A 0.450 kg hammer is moving horizontally at 6.00 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?

d = .5 a t^2

a = 6/t

.01 = .5 (6/t)t^2 = 3 t
t = .00333 s

F = change in momentum/change in time
= .45 *6/.00333 = 810 Newtons

answer is correct go ahead

good

To calculate the duration of the impact and the average force exerted on the nail, we can use the principles of conservation of linear momentum and work-energy theorem. Here is how to find the answers to both parts of the question:

(a) To calculate the duration of the impact, we can use the principle of conservation of linear momentum. Initially, the hammer is moving at a speed of 6.00 m/s, and after striking the nail, it comes to rest. The linear momentum before and after the impact should be equal.

We can use the equation:
(initial momentum) = (final momentum)

The initial momentum is the product of the hammer's mass and its initial velocity:
initial momentum = mass * initial velocity

The final momentum is zero because the hammer comes to rest:
final momentum = 0

Setting the initial momentum equal to zero, we have:
mass * initial velocity = 0

Now, we can solve for the duration of the impact by finding the time it takes for the hammer to decelerate from 6.00 m/s to 0 m/s using the equation of motion: v = u + at (where v is final velocity, u is initial velocity, a is acceleration, and t is time).

0 = 6.00 m/s + a * t
Since v = 0 m/s, we can rearrange the equation:
6.00 m/s = a * t

We also need to find the acceleration using the equation:
a = (change in velocity) / time
Since the change in velocity is 6.00 m/s (initial velocity of 6.00 m/s minus final velocity of 0 m/s), we have:
a = 6.00 m/s / t

Substituting this value of acceleration into the previous equation, we have:
6.00 m/s = (6.00 m/s / t) * t
6.00 m/s = 6.00 m/s
Thus, the duration of the impact is t = 1.00 seconds.

(b) To calculate the average force exerted on the nail, we can use the work-energy theorem. The work done by the force exerted on the nail is equal to the change in kinetic energy of the hammer:

Work = Change in Kinetic Energy

The initial kinetic energy is given by:
Initial kinetic energy = (1/2) * mass * initial velocity^2

The final kinetic energy is zero because the hammer comes to rest:
Final kinetic energy = 0

Therefore, the work done is equal to:
Work = Final kinetic energy - Initial kinetic energy = 0 - [(1/2) * mass * initial velocity^2]

Now, the work done is also equal to the force acting on the nail multiplied by the distance the nail moves into the board (displacement). In this case, the displacement is 1.00 cm, which is equivalent to 0.01 m.

Therefore, we can write:
Work = Force * displacement

Substituting the values into the equation, we have:
0 - [(1/2) * mass * initial velocity^2] = Force * 0.01 m

Solving for the force, we get:
Force = [(1/2) * mass * initial velocity^2] / 0.01 m

Substituting the known values, we have:
Force = [(1/2) * 0.450 kg * (6.00 m/s)^2] / 0.01 m

Calculating this expression, we find the average force exerted on the nail.

This is horribly set up; please improve