The National Transportation Safety Board is testing the crashworthiness of a new car. The 1.87 103 kg vehicle, moving at 11.3 m/s, is allowed to collide with a bridge abutment, being brought to rest in a time of 0.463 s. What force, assumed constant, acted on the car during impact?
Well, it seems like this car had a pretty rough collision! Let me calculate the force for you.
Using Newton's second law (F = m * a), we can calculate the acceleration of the car. We know the initial velocity of the car is 11.3 m/s and it comes to rest in a time of 0.463 s. So the acceleration would be -11.3 m/s divided by 0.463 s.
Now, using the calculated acceleration, we can find the force. F = m * a, where m is the mass of the car (1.87 * 10^3 kg) and a is the acceleration we calculated earlier.
Calculating all that, we find that the force acting on the car during the impact is approximately -58071 N.
I hope this answer didn't crash your expectations!
To find the force acted on the car during impact, we can use the equation for force:
Force = (mass * change in velocity) / time
Given:
Mass (m) = 1.87 * 10^3 kg
Initial velocity (u) = 11.3 m/s
Final velocity (v) = 0 m/s
Time (t) = 0.463 s
Change in velocity (Δv) = v - u = 0 - 11.3 = -11.3 m/s
Now we can substitute these values into the formula to calculate the force:
Force = (mass * change in velocity) / time
Force = (1.87 * 10^3 kg * (-11.3 m/s)) / 0.463 s
Calculating it:
Force = (-1.87 * 10^3 kg * 11.3 m/s) / 0.463 s
Force = (-2.1103 * 10^4 kg · m/s) / 0.463 s
Force ≈ -45,599.14 N
Therefore, the force acted on the car during impact is approximately -45,599.14 N, assuming it is a negative force because it opposes the motion of the car.
To find the force acted on the car during impact, 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.
First, let's calculate the acceleration of the car using the change in velocity and the time:
Acceleration (a) = (final velocity - initial velocity) / time
a = (0 - 11.3 m/s) / 0.463 s
Substituting the values into the equation:
a = - 11.3 m/s / 0.463 s
a ≈ -24.43 m/s²
Since the car is brought to rest, the acceleration is negative because it opposes the motion.
Now, we can calculate the force using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
F = (1.87 × 10³ kg) * (-24.43 m/s²)
Substituting the values into the equation:
F ≈ - 45,655.41 N
The negative sign indicates that the force is acting in the opposite direction to the initial motion of the car.
Therefore, the force acted on the car during impact is approximately -45,655.41 Newtons.