Question

A hammer of mass 50 kg moving at 50 m/s strikes a nail. The nail stops the hammer in a very short time of 5 sec. What is the force of the nail on the hammer ?​

Answer 1

F = ma

$mass = 50kg \\ acceleration = \frac{v - u}{t} = \frac{final \: velocity - initial \: velocity}{time}$

The nail stops the hammer this means that the final velocity of this hammer is 0m/s.

$50kg \times \frac{(0 - 50)ms {}^{ - 1} }{5s} \\ 50kg \times \frac{ - 50ms {}^{ - 1} }{5s} \\ 50kg \times ( - 10ms {}^{ - 2} ) \\ = - 500 \: newtons$

If we talk about magnitude then its 500 N.

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Answer 2

$\Huge{\underline{\sf{\orange{Required \; Solution : }}}}$

Answer : 500 N (in opposite direction)

As per the provided information in the given question, we have :

• Mass of hammer, m = 50 kg
• Initial velocity, u = 50 m/s
• Final velocity, v = 0 m/s [as it stops]
• Time taken, t = 5 sec

We've been asked to calculate the force of the nail on the hammer.

Force is the product of mass, i.e $\huge{\sf{\orange{ F = ma }}}$

• F denotes force
• m denotes mass
• a denotes acceleration

Acceleration is the rate of change in velocity. Or mathematically, $\huge{\sf{\orange{ a= \dfrac{v-u}{t} }}}$

• v denotes final velocity
• u denotes initial velocity
• t denotes time
• a denotes acceleration

$\longrightarrow{\huge{\sf{\orange{F= ma}}}}$

$\longrightarrow\sf{F = m\Bigg \lgroup \dfrac{v-u}{t} \Bigg \rgroup}$

$\longrightarrow\sf{F = 50 \Bigg \lgroup \dfrac{0-50}{5} \Bigg \rgroup \; N}$

$\longrightarrow\sf{F = 50 \Bigg \lgroup \dfrac{-50}{5} \Bigg \rgroup \; N}$

$\longrightarrow\sf{F = 50 \Bigg \lgroup -10 \Bigg \rgroup \; N}$

$\longrightarrow\boxed{\pmb{\sf {\orange{F = -500 \; N}}}}$

Therefore, force of the nail on the hammer is 500 N. Negative sign indicates that force has been applied in the opposite direction.