#496 An object has a kinetic energy of 284

An object has a kinetic energy of 284 - Physics

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Free Chegg Question

An object has a kinetic energy of 284 J and a momentum of magnitude 23.5 kg · m/s.

(a) Find the speed of the object.
m/s

(b) Find the mass of the object.
kg

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Free Chegg Answer

General guidance

Concepts and reason

The concept used to solve this problem is related energy and momentum of an object.

First, eliminate the mass by dividing the expression of kinetic energy by momentum. It gives the velocity of the object. Finally, rearrange the expression of momentum for mass and calculate it.

Fundamentals

The expression of kinetic energy of a moving object is given by,

K=21​mv2

Here, $m$is mass of the object,$v$ is the velocity.

The expression of kinetic energy of a moving object is given by,

$p=mv$

Here, $m$is mass of the object,$v$ is the velocity.

Step 1 of 2

(a)

Calculate the velocity of the object.

The expression of kinetic energy of a moving object is given by,

K=21​mv2

Here, $m$is mass of the object,$v$ is the velocity.

The expression of kinetic energy of a moving object is given by,

$p=mv$

Here, $m$is mass of the object,$v$ is the velocity.

Divide the expression K=21​mv2 by$p=mv$,

pK​=mv21​mv2​=21​v​

Rearrange it for$v$,

v=p2K​

Substitute $284\mathrm{J}$ for $K$ and 23.5kg⋅m⋅s−1 for$p$,

v=23.5kg⋅m⋅s−12(284J)​=24.2m⋅s−1​

Part a

The velocity of the object is24.2m⋅s−1.

Explanation | Common mistakes | Hint for next step

Divide the kinetic energy by the momentum of the particle. By dividing it, we eliminate the mass. Then, substitute the known values in the expression of velocity.

Step 2 of 2

(b)

Calculate the mass of the object.

Rearrange the expression of momentum as follows,

m=vp​

Substitute 23.5kg⋅m⋅s−1 for $p$ and 24.2m⋅s−1 for$v$,

m=24.2m⋅s−123.5kg⋅m⋅s−1​=0.971kg​

Part b

The mass of the object is$0.971\mathrm{k}\mathrm{g}$.

Explanation | Common mistakes

Rearrange the expression of momentum foe mass and substitute the values of momentum and velocity in it.

Answer

Part a

The velocity of the object is24.2m⋅s−1.

Part b

The mass of the object is$0.971\mathrm{k}\mathrm{g}$.