A car has a crumple zone that is 0.80 m (80 cm) long. In this car, the distance from the dummy to the steering wheel is 0.50 m. The car has a mass of 1,600 kg and the dummy has a mass of 75 kg. At the time of the crash, the car has a speed of 18 m/s. Based on the work-energy theorem, what is the smallest possible force that the dummy could experience during the crash?
An SUV crashes into a wall. The mass of the vehicle is 2,150 kg and the crumple zone rigidity is 342 kN. Assuming the safety cell is perfectly rigid, what will be the acceleration of the SUV during a crash as the crumple zone is collapsing?
please help thanks:)
A.) -9.35 kN
C.) -159 m/s squared
The right answer is -9.35
wow this app truly helped me
Thank you
To find the minimum force experienced by the dummy during the crash, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
First, let's calculate the initial kinetic energy of the car:
Kinetic energy = (1/2) * mass * velocity^2
= (1/2) * 1600 kg * (18 m/s)^2
Next, let's calculate the final kinetic energy of the car. We know that the car comes to a stop, so the final velocity is 0 m/s:
Final kinetic energy = (1/2) * mass * (0 m/s)^2
= 0 J (Joules)
The work done on the car during the crash is equal to the change in its kinetic energy:
Work = Final kinetic energy - Initial kinetic energy
= 0 J - [ (1/2) * 1600 kg * (18 m/s)^2 ]
Now, let's find the work done on the car by the force experienced by the dummy. The work done by a force is given by the equation:
Work = force * displacement * cos(theta)
In this case, the displacement is the distance from the dummy to the steering wheel, which is 0.50 m, and theta is the angle between the force and the displacement, which is 0 degrees because the angle is assumed to be in the same direction as the displacement.
Therefore, we can rewrite the equation as:
Force * 0.50 m * cos(0 degrees) = [ (1/2) * 1600 kg * (18 m/s)^2 ]
cos(0 degrees) equals 1, so the equation becomes:
Force * 0.50 m = [ (1/2) * 1600 kg * (18 m/s)^2 ]
Simplifying further:
Force = [ (1/2) * 1600 kg * (18 m/s)^2 ] / 0.50 m
Now, plug in the numbers to calculate the minimum force experienced by the dummy:
Force = [ (1/2) * 1600 kg * (18 m/s)^2 ] / 0.50 m
This gives us the minimum force experienced by the dummy during the crash.
For the second question, we can calculate the acceleration of the SUV during the crash using Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
Rearranging the equation, we have:
Force = mass * acceleration
In this case, the force is the rigidity of the crumple zone, which is given as 342 kN (kilonewtons) or 342,000 N (newtons).
The mass of the SUV is 2,150 kg.
So, we can rewrite the equation as:
342,000 N = 2,150 kg * acceleration
Now, solve for the acceleration:
acceleration = 342,000 N / 2,150 kg
This will give you the acceleration of the SUV during the crash as the crumple zone is collapsing.
Damon would it be -0.159 or -159?
–199 kN
Normally I would use momentum but since you say use wok energy then'
initial KE of dummy = (1/2) m v^2 = .5 * 75 * 18^2
the dummy stops in .5 + .8 = 1.3 meters
force * distance = work = change in Ke
so
F * 1.3 = .5 * 75 * 18^2
==========================================
F = m a
342,000 = 2,150 a