Suppose you hit a steel nail with a 0.495 kg hammer that is moving at 2.5 m/s wh

Question

Suppose you hit a steel nail with a 0.495 kg hammer that is moving at 2.5 m/s when it strikes the head of the nail and is subsequently brought to rest in 5.2 mm. In this problem you may ignore the interaction of gravity with the nail or the hammer. a)What average force, in Newtons, is exerted on the nail? b) While the force is acting, how much is the nail compressed if it is 2.4 mm in diameter and 5.85 cm long? Give your anser in meters, and assume Young's modulud of steel is 2.10 x 10^11 N/m^2. c) If the force you found in part (a) were transmitted in full through the 1.00 mm diameter tip of the nail, what pressure, in pascals, would the tip exert on the material it is entering?

Explanation / Answer

mass of hammer m = 0.495 kg

velocity v = 2.5 m/s

the distance moved by the hammer before come to rest on nail is s = 5.2 mm

a) average force exerted on the nail is  

workd energy theoremis work done = change in k.e

F*s = 0.5*m(v2^2-v1^2)

F = 0.5*m(v2^2-v1^2)/s

F = 0.5*0.495(0 - 2.5^2)/(5.2*10^-3) N

F = 297.5 N

b)

Nail diameter is d = 2.4 mm, length is l = 5.85 cm

the young's modulus of steel is y = 2.10*10^11 N/m2

we knwo the formula is Y = F*l/(A*dl)

dl = F*l/(A*Y)

dl = 297.5*0.0585/(pi*(1.2*10^-3)^2*2.10*10^11) m

dl = 1.8319397*10^-5 m

the compression in tehe nail is 1.8319397*10^-5 m

c) the pressure is P = F/A = 297.5 /(pi*0.5*10^-3)^2 = 120572208.53 N/m2 = 1205.7220853*10^5 Pa

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.