You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50 km/h (30 mph). A new model of mass 1500 kg takes 0.11 s from the time of impact until it is brought to rest. (Take the positive direction to be the original direction of motion.)
(a) Calculate the average force exerted on the car by the barrier
(b) Calculate the average deceleration of the car.
To solve this problem, we can use Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration. We can also use the equation for average acceleration, which is the change in velocity divided by the change in time.
(a) To calculate the average force exerted on the car by the barrier, we first need to find the change in velocity. We know that the car starts from a speed of 50 km/h and comes to rest, so the change in velocity is from 50 km/h to 0 km/h.
To convert from km/h to m/s, we divide by 3.6:
Initial velocity (u) = 50 km/h = (50/3.6) m/s ≈ 13.89 m/s
Final velocity (v) = 0 m/s
Since the acceleration is in the opposite direction to the initial motion, we take the final velocity as negative (-ve).
Using the equation for average acceleration:
Average acceleration (a) = (Change in velocity) / (Change in time)
a = (v - u) / t
Plugging in the values:
a = (0 - 13.89) / 0.11 ≈ -126.27 m/s^2
Now, we can calculate the average force using Newton's second law:
Force (F) = mass (m) * acceleration (a)
F = 1500 kg * -126.27 m/s^2 ≈ -189,405 N
The negative sign indicates that the force is acting in the opposite direction to the original motion of the car.
(b) To calculate the average deceleration of the car, we can use the same average acceleration value calculated in part (a) because deceleration is just negative acceleration.
Average deceleration = -126.27 m/s^2 (from part (a))