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

227 m/s

Step-by-step explanation:

Kinetic energy formula:

• 
  `\displaystyle \text{KE} = (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} = (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 = (1)/(2) (.00270)v^2`
• 
  `\displaystyle (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.