In a head-on collision, a car stops in 0.30s from a speed of 30m/s . The driver has a mass of 73kg , and is, fortunately, tightly strapped into his seat.
What force is applied to the driver by his seat belt during that fraction of a second?
force*time=masscar*changevelocity
To find the force applied to the driver by his seat belt during the collision, 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
First, let's find the acceleration. The car stops in 0.30s, so the time taken (t) is 0.30s. The initial velocity (u) is 30 m/s, and the final velocity (v) is 0 m/s since the car comes to a stop. We can use the formula of acceleration (a) to find its value:
a = (v - u) / t
Substituting the given values:
a = (0 - 30) / 0.30
a = -100 m/s² (since the velocity changes from 30 m/s to 0 m/s, we take a negative value for the acceleration)
Now, let's find the force by multiplying the mass and acceleration:
F = m * a
F = 73 kg * (-100 m/s²)
F = -7300 N (since force can have negative values)
Therefore, the force applied to the driver by his seat belt during the collision is -7300 N.
To determine the force applied to the driver by his seat belt, 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, the acceleration can be calculated using kinematic equations. The initial velocity (u) is 30 m/s, the final velocity (v) is 0 m/s, and the time taken (t) is 0.30 s. Using the formula v = u + at, we can solve for the acceleration (a).
v = u + at
0 = 30 + a * 0.30
Solving for a, we get:
a = (0 - 30) / 0.30
a = -100 m/s^2 (negative because the car is decelerating)
Now that we have the acceleration, we can calculate the force applied to the driver using Newton's second law. The mass of the driver is given as 73 kg.
F = m * a
F = 73 kg * (-100 m/s^2)
F = -7300 N
Therefore, the force applied to the driver by his seat belt during the collision is -7300 Newtons. The negative sign indicates that the force is in the opposite direction of the car's motion, providing a restraining force to stop the driver.