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 56 km/h (35mph ). A new model of mass 1900 kg takes 0.15 s from the time of impact until it is brought to rest.
1. Calculate the average force exerted on the car by the barrier.
2. Calculate the average deceleration of the car.
Favg = delta p/ delta t
1. To calculate the average force exerted on the car by the barrier, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, acceleration can be calculated using the formula a = (change in velocity) / (time). Here's how you can find the average force:
Step 1: Convert the speed from km/h to m/s. The conversion factor is 1 km/h = 0.2778 m/s. Therefore, 56 km/h is equal to (56 x 0.2778) = 15.56 m/s.
Step 2: Calculate the change in velocity. Since the car is brought to rest, the change in velocity is equal to the initial velocity. The initial velocity is 15.56 m/s.
Step 3: Calculate the acceleration. Using the formula a = (change in velocity) / (time), we can substitute the values. In this case, time is given as 0.15 s, and the change in velocity is 15.56 m/s. So, a = 15.56 m/s / 0.15 s = 103.73 m/s^2.
Step 4: Calculate the average force. Now we can use Newton's second law to find the average force. F = m x a, where m is the mass of the car given as 1900 kg, and a is the calculated acceleration in the previous step. Thus, F = 1900 kg x 103.73 m/s^2 = 197,084 N.
Therefore, the average force exerted on the car by the barrier is 197,084 Newtons.
2. To calculate the average deceleration of the car, we can use the formula for deceleration, which is the negative acceleration (a) from the previous calculation. Deceleration is simply the rate at which the velocity decreases. So, the average deceleration of the car is equal to 103.73 m/s^2 (as calculated in the previous answer).
Therefore, the average deceleration of the car is 103.73 m/s^2.