Question

What is the mass of an object with kinetic energy of 1000 Joules and velocity of 5 meters per second?

Answer 1

Understanding the question: This question says that we have to find out the mass of an object with kinetic energy of 1000 Joules and velocity of 5 meters per seconds. Let's solve this question!

Provided that:

• Kinetic energy = 1000 Joules

• Velocity = 5 m/s

To calculate:

• Mass of the object

Solution:

• Mass of the object = 80 kg

Using concept:

• Formula to calculate kinetic energy

Using formula:

• ${\sf{E_k \: = \dfrac{1}{2} mv^2}}$

• Where, E_k denotes kinetic energy, m denotes mass, v denotes velocity

Full solution:

$:\implies \sf E_k \: = \dfrac{1}{2} mv^2 \\ \\ :\implies \sf 1000 = \dfrac{1}{2} \times m \times (5)^{2} \\ \\ :\implies \sf 1000 = \dfrac{1}{2} \times m \times 25 \\ \\ :\implies \sf 1000 = \dfrac{1}{2} \times 25m \\ \\ :\implies \sf 1000 = \dfrac{25m}{2} \\ \\ :\implies \sf 1000 = 12.5m \\ \\ :\implies \sf \dfrac{1000}{12.5} \: = m \\ \\ :\implies \sf \dfrac{10000}{125} \: = m \\ \\ :\implies \sf \dfrac{10000}{125} \: = m \\ \\ :\implies \sf 80 \: = m \\ \\ :\implies \sf m \: = 80 \: kg \\ \\ :\implies \sf Mass \: = 80 \: kilograms$

Therefore, the mass of the object is 80 kilograms!

Verification:

$:\implies \sf E_k \: = \dfrac{1}{2} mv^2 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 80 \times (5)^{2} \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 80 \times 25 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 2000 \\ \\ :\implies \sf E_k \: = \dfrac{2000}{2} \\ \\ :\implies \sf E_k \: = 1000 \: J \\ \\ :\implies \sf Kinetic \: energy \: = 1000 \: Joules$

Henceforth, verified!

Answer 2

Explanation:

Given:-

Kinetic Energy=1000J

Velocity=v=5m/s

To find:-

Mass if the object=m

Solution:-

We know that

$\boxed{\sf K.E=\dfrac{1}{2}mv^2}$

• Substitute the values

$\\ \sf\hookrightarrow 1000=\dfrac{1}{2}m\times (5)^2$

$\\ \sf\hookrightarrow 1000=\dfrac{m}{2}\times 25$

$\\ \sf\hookrightarrow m=\dfrac{1000\times 2}{25}$

$\\ \sf\hookrightarrow m=\dfrac{2000}{25}$

$\\ \sf\hookrightarrow m=80kg$

Hence

Mass of the object is 80kg