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Kyrre Hovda said:Hi everyone!
need to calculate the impact force done by the ladder to the head explained in the drawing. Can anyone help?
Kyrre
Kyrre Hovda said:Hi PeroK,
the ladder is falling onto the head
PeroK said:The force depends on the rigidity of the ladder and your skull. If the ladder had a thick foam coating, then that would reduce the impact force. It also critically depends on how much you are able to move during the impact. If you stand rigidly then there will be a much higher force than if you bend your knees as the ladder strikes.
Kyrre Hovda said:The ladder is made from aluminium. Assume the head doesn't move much during impact.
PeroK said:That data is just as important as the mass of the ladder or the height of the person. You would need to measure the movement of the head during the impact to determine the force. If the head doesn't move at all, then the force tends to an infinite force.
Kyrre Hovda said:Lets say the head moves 5 cm. How do you calculate the force?
PeroK said:I take it this isn't homework, but an accident investigation of sorts?
How much physics do you know? Do you know what angular momentum is?
Kyrre Hovda said:Yes, it was an accident. I have calculated the angular speed using the equation in the piqture.
I have calculated the kinetic energy. Again see the picture :PPeroK said:As suggested by @jbriggs444 above, there is a shortcut simply by considering energy. The force acting over the distance (e.g. ##d = 5cm##) must equal the kinetic energy lost by the ladder. And the kinetic energy of the ladder is equal to the gravitational potential energy lost.
Approximately, therefore, the force is given by ##F = \frac{mgh}{d}##, where ##h## can be calculated from the length and angle of the ladder:
##h = \frac{L}{2}(1 - \cos \theta)##
Although, quite what this calculation means in physical terms is not clear.
Note: if you assume that the angle you have is the final angle, then that takes care of any additional PE lost in the collision itself.
Kyrre Hovda said:I have calculated the kinetic energy. Again see the picture :P
The first two terms in the series expansion of ##\cos \theta## yield ##1 - \frac{\theta^2}{2}##. This means that for "small" rotations, the 1's cancel and you have a kinetic energy scales as the square of the lean angle at impact.PeroK said:##h = \frac{L}{2}(1 - \cos \theta)##
Although, quite what this calculation means in physical terms is not clear.
Force of impact refers to the amount of force that is exerted on an object or person when it collides with another object or surface. It is typically measured in units of newtons (N).
The force of impact is calculated by using the formula F=ma, where F is the force, m is the mass of the object, and a is the acceleration of the object during the impact. The greater the mass and acceleration, the higher the force of impact.
The force of impact in a ladder to head collision can be affected by various factors such as the height from which the ladder falls, the weight of the ladder, the speed of the fall, and the angle of impact. The surface on which the head lands can also affect the force of impact.
A high force of impact to the head can result in serious injuries, such as traumatic brain injuries, skull fractures, and concussions. These injuries can lead to long-term consequences and may require immediate medical attention.
To reduce the force of impact in a ladder to head collision, safety precautions such as wearing a helmet, using proper ladder placement and securing the ladder, and avoiding working at heights alone can be implemented. It is also important to follow proper ladder safety guidelines and receive proper training before using a ladder.