Question

what is the linear momentum of a 15 kg object traveling at a constant velocity that has 270 j of kinetic energy

Answer 1

The linear momentum of a
`\(15 \ \text{kg}\)` object with
`\(270 \ \text{J}\)` kinetic energy is found by calculating the velocity using the kinetic energy formula and then applying the linear momentum formula.

The linear momentum p of an object can be calculated using the relationship between kinetic energy KE and linear momentum. The formula relating these two quantities is:

`\[ KE = (1)/(2)mv^2 \]`

where:

• KE is the kinetic energy,

• m is the mass of the object, and

• v is the velocity of the object.

Given that the object has a kinetic energy
`(\( KE \)) of \( 270 \ \text{J} \)`and a mass
`(\( m \)) of \( 15 \ \text{kg} \)`, we can rearrange the kinetic energy formula to solve for velocity v :

`\[ v = \sqrt{(2 * KE)/(m)} \]`

Now, plug in the values:

`\[ v = \sqrt{(2 * 270)/(15)} \]`

Calculate the velocity.

Once the velocity is determined, the linear momentum p can be found using the formula:

`\[ p = m * v \]`

Substitute the mass and velocity values into the formula to calculate the linear momentum.

`\[ p = 15 * \text{(velocity)} \]`

Now, the linear momentum of the
`\( 15 \ \text{kg} \)` object traveling at a constant velocity with
`\( 270 \ \text{J} \)` of kinetic energy can be determined.