Question

Which has greater kinetic energy: a tennis ball that has a mass of 0.3 kg travelling at 80 m/s, or a train that has a mass of 10000 kg and is moving at 0.1 m/s?

Answer 1

Answer:

• K.E. of the tennis ball is greater than the K.E. of Train.

Explanation:

Given:-

• Mass of tennis ball, m = 0.3 kg
• the velocity of Tennis ball, v = 80 m/s

• Mass of Train, M = 10000 kg
• the velocity of Train, V = 0.1 m/s

To find:-

• Which among the tennis ball and Train will have a greater kinetic energy

Formula required:-

• Formula to calculate Kinetic energy

        K.E. = 1/2 m v²

[ Where K.E. is kinetic energy, m is mass and v is the velocity of Body ]

Solution:-

Using the formula for Kinetic energy

→ K.E. of tennis ball = 1/2 m v²

→ K.E. of tennis ball = 1/2 × 0.3 × 80²

→ K.E. of tennis ball = 960 J

and,

→ K.E. of Train = 1/2 M V²

→ K.E. of Train = 1/2 × 10000 × 0.1²

→ K.E. of Train = 50 J

We can clearly conclude that,

• The kinetic energy of the tennis ball is greater than the kinetic energy of the Train.

Answer 2

$\large{\underline{\boxed{\boxed{ \sf Let's \: Understand \: Concept!}}}}$

Here, we have given Mass and Velocity of a tennis ball and a train and we have to find whose kinetic energy is greater. Here, we simply use Formula for kinetic energy in both cases and will find whose kinetic energy is greater.

Let's Do This⚡

$\huge{\underline{\boxed{\bf{AnSwer}}}}$

____________________________

$\large{\underline{\textbf{Given:-}}}$

• Mass of Tennis Ball = 0.3kg
• Velocity of Tennis Ball = 80m/s
• Mass of Train = 10000kg
• Velocity of Train = 0.1m/s

$\large{\underline{\textbf{Find:-}}}$

• Which object has greater kinetic energy.

$\large{\underline{\textbf{Solution:-}}}$

Here, Using

$\underline{\boxed{\blue{\sf Kinetic \: Energy = \dfrac{1}{2}mv^2}}}$

$\underline{\red{\textbf{ For Tennis Ball: }}}$

$\small{\begin{cases} \sf m = 0.3kg \\ \sf v = 80m/s \end{cases}}$

☯Substituting these values:-

$\dashrightarrow\sf Kinetic \: Energy_{Tennis\:Ball} = \dfrac{1}{2}mv^2$

$\dashrightarrow\sf Kinetic \: Energy_{Tennis\:Ball} = \dfrac{1}{2} \times (0.3) \times (80)^2$

$\dashrightarrow\sf Kinetic \: Energy_{Tennis\:Ball} = \dfrac{1}{2} \times 0.3\times 6400$

$\dashrightarrow\sf Kinetic \: Energy_{Tennis\:Ball} = \dfrac{1}{2} \times 1920$

$\dashrightarrow\sf Kinetic \: Energy_{Tennis\:Ball} = \dfrac{1920}{2}$

$\dashrightarrow\sf Kinetic \: Energy_{Tennis\:Ball} = 960J$

$\small{ \boxed{\therefore\sf Kinetic \: Energy_{Tennis\:Ball} = 960J}}$

Now,

$\underline{\pink{\textbf{ For Train: }}}$

$\small{\begin{cases} \sf m = 10000kg \\ \sf v = 0.1m/s \end{cases}}$

✪Substituting these values:-

$\dashrightarrow\sf Kinetic \: Energy_{Train} = \dfrac{1}{2}mv^2$

$\dashrightarrow\sf Kinetic \: Energy_{Train} = \dfrac{1}{2} \times 10000 \times (0.1)^2$

$\dashrightarrow\sf Kinetic \: Energy_{Train} = \dfrac{1}{2} \times 10000 \times 0.01$

$\dashrightarrow\sf Kinetic \: Energy_{Train} = \dfrac{1}{2} \times 100$

$\dashrightarrow\sf Kinetic \: Energy_{Train} = \dfrac{100}{2}$

$\dashrightarrow\sf Kinetic \: Energy_{Train} = 50J$

$\small{ \boxed{\therefore\sf Kinetic \: Energy_{Train} = 50J}}$

___________________________

Here, we can easily see that

➜ Kinetic Energy$\sf _{Tennis\:Ball}$ > Kinetic Energy$\sf _{Train}$

Hence, Kinetic Energy of Tennis Ball is greater than Kinetic Energy of Train.