Question

What average force is exerted on the nail when a 0.500-kg hammer, initially moving at 15.0 m/s, is brought to rest in 2.80 mm?

A) 17,857 N
B) 35,714 N
C) 71.4 N
D) 35.7 N

How much is the nail compressed if it is 2.50 mm in diameter and 6.00-cm long?

A) 1.75 mm
B) 2.80 mm
C) 3.50 mm
D) 5.60 mm

Answer 1

The average force exerted on the nail is approximately 35.71 N.

Step-by-step explanation:

To calculate the average force exerted on the nail, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the hammer is brought to rest, so its final velocity is 0. The initial velocity is given as 15.0 m/s.

Using the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we can find the acceleration. Rearranging the equation, we have a = (v² - u²) / (2s).

Substituting the given values, we get a = (0 - (15.0²)) / (2 * (-2.80 * 10⁻³)).

Now we can calculate the force using F = ma.

Substituting the mass and acceleration, we have F = 0.500 kg * ((0 - (15.0²)) / (2 * (-2.80 * 10⁻³))).

Simplifying the equation, we find that the average force exerted on the nail is approximately 35.71 N.