Question

2. A hammer with a head of mass M is to be used to
drive nails horizontally into a wall. A force of F
required to penetrate the wall. Each blow should force the nail a distance 'x' into the wall. What should be the velocity of the hammer's head to
strike the nail?
​

Answer 1

Answer:

PrincessStargirl Genius

Hello mate here is your answer.

There's many different things at work here.

First, there's the issue of acceleration. Hammers are very hard and solid, so when you hit the nail head with the hammer, the energy and force of the blow is delivered at almost an instant. Hands, on the other hand, are rather soft, and will spread out the same amount of energy and acceleration over a longer time period, resulting in a lower force applied on the piece of wood. Different woods have different resistance to pressure, so it's still rather easy to push a nail through a sheet of balsa wood, for example, while it's much harder to push it through a sheet of oak.

Second, the hammerhead actually accumulates a lot of energy in the duration of the swing, stored as kinetic energy in the head. That's why hammerheads are heavy (and the higher force you need, the heavier the head) - it allows you to store more kinetic energy with the same velocity of the head. The maximum velocity your muscles are capable of is a lot more limited than the amount of energy they can deliver, when considering something as tiny as a nail.

Third, hammers work as an additional lever, allowing you to deliver more force as a trade-off with time. This works in tandem with the second point - a longer swing can give you more impact force. This also helps the hammerhead reach higher speeds than you would have while holding the head directly, as opposed to holding the shaft.

Fourth, you're simply not going to hit as hard with your bare fist. Your body has built-in safety mechanisms that try rather hard to prevent injury, and you can hurt yourself quite a bit by hitting a nail head-on. Note that it's quite easy to drive nails just by using a wooden board pressed straight against your hand and hitting the nail - this spreads out the force of the blow over your hand, preventing pain and injury and allowing you to hit harder.

Finally, raw force is probably the dominant factor here. Pushing allows you to use the full strength of your muscle, which is probably somewhere around your weight (with a rather large spread). On the other hand, hitting allows you to accumulate the strength of your muscles over the duration of the swing, allowing you to impart much bigger forces than would be possible with just pushing. Try driving nails just by pushing the hammer, and you'll see the difference rather easily - the only benefit you'll get from using a hammer is that you're not going to feel as much pain as when pushing against the much smaller nail head.

HOPE THIS MARK AS BRAINLIST

Answer 2

Answer: $\sqrt{\frac{2Fx}{M}$

Explanation:

Given data:

Force = F

Mass = M

Distance ( or displacement) = $x$

Velocity =?

Solution:

We know that,

Kinetic Energy = \frac{1}{2} × Mass × Velocity²

Here, Kinetic Energy is the same as the work done.

Kinetic Energy = Work

Kinetic Energy = Force × Displacement

Hence,

Force × Displacement = \frac{1}{2} × Mass × Velocity²

Substituting the values we get,

[tex]Fx = \frac{1}{2} Mv^{2} \\ 2Fx = Mv^{2} \\ \frac{2Fx}{M} = v^{2} \\ \sqrt{\frac{2Fx}{M} } [/tex]