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

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

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Trúc Chi 5 years 2021-08-05T12:00:55+00:00 1 Answers 186 views 1

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  1. hongcuc2
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    2021-08-05T12:02:39+00:00
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    Answer:

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

    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=\frac{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= \frac{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 = \frac{1}{2} m (100 \ m^2/s^2)

    Multiply on the right side.

    105 \ kg *m^2/s^2 = m (\frac{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}= \frac{ 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.

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