Question

A 120 kg airplane wheel moves at 98 m/s. how fast must a 2.35 g toy car wheel move in order to have the same kinetic energy as the airplane wheel?

Answer 1

Answer:

$\bigstar{\bold{Velocity\:of\:the\:toy\:car =22145.4\:m/s}}$

Explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• Mass of airplane wheel (M) = 120 kg
• Velocity of airplave wheel (V) = 98 m/s
• Mass of toy car (m) = 2.35 g = 2.35 × 10⁻³ kg

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• Velocity of the toy car (v)

$\Large{\underline{\underline{\it{Solution:}}}}$

➣ Here we have to find the velocity of the toy car so as to have the same K.E of the airplane wheel.

➣ First we have to find the kinetic energy of the airplane wheel.

➣ K.E of a body is given by

    K. E = 1/2 × m × v²

    where m is the mass

    v is the velocity

➣ Substituting the data,

    K.E of airplane wheel = 1/2 × 120 × 98 × 98

    K.E of airplane wheel = 60 × 98 × 98

    K.E of airplane wheel = 576240 J

➣ Hence the K.E of the airplane wheel is 576240 J

➣ Now it is given that the toy car must have the same K.E

➣ Hence,

    K.E of the toy car = 576240 J

    1/2 × m × v² = 576240

➣ Substituting the data, we get the value for v

    1/2 × 2.35 × 10⁻³ × v² = 576240

    1.175 × 10⁻³× v² = 576240

     v² = 490417021.3

     v = √490417021.3

     v = 22145.4 m/s

➣ Hence the velocity of the toy car must be 22145.4 m/s

   $\boxed{\bold{Velocity\:of\:the\:toy\:car =22145.4\:m/s}}$

$\Large{\underline{\underline{\it{Notes:}}}$

➣ The kinetic energy of a body is defined as the enery possessed by it due to virtue of its motion.

➣ It is given by,

    K.E = 1/2 × m × v²

    where m is the mass and v is the velocity