An object that gradually accelerates or decelerates exerts a force that you can sometimes gauge through sense of touch. You can tell how fast a car is accelerating by the pressure of the seat on your back, or how quickly you accelerate someone's motion when you push him on a swing. But impact forces (which we usually avoid, if possible) seem to slow an object all at once. Actually, every object will deform at least slightly and distribute the impact over a small time and distance. Therefore, you can calculate impact similarly to other forces, using kinetic equations.
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Obtain the mass and the initial dimensions of the object. You can determine mass by weighing smaller objects or consulting manufacturer data for larger objects. Measure the dimensions of the object along any direction in which it might make the impact of collision.
Determine the speed of the object immediately prior to impact. You can determine the speed of an object in free fall by using an energy balance equation where you equate its potential energy at the initial position to its kinetic energy immediately before impact. The equation is m * g * h = m * v * v, where m = mass, g = acceleration due to gravity, h = initial height and v = velocity immediately prior to impact. If you cannot accurately determine its speed with a formula, you can measure it using a high-speed camera.
Determine the magnitude of the object's deformation along the line of impact. For example, if a vehicle crashed into a wall head-on, you would measure the resulting distance from the front to the back of the car, and subtract that distance from its initial length. Other deformations, such as a ballooning in width, are not important.
Calculate kinetic energy immediately prior to impact. Substitute its velocity at this point into the formula, KE = 0.5 * m * v * v, where KE equals kinetic energy, m equals mass and v = velocity.
Set up an equation that balances the amount of work that went into the object with its change in kinetic energy. Work is defined as an amount of force that acts through a certain distance. Therefore, the work on this object equals some force multiplied by the measured deformation, or F * d. Its change in kinetic energy equals the kinetic energy immediately prior to impact minus the kinetic energy at the point of maximum deformation. Because the object does not move when maximally deformed, the kinetic energy is zero and the change is equal to the kinetic energy previously calculated. Balancing kinetic energy and work results in the equation, KE = F * d. Solve for F.
Tips and warnings
- This process only works for an inelastic object that maintains its deformation after impact. It would not work for a rubber ball, unless you somehow knew exactly how much it deformed when it hit. The easiest way to calculate the force of shock for elastic collisions is to use a high-speed camera to measure how long the object took to maximally deform. In this case, is easier to use the formula force = mass * acceleration.
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