from what height can a 1 kg falling object cause fracture of the skull?assume that the object is hard and the area of contact with the skull is 1 cm sq. and that the duration of the impact is 10^-3 sec.rupture strength for skull is 10^8N/m^2

To determine the height from which a 1 kg falling object can cause a skull fracture, we need to use the concept of energy and the relationship between force, area, and pressure.

First, let's calculate the energy that the falling object possesses at a certain height. The potential energy (PE) of an object is given by the equation:

PE = m * g * h,

where m is the mass of the object (1 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height from which the object is dropped.

Next, we need to calculate the force exerted by the falling object on the skull when it comes into contact. We can use the equation:

Force = Pressure * Area,

where Pressure is the maximum pressure exerted on the skull and Area is the area of contact (1 cm^2, which is equal to 0.0001 m^2).

Given that the rupture strength of the skull is 10^8 N/m^2, we can substitute these values into the equation to find the force:

Force = (10^8 N/m^2) * (0.0001 m^2) = 10^4 N.

Now, to determine whether this force can cause a skull fracture, we compare it to the force required to fracture the skull. If the force exerted by the falling object is greater than the force required for fracture, then a skull fracture will occur.

Therefore, the condition for fracture is:

Force > Force required for fracture.

In this case, the force required for fracture is not given, so we cannot determine the exact height from which the object will cause a fracture. However, we can set up the equation to find this height. By equating the force exerted by the object to the force required for fracture, we can solve for the height:

PE = Force * Distance,

where Distance is the distance over which the impact occurs (which is not given). However, we know that the duration of the impact is 10^-3 sec, so we can assume that the distance over which the impact occurs is equal to the velocity of the falling object multiplied by the duration of impact.

Thus, the equation becomes:

PE = Force * (Velocity * Time),

where Velocity = g * Time (assuming no air resistance), and PE is the potential energy calculated earlier.

By substituting the known values and solving for the height (h), we can find from what height the 1 kg falling object can cause a fracture of the skull.

Note: Please keep in mind that this is a simplified explanation, and real-life factors such as bone density, angle of impact, and other variables may also affect the fracture threshold. If you have a specific case or concern, it is recommended to consult a medical professional.