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Mathematically, explain how a car (A) with mass of 500 kg and velocity of 2 m/s has the same kinetic energy as a car (B) with mass of 20000 g and velocity of 10 m/s.

Respuesta :

elcharly64

Answer:

Both kinetic energies are equal

Explanation:

Kinetic Energy

Is the type of energy of an object due to its state of motion. It's proportional to the mass and the square of the speed.

The equation for the kinetic energy is:

[tex]\displaystyle K=\frac{1}{2}mv^2[/tex]

Where:

m = mass of the object

v = speed of the object

The kinetic energy is expressed in Joules (J)

There are two cars:

Car (A) with mass ma=500 kg and speed va= 2 m/s

Car (B) with mass mb=20,000 gr and speed vb= 10 m/s

Calculate the kinetic energy of both cars:

[tex]\displaystyle K_a=\frac{1}{2}m_av_a^2[/tex]

[tex]\displaystyle K_a=\frac{1}{2}500*2^2[/tex]

[tex]\displaystyle K_a=250*4=1,000 J[/tex]

To calculate the Kb, the mass must be expressed in kg:

mb=20,000/1,000 =20 Kg

[tex]\displaystyle K_b=\frac{1}{2}m_bv_b^2[/tex]

[tex]\displaystyle K_b=\frac{1}{2}20*10^2[/tex]

[tex]\displaystyle K_b=10*100=1,000 J[/tex]

Both kinetic energies are equal

The calculated kinetic energy values of the cars are the same. The kinetic energy is 1000 J for each of the cars.

Then, we can conclude that, car (A) with mass 500 kg and velocity of 2 m/s has the same kinetic energy as a car (B) with mass of 20000 g and velocity of 10 m/s.

Kinetic energy can be calculated using the formula

[tex]K.E = \frac{1}{2} mv^{2}[/tex]

Where K.E is the kinetic energy

m is the mass

and v is the velocity

  • For car (A)

m = 500 kg

and v = 2 m/s

Then,

[tex]K.E_{(A)} = \frac{1}{2} \times 500 \times 2^{2}[/tex]

[tex]K.E_{(A)} = \frac{1}{2} \times 500 \times4[/tex]

[tex]K.E_{(A)} = 1000 \ J[/tex]

  • For car (B)

m = 20000 g = 20 kg

v = 10 m/s

Then,

[tex]K.E_{(B)} = \frac{1}{2} \times 20 \times 10^{2}[/tex]

[tex]K.E_{(B)} = \frac{1}{2} \times 20 \times 100[/tex]

[tex]K.E_{(B)} =1000 \ J[/tex]

From above, we can observe that the calculated kinetic energy values of the cars are the same.

Hence, car (A) with mass 500 kg and velocity of 2 m/s has the same kinetic energy as a car (B) with mass of 20000 g and velocity of 10 m/s.

Learn more on calculating kinetic energy here: https://brainly.com/question/11580018

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