A(n) 4.5 lb hammer head, traveling at 4.7 ft/s

strikes a nail and is brought to a stop in
0.0009 s.
The acceleration of gravity is 32 ft/s
2
.
What force did the nail receive?
Answer in units of lb

Force * time = (hammer head momentum) = (mass)* (velocity)

The mass must be in slugs. Divide weight by g for slugs.

4.5 lb = 0.141 slugs

The force will be in pounds if velocity is in ft/s.

Well, looks like we have quite the hammerhead collision here! Let's calculate the force the nail received.

First, let's convert the weight of the hammerhead from pounds to mass in slugs. Since weight is given in pounds, we divide by the acceleration due to gravity to get the mass. So, 4.5 lb / 32 ft/s^2 = 0.140625 slugs.

Now, let's calculate the change in velocity. The initial velocity is 4.7 ft/s, and the final velocity is 0 ft/s since the hammerhead is brought to a stop. So, the change in velocity is 0 - 4.7 = -4.7 ft/s.

Then, we can calculate the force using Newton's second law, which states that force equals mass times acceleration. The acceleration is the change in velocity divided by the time it took, which is -4.7 ft/s / 0.0009 s = -5222.22222 ft/s^2.

Finally, we can calculate the force using F = ma. So, Force = 0.140625 slugs * -5222.22222 ft/s^2 = -732.638889 lb.

Ah, well, it appears the nail received a force of -732.638889 lb. I guess it really nailed the impact!

To find the force received by the nail, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the mass of the hammer head is given as 4.5 lb, and the acceleration is the change in velocity divided by the time taken.

First, let's convert the mass of the hammer head from lb to slugs. Since 1 slug is equal to the mass that would be accelerated at 1 ft/s² when a force of 1 lbf is applied, we divide the mass by the acceleration due to gravity, 32 ft/s².

Mass (in slugs) = Mass (in lb) / Acceleration due to gravity
Mass (in slugs) = 4.5 lb / 32 ft/s²

Next, let's calculate the acceleration using the formula:
Acceleration (a) = Change in velocity (Δv) / Time (t)
Acceleration (a) = (Final velocity - Initial velocity) / Time (t)
Acceleration (a) = (0 ft/s - 4.7 ft/s) / 0.0009 s

Finally, let's calculate the force using Newton's second law:
Force (F) = Mass (m) × Acceleration (a)

Now let's put it all together:

Mass (in slugs) = 4.5 lb / 32 ft/s² = 0.140625 slugs

Acceleration (a) = (0 ft/s - 4.7 ft/s) / 0.0009 s = -5200 ft/s² (negative sign indicates deceleration)

Force (F) = Mass (m) × Acceleration (a)
Force (F) = 0.140625 slugs × -5200 ft/s²

Finally, we can convert the force from slugs × ft/s² to lb by multiplying by the acceleration due to gravity, 32 ft/s².

Force (F) = 0.140625 slugs × -5200 ft/s² × 32 ft/s²

Calculating this gives us:
Force (F) ≈ -290 lb (approximately)

Therefore, the force received by the nail is approximately -290 lb. The negative sign indicates that the force is acting in the opposite direction of motion.

To find the force received by the nail, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the mass of the hammer head is given as 4.5 lb, and the acceleration can be calculated using the change in velocity and time.

1. First, let's calculate the acceleration (a) of the hammer head using the given information. We'll use the formula a = Δv / t, where Δv is the change in velocity and t is the time taken.

Given:
Initial velocity (u) = 4.7 ft/s
Final velocity (v) = 0 ft/s (stopped)
Time (t) = 0.0009 s

Δv = v - u
Δv = 0 - 4.7
Δv = -4.7 ft/s (negative because the velocity decreases)

a = Δv / t
a = -4.7 / 0.0009 ft/s^2
a ≈ -5222.22 ft/s^2 (approximated to five decimal places)

2. Now let's calculate the force (F) applied to the nail using Newton's second law of motion: F = m * a.

Given:
Mass of hammer head (m) = 4.5 lb
Acceleration (a) = -5222.22 ft/s^2 (negative because it opposes the motion)

F = m * a
F = 4.5 lb * (-5222.22 ft/s^2)
F ≈ -23499.99 lb*ft/s^2 (approximated to two decimal places)

Therefore, the force received by the nail is approximately -23499.99 lb. Note that the negative sign indicates that the force is opposing the motion.