Answer:
a) -586 N
b) -2148 N
Explanation:
If the hammer head has a weight of 4.9 N
f = m * a
m = f / a
m = 4.9 / 9.8 = 0.5 kg
The hammer head has a mass of 0.5 kg.
It had a speed of 3.2 m/s when it hit the nail, and was completely stopped in 0.45 cm. During the stopping it had constant acceleration.
I set up a reference system with origin at the point where the hammer first hits the nail and the positive X axis pointing down.
Then I use the equation for movement onder cosntant acceleration.
X(t) = X0 + V0 * t + 1/2 * a * t^2
X0 = 0
X(t) = V0 + 1/2 * a * t^2
At X = 0.45 cm the velocity will be zero
The equation for velocity under constant acceleration is:
V(t) = V0 + a * t
0 = V0 + a * t
a * t = -V0
a = -V0 / t
Replacing
X(t) = V0 * t - 1/2 * V0 / t * t^2
0.0045 = 3.2 * t - 1.6 * t
0.0045 = 1.6 * t
t = 0.0045 / 1.6
t = 0.0028 s
a = -3.2 / 0.0028 = -1143 m/s^2
Then the total force on the hammer is of:
f = m * a
f = 0.5 * -1143 = -571 N
This force will be the resultant of the reaction force from the nail (negative) and the force applied y the person (+15 N)
ft = fn + fp
fn = ft - fp
fn = -571 - 15 = -586 N
If the distance traveled was 0.12 cm
0.0012 = 3.2 * t - 1.6 * t
0.0012 = 1.6 * t
t = 0.0012 / 1.6
t = 0.00075 s
a = -3.2 / 0.00075 = -4267 m/s^2
f = 0.5 * -4267 = -2133 N
ft = -2133 - 15 = -2148 N