as a 145-g baseball moving at 31.0 m/s

Answer 1

Answer:

227 m/s

Explanation:

Kinetic energy formula:

• $\displaystyle \text{KE} = \frac{1}{2} mv^2$

• where m = mass of the object (kg)
• and v = speed of the object (m/s)

Let's find the kinetic energy of the 145-g baseball moving at 31.0 m/s.

First convert the mass to kilograms:

• 145-g → 0.145 kg

Plug known values into the KE formula.

• $\displaystyle \text{KE} = \frac{1}{2} (.145)(31.0)^2$
• $\displaystyle \text{KE} = 69.6725 \ \text{J}$

Now we want to find how fast a 2.70-g ping pong ball must move in order to achieve a kinetic energy of 69.6725 J.

First convert the mass to kilograms:

• 2.70-g → 0.00270 kg

Plug known values into the KE formula.

• $\displaystyle 69.6725 = \frac{1}{2} (.00270)v^2$
• $\displaystyle \frac{2(69.6725)}{.00270} =v^2$
• $57609.25926=v^2$
• $v=227.1767137$

The ping-pong ball must move at a speed of 227 m/s to achieve the same kinetic energy as the baseball.