Question

What is the mass of a baseball that has a kinetic energy of 105 J and is traveling at 10 m/s?​

Answer 1

`\boxed {\boxed {\sf 2.1 \ kilograms}}`

Step-by-step explanation:

Kinetic energy is the energy an object possesses due to motion. The formula 1/2 the product of mass and the squared velocity.

`E_k=(1)/(2) mv^2`

We know the baseball's kinetic energy is 105 Joules. It is also traveling at a velocity of 10 meters per second. `

First, convert the units of Joules to make unit cancellation easier later in the problem. 1 Joule (J) is equal to 1 kilogram square meter per square second (kg*m²/s²). The baseball's kinetic energy of 105 J is equal to 105 kg*m²/s².

Now we know 2 values:

• 
  `E_k= 105 \ kg*m^2/s^2`

• 
  `v= 10 \ m/s`

Substitute these values into the formula.

`105 \ kg*m^2/s^2= (1)/(2) m (10 \ m/s)^2`

Now we need to solve for m, the mass. Solve the exponent.

• (10 m/s)²= 10 m/s * 10 m/s = 100 m²/s²

`105 \ kg *m^2/s^2 = (1)/(2) m (100 \ m^2/s^2)`

Multiply on the right side.

`105 \ kg *m^2/s^2 = m ((1)/(2) * 100 \ m^2/s^2)`

`105 \ kg *m^2/s^2 = m (50 \ m^2/s^2)`

The variable, m, is being multiplied by 50 square meters per square second. The opposite of multiplication is division, so we divide both sides by that value.

`\frac {105 \ kg *m^2/s^2 }{50 \ m^2/s^2}= ( m (50 \ m^2/s^2))/(50 \ m^2/s^2)`

`\frac {105 \ kg *m^2/s^2 }{50 \ m^2/s^2}= m`

The units of square meter per square second will cancel out.

`\frac {105 }{50} \ kg= m`

`2.1 \ kg=m`

The mass of the baseball is 2.1 kilograms.