A family car has a mass of 1400 kg. In an accident it hits a wall and goes from a speed of 27 m/s to a standstill in 1.5 seconds. By how much would the force have been reduced if the car had had a crumple zone that increased the collision time to 2.2 seconds?
To determine the force reduction with the presence of a crumple zone, we need to first calculate the force experienced by the car in both scenarios. We can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In the given scenario, the initial speed of the car is 27 m/s, and it comes to a stop in 1.5 seconds. Therefore, we can calculate the acceleration using the formula:
acceleration = (final velocity - initial velocity) / time
acceleration = (0 m/s - 27 m/s) / 1.5 s
acceleration = -18 m/s^2 (Note: the negative sign indicates acceleration in the opposite direction)
To find the force experienced by the car, we can multiply the acceleration by the mass of the car:
force = mass * acceleration
force = 1400 kg * -18 m/s^2
force = -25200 N (Note: the negative sign indicates the force is acting in the opposite direction)
Now, let's consider the scenario with a crumple zone that increases the collision time to 2.2 seconds.
Using the same initial speed of 27 m/s and a final velocity of 0 m/s, we can calculate the acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (0 m/s - 27 m/s) / 2.2 s
acceleration = -12.27 m/s^2 (Note: the negative sign indicates acceleration in the opposite direction)
Next, we can calculate the force experienced by the car with the crumple zone:
force = mass * acceleration
force = 1400 kg * -12.27 m/s^2
force = -17178 N (Note: the negative sign indicates the force is acting in the opposite direction)
To determine the force reduction, we subtract the force experienced with the crumple zone from the force experienced without it:
force reduction = force without crumple zone - force with crumple zone
force reduction = -25200 N - (-17178 N)
force reduction = -25200 N + 17178 N
force reduction = -8022 N
Therefore, the force would be reduced by 8022 Newtons if the car had a crumple zone that increased the collision time to 2.2 seconds.
To calculate the force exerted in the accident, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
To find the acceleration, we can use the formula:
a = (Vf - Vi) / t
where Vf is the final velocity, Vi is the initial velocity, and t is the time taken.
Given:
Mass of the car (m) = 1400 kg
Initial velocity (Vi) = 27 m/s
Final velocity (Vf) = 0 m/s
First, let's calculate the force exerted in the initial scenario:
1. Calculating the initial acceleration:
a1 = (Vf - Vi) / t
= (0 - 27) / 1.5
= -18 m/s^2
2. Calculating the force:
F1 = m * a1
= 1400 kg * -18 m/s^2
= -25200 N
So, in the initial scenario, the force exerted on the car is -25200 N (it's negative because the force is opposite to the direction of motion).
Now let's calculate the force exerted in the scenario with a crumple zone:
Given:
Increased collision time (t2) = 2.2 s
1. Calculating the initial acceleration using the initial velocity and the common final velocity (0 m/s):
Vc = 0 m/s (common final velocity)
a2 = (Vc - Vi) / t2
= (0 - 27) / 2.2
2. Calculating the force:
F2 = m * a2
= 1400 kg * [(0 - 27) / 2.2]
By comparing the magnitudes of both forces, we can determine the reduction in force:
Force reduction = |F2| - |F1|
Finally, plug in the values to calculate the reduction in force.
p = momentum = 1400 * 27 = 37800 kg m/s
force = change in momentum / change in time
first one F1 = 37800 / 1.5 = 25200 Newtons
second one F2 = 37800 / 2.2 = 17182 Newtons
subtract