Calculating Average Force on a Dummy in Crash Test | Physics Homework Help

[sheri1987]

1. A set of crash tests consists of running a test car moving at a speed of 11.6 m/s (25.52 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 55 kg (121 lbs) dummy is found to move a distance of 0.81 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.

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The Attempt at a Solution

 

[cristo]

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[m2003]

The average force acting on the dummy can be calculated using the formula F = m*a, where F is the force, m is the mass of the dummy, and a is the acceleration. In this case, the acceleration can be calculated using the formula a = (vf-vi)/t, where vf is the final velocity (0 m/s), vi is the initial velocity (11.6 m/s), and t is the time it takes for the car to come to a complete stop.

First, we need to convert the initial velocity from m/s to m/h. We can do this by multiplying 11.6 m/s by 3600 seconds (1 hour). This gives us an initial velocity of 41,760 m/h.

Next, we need to calculate the time it takes for the car to come to a complete stop. This can be done using the formula t = d/v, where d is the distance (0.81 m) and v is the initial velocity (41,760 m/h). This gives us a time of 0.0000194 seconds.

Now, we can plug in the values into the formula for acceleration: a = (0 - 41,760)/0.0000194 = -2,151,546,392 m/s^2

Finally, we can use the formula for force to calculate the average force acting on the dummy: F = 55 kg * -2,151,546,392 m/s^2 = -1.18 x 10^11 N.

This means that the average force acting on the dummy during the crash test is approximately 118 billion newtons (N). This is an incredibly large force and highlights the importance of advanced seat belt systems in protecting occupants during car crashes. It also emphasizes the need for continued research and development in car safety to reduce the impact and force experienced by passengers during accidents.