A 1.1 kg hammer slams down on a nail at 5.0 m/s and bounces back at 1.0 m/s. If the impact lasts 1.0 ms, what average force is exerted on the nail?
To calculate the average force exerted on the nail, we can use the principle of impulse-momentum.
The impulse experienced by an object can be calculated using the equation:
Impulse = Change in momentum
The momentum of the hammer just before the impact can be calculated using the equation:
Initial momentum = Mass × Initial velocity
Similarly, the momentum of the hammer just after the impact can be calculated using the equation:
Final momentum = Mass × Final velocity
Now, the change in momentum is given by:
Change in momentum = Final momentum - Initial momentum
The impulse experienced by the nail during the impact is equal to the change in momentum. Since impulse is equal to the average force applied multiplied by the time of impact, we can write:
Impulse = Average force × Time of impact
By equating these two equations, we can find the average force exerted on the nail.
Step-by-step calculation:
1. Calculate the hammer's initial momentum:
Initial momentum = Mass × Initial velocity
= 1.1 kg × 5.0 m/s
2. Calculate the hammer's final momentum:
Final momentum = Mass × Final velocity
= 1.1 kg × (-1.0 m/s) [The negative sign indicates the opposite direction]
3. Calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
4. Calculate the impulse:
Impulse = Average force × Time of impact
5. Rearrange the equation to solve for the average force:
Average force = Impulse / Time of impact
Plug in the values and calculate to find the average force exerted on the nail.