Question

A 0.850 kg hammer is moving horizontally at 9.00 m/s when it strikes a nail and comes to rest after driving it 1.00 cm into a board.

(a) Calculate the duration of the impact.

(b) What was the average force exerted on the nail?
N (downward)

Answer 1

We know from the work energy theorem
Work = change in kinetic energy
Work = force*distance
Force*distance = Initial kinetic energy - Final kinetic energy
F*(d) = (1/2)mV² - 0
since finally hammer stops therefore the final energy is zero
d is distance travelled by nail = 1*10^-2 m
m is mass of hammer = 0.85 kg
V is velocity of hammer = 9 m/s
F*(1*10^-2) = (1/2)*(0.85)*9²
F = 3442.5 N
(a) We know that
Impulse = change in momentum
Force*time = Initial momentum - final momentum
F*t = mV - 0
3442.5 *t = 0.85*9
t = 0.0022 s
(b) we have already calculated the force
F = 3442.5 N