Final answer:
In this physics question, a hammer strikes a nail and comes to rest after driving the nail into a board. We calculate the duration of the impact and the average force exerted on the nail. The impact duration is 0.0014 seconds and the average force exerted on the nail is -2250 Newtons.
Step-by-step explanation:
In this question, we are given the mass of a 0.450-kg hammer moving horizontally at 7.00 m/s. The hammer strikes a nail and comes to rest after driving the nail 1.00 cm into a board. We are asked to calculate the duration of the impact and the average force exerted on the nail.
To calculate the duration of the impact, we can use the equation distance = velocity * time. The distance the nail is driven into the board is given as 1.00 cm, which is equal to 0.01 m. The hammer initially has a velocity of 7.00 m/s and comes to rest, so its final velocity is 0.00 m/s. Therefore, the change in velocity is -7.00 m/s.
By substituting the known values into the equation, distance = velocity * time, we can solve for the time:
- distance = velocity * time
- 0.01 m = -7.00 m/s * time
- time = -0.01 m / -7.00 m/s
Simplifying the equation gives us:
time = 0.0014 s
Therefore, the duration of the impact is 0.0014 seconds.
To calculate the average force exerted on the nail, we can use the equation force = mass * acceleration. The hammer has a mass of 0.450 kg and comes to rest in the duration of the impact, which is 0.0014 seconds. Therefore, the acceleration is given by:
- acceleration = change in velocity / time
- acceleration = (-7.00 m/s - 0.00 m/s) / 0.0014 s
Simplifying the equation gives us:
acceleration = -5000 m/s²
By substituting the mass and acceleration into the equation force = mass * acceleration, we can solve for the average force:
- force = mass * acceleration
- force = 0.450 kg * -5000 m/s²
Simplifying the equation gives us:
force = -2250 N
Therefore, the average force exerted on the nail is -2250 Newtons.