A 25 N hammer head traveling at 4 ms strikes a steel spike n

A 2.5 N hammer head traveling at 4 m/s strikes a steel spike nail. The nail is 3.5 mm diam x 80 mm long.

Estimate the impact force from the hammer. Assume negligible velocity after impact and negligible nail mass

Ans. 9950 N

Solution

>> Now,

Here, m = mass of hammere = 2.5/9.81 Kg

v = Velocity of travelof hammere head = 4 m/s

a = Deceleration of the hammer head when it hits the nail.

Now, Let\'s say that the hammer compresses the nail x = 3.85 mm=0.00385 m in one stroke, and further assume that the deceleration of the hammer head is constant .

So, a = 4/t ,

Then , by using Newton\'s 2nd Equation of Motion,

s = ut + (1/2)at²

=> 0.08 = 4t + 0.5*a*t² ........(1).....

Now, when nail is compressing,

Then Equation of Motion is :

x = (1/2)a*t²

Putting, a = 4/t and, as, x = 0.0035 m

=> t = 0.0192 sec

Putting this in Equation (1).

and, a = 39043.8 m/s²

So, Force exerting = m*a = (2.5/9.81)*39043.8 = 9950 N ...ANSWER....