a car crashes into a wall at 25m/s and is brought to rest in .1seconds. Calculate the average force exerted on a 75kg test dummy by the seat belt. How many g-forces is this? (Remember g-force= Force/mg)
Your questions are all the same.
av force = change in momentum/change in time
or for vanishingly small time and constant mass
force = mass * acceleration
initial momentum = m v = 75 * 25
final momentum = 0
change in momentum = -75*25
change in time = .1
so
average force = -75*25/.1 = -75*250 newtons
for number of g s
75*250/9.8
To calculate the average force exerted on the test dummy by the seat belt, you need to use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the acceleration of the car during the collision. We can use the formula:
acceleration = change in velocity / time
Given that the car is initially traveling at 25 m/s and is brought to rest (0 m/s) in 0.1 seconds:
acceleration = (0 m/s - 25 m/s) / 0.1 s
acceleration = -250 m/s^2
Notice the negative sign in front of the acceleration value. This indicates that the car is decelerating during the collision.
Next, we can calculate the force exerted on the test dummy using the formula:
force = mass × acceleration
Given that the mass of the test dummy is 75 kg:
force = 75 kg × (-250 m/s^2)
force = -18750 N
Again, the negative sign signifies that the force is in the opposite direction to the motion of the car.
To calculate the g-forces experienced by the test dummy, we can use the formula:
g-force = force / (mass × acceleration due to gravity)
The acceleration due to gravity is approximately 9.8 m/s^2.
g-force = (force / mass) / acceleration due to gravity
g-force = (-18750 N / 75 kg) / 9.8 m/s^2
g-force ≈ -24.18 g
The negative sign indicates that the g-forces are acting in the opposite direction to the force of gravity.
Therefore, the average force exerted on the 75 kg test dummy by the seat belt is approximately -18,750 Newtons, and this corresponds to approximately -24.18 g-forces.