A hammer with a 500-g head exerts an average force of 810n on a nail speed as it drives the nail 4 mm into wall. What was the speed of the hammer head when it hit the nail?
work done = change in Ke
(1/2) (.5)(v^2) = 810 * 4 * 10^-3
To find the speed of the hammer head when it hit the nail, we can use the principle of conservation of energy.
The work done by the hammer on the nail is equal to the change in kinetic energy of the hammer head. This can be represented as:
Work = Change in kinetic energy
The work done by the hammer is equal to the force applied by the hammer multiplied by the distance over which the force is applied. In this case, the force applied is 810 N and the distance is 4 mm (or 0.004 m). Therefore, we can write:
Work = Force * Distance
Substituting the given values:
Work = 810 N * 0.004 m
Now, let's consider the change in kinetic energy of the hammer head. The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy. Since the hammer head starts from rest, the initial kinetic energy is zero. The final kinetic energy can be calculated using the formula:
Kinetic energy = (1/2) * mass * velocity^2
The mass of the hammer head is given as 500 g, which can be converted to 0.5 kg. Now, let's assume the final velocity of the hammer head is v m/s. Therefore, the final kinetic energy can be written as:
Final kinetic energy = (1/2) * 0.5 kg * v^2
Since the hammer does work on the nail, the work done by the hammer is equal to the change in kinetic energy:
Work = Final kinetic energy - Initial kinetic energy
Substituting the values:
810 N * 0.004 m = (1/2) * 0.5 kg * v^2
Now, we can solve for the velocity of the hammer head (v):
v^2 = (2 * 810 N * 0.004 m) / 0.5 kg
v^2 = 648 m^2/s^2
v = sqrt(648) m/s
v ≈ 25.45 m/s
Therefore, the speed of the hammer head when it hit the nail was approximately 25.45 m/s.