Question

2. A hammer of mass 1 kg falls freely from a height of 20 m. a. Calculate the KE of the hammer just before it touches the ground. b. Calculate the velocity of the hammer just before it touches the ground. c. Does the velocity of a hammer depend on the mass of the hammer?

Answer 1

Answer

• Velocity = 20 m/s
• Kinetic Energy = 200 J

Explanation

Given

• Mass of the hammer = 1 kg
• Height = 20 m

To Find

• Kinetic Energy just before the hammer touch the ground
• Velocity of thr hammer
• If the Velocity depend on the mass of the body

Solution

• We shall first find the velocity of the body as we need that to find the Kinetic Energy.

✭ Velocity of the Hammer

→ v = √2gh

• G = 10 m/s²
• H = 20 m

→ v = √{2 × 10 × 20}

→ v = √400

→ v = 20 m/s

✭ Kinetic Energy of the Hammer

→ KE = ½ mv²

→ KE = ½ × 1 × 20²

→ KE = ½ × 400

→ KE = 200 J

Qn 3

• Yes Velocity depends on mass. As mass increases Velocity decrease and as mass decrease velocity increase

Answer 2

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have given a hammer of mass 1kg which falls freely from the height of 20m. Then, we have to find it's:-

• Kinetic Energy just before reaching the ground.
• It's velocity just before reaching the ground.

Does, the Velocity of the hammer depend upon the mass of the hammer.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, f1st of all we will calculate the velocity of the hammer by using 3rd eq. if motion we will substitute the given values in it and hence, will got the value of velocity. Then we will find the Kinetic Energy using Kinetic Energy's formula and substituting the values in it. Then we will be able to get the Kinetic Energy of hammer and at last we will simply find that does the velocity of hammer depend upon mass of the hammer.

Let's Do It ⚡

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

_____________________________

Given:-

• Mass of the hammer = 1kg
• Height from which the hammer is dropped = 20m

Find:-

• Kinetic Energy of the hammer.
• Velocity of the hammer just before reaching the ground.
• Is velocity is depend upon mass of the hammer.

Solution:-

➋ $\underline{\red{\textsf{Calculating the velocity of the hammer:}}}$

Here, using

$:\implies \: \: \underline{\boxed{\sf v^2 - u^2 = 2gs}} \quad \bigg\lgroup\sf {3}^{rd}eq. \: of \: motion \bigg\rgroup$

$\sf where \small{ \begin{cases} \sf u = 0 m/s \\ \sf g = 9.8 {m/s}^{2} \\ \sf s = 20m\end{cases}}$

⛂ Substituting these values:

$:\Longrightarrow \: \: \sf v^2 - u^2 = 2gs$

$:\Longrightarrow \: \: \sf v^2 - (0)^2 = 2(9.8)(20)$

$:\Longrightarrow \: \: \sf v^2 -0= 2(196)$

$:\Longrightarrow \: \: \sf v^2=392$

$:\Longrightarrow \: \: \sf v= \sqrt{392}$

$:\Longrightarrow \: \: \sf v=19.79m(approx.)$

$:\Longrightarrow \: \: \sf v=19.8m/s$

$\underline{\boxed{\sf \therefore Velocity\:of\:the\: hammer\:just\: before\: reaching \: the \: ground \: is \: 19.8m/s}}$

______________________________

➊ $\underline{\green{\textsf{Calculating the Kinetic Energy of the hammer:}}}$

Here, using

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

$\sf where \small{ \begin{cases} \sf m = 1kg \\ \sf v = 19.8m/s\end{cases}}$

⛇ Substituting these values:

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

$\dashrightarrow\sf K.E. = \dfrac{1}{2} \times 1 \times (19.8)^{2}$

$\dashrightarrow\sf K.E. = \dfrac{1}{2} \times 1 \times 392.04$

$\dashrightarrow\sf K.E. = \dfrac{392.04}{2}$

$\dashrightarrow\sf K.E. = 196.02J$

$\underline{\boxed{\sf \therefore Kinetic \: Energy\:of\:the\: hammer\:just\: before\: reaching \: the \: ground \: is \: 196.02J}}$

___________________________

➌ $\underline{\pink{\textsf{Is the velocity of the hammer depend on the mass of the hammer:}}}$

No, the velocity of the hammer is not depended upon the mass of the hammer as velocity is given by v = √(2gs) which can be seen easily that it doesn't depend upon the mass.