Question

Молоток массой m= 0.8 кг в момент удара о шляпку гвоздя имеет скорость v=4 м/с. в результате удара гвоздь входит в стену на s=1.5 см. определите среднюю силу сопротивления материала

Answer 1

M*V^2/2=F*S
F=m*V^2/2*S=0,8*16/2*0,015=426,7Н

Answer 2

Problem Analysis

We are given the mass of a hammer, the velocity of the hammer when it strikes a nail, and the distance the nail penetrates into a wall. We need to determine the average resistance force exerted by the material.

Solution

To find the average resistance force exerted by the material, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. The momentum of an object is given by the product of its mass and velocity.

Let's denote the mass of the hammer as m (0.8 kg), the velocity of the hammer as v (4 m/s), and the distance the nail penetrates into the wall as s (1.5 cm or 0.015 m).

The momentum before the collision is given by m * v. The momentum after the collision is zero because the nail comes to rest in the wall. Therefore, we can equate the two momenta:

m * v = 0

Solving for the average resistance force, we have:

Average resistance force = m * v / t

where t is the time taken for the nail to come to rest in the wall.

To find t, we can use the equation of motion:

s = v0 * t + (1/2) * a * t^2

where s is the distance, v0 is the initial velocity (which is zero in this case), and a is the acceleration.

Since the nail comes to rest, the final velocity is zero. Therefore, the equation simplifies to:

s = (1/2) * a * t^2

Solving for t, we have:

t = sqrt(2 * s / a)

where sqrt denotes the square root.

Now we can substitute the values into the equations to find the average resistance force.

Calculation

Given: - Mass of the hammer, m = 0.8 kg - Velocity of the hammer, v = 4 m/s - Distance the nail penetrates into the wall, s = 1.5 cm = 0.015 m

We need to find the average resistance force.

Using the equation t = sqrt(2 * s / a), we need to find the acceleration a.

From the equation s = (1/2) * a * t^2, we can solve for a:

a = 2 * s / t^2

Substituting the given values, we have:

a = 2 * 0.015 / t^2

Now we can substitute the values of m, v, and t into the equation for the average resistance force:

Average resistance force = m * v / t

Answer

The average resistance force exerted by the material is 0.8 * 4 / t, where t is the time taken for the nail to come to rest in the wall, given by t = sqrt(2 * 0.015 / (2 * 0.015 / t^2)).

Let's calculate the value of t and then substitute it into the equation to find the average resistance force.