A 1000 kg car traveling at 72 km/h strikes a concrete wall and comes to a full stop in 2 sec. What is the average force of impact exerted on the car?
To find the average force of impact exerted on the car, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration.
Given:
Mass of the car (m) = 1000 kg
Initial velocity (v) = 72 km/h
Time taken to come to a stop (t) = 2 sec
First, let's convert the initial velocity from km/h to m/s:
Velocity (v) = 72 km/h = (72 * 1000 m) / (60 * 60 s) ≈ 20 m/s
Next, we need to find the acceleration using the equation:
Acceleration (a) = Change in velocity / Time taken = (0 - 20 m/s) / 2 s = -10 m/s^2 (negative because the car is decelerating)
Now, we can calculate the average force of impact using Newton's second law:
Force (F) = mass (m) * acceleration (a) = 1000 kg * (-10 m/s^2) = -10000 N
Since force is a vector quantity, the negative sign indicates that the force is in the opposite direction of the car's motion. Therefore, the average force of impact exerted on the car is approximately 10000 Newtons in the opposite direction of motion.
To find the average force of impact exerted on the car, you can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
First, let's calculate the initial momentum of the car:
Initial momentum = mass × velocity
= 1000 kg × (72 km/h)
However, it is important to note that the momentum must be in SI units, so we need to convert the velocity from km/h to m/s:
1 km/h = 1000 m/3600 s (since there are 1000 meters in a kilometer and 3600 seconds in an hour)
=(1/3.6) m/s
So, the velocity of the car in m/s will be:
72 km/h × (1/3.6) m/s
= 20 m/s
Now, we can calculate the initial momentum:
Initial momentum = 1000 kg × 20 m/s
Next, let's calculate the final momentum. Since the car comes to a full stop, the final velocity is 0 m/s.
So, the final momentum is:
Final momentum = mass × final velocity
= 1000 kg × 0 m/s
= 0 kg·m/s
Now, we can find the change in momentum:
Change in momentum = Final momentum - Initial momentum
= 0 kg·m/s - (1000 kg × 20 m/s)
= - (1000 kg × 20 m/s)
= -20000 kg·m/s
Since the force is equal to the rate of change of momentum, we can calculate the force of impact:
Average force = Change in momentum / Time
The given time is 2 seconds. Substituting the values, we have:
Average force = -20000 kg·m/s / 2 s
= -10000 N
The negative sign indicates that the force is acting in the opposite direction of the initial velocity of the car, which is expected in a collision scenario.
Therefore, the average force of impact exerted on the car is 10000 Newtons (N).