a car with two passengers travelling at 15m/s collides with a tree. one of the passengers who is not wearing a seat belt strikes the windshield head first and comes to rest in 0.03 s. the area of contact between the head and the windshield is approximately 5 X 10 to the power of -4 m to the power of -2 and the mass of the head is 5.4 kg. the other passenger who is wearing his seat belt comes at rest in 0.50 s. the mass of this passenger is 75 kg. the area of the seat belt in contact with this passenger is about 0.12 m to the power of 2. find the average force and the force per unit area exerted on the two passengers
force = change of momentum/time
= - m v /t
force / area = force / given area
by the way your units for first person's head area are wrong.
To find the average force exerted on the two passengers, we can use the equation:
Force = (Change in momentum) / (Time taken)
First, let's calculate the change in momentum for the passenger who strikes the windshield:
Change in momentum = mass x (final velocity - initial velocity)
The initial velocity of the passenger is the same as the car's velocity, which is 15 m/s. The final velocity is 0 m/s since the passenger comes to rest.
Change in momentum = 5.4 kg x (0 m/s - 15 m/s)
= -81.0 kg·m/s
Next, let's calculate the average force for this collision:
Force = (-81.0 kg·m/s) / (0.03 s)
= -2700 N (Note: The negative sign indicates that the force is acting in the opposite direction of motion)
Now, let's calculate the force per unit area for the passenger who strikes the windshield:
Force per unit area = Force / Area of contact
Area of contact = 5 x 10^(-4) m^2
Force per unit area = (-2700 N) / (5 x 10^(-4) m^2)
= -5.4 x 10^6 N/m^2
Next, let's calculate the change in momentum for the passenger who is wearing the seat belt:
Change in momentum = mass x (final velocity - initial velocity)
The initial velocity of the passenger is also 15 m/s. The final velocity is 0 m/s since the passenger comes to rest.
Change in momentum = 75 kg x (0 m/s - 15 m/s)
= -1125 kg·m/s
Now, let's calculate the average force for this collision:
Force = (-1125 kg·m/s) / (0.50 s)
= -2250 N (Note: The negative sign indicates that the force is acting in the opposite direction of motion)
Finally, let's calculate the force per unit area for the passenger wearing the seat belt:
Force per unit area = Force / Area of contact
Area of contact = 0.12 m^2
Force per unit area = (-2250 N) / (0.12 m^2)
= -18.75 x 10^3 N/m^2
So, the average force exerted on the passenger who strikes the windshield is -2700 N, and the force per unit area exerted on them is -5.4 x 10^6 N/m^2.
The average force exerted on the passenger wearing the seat belt is -2250 N, and the force per unit area exerted on them is -18.75 x 10^3 N/m^2.
To find the average force and force per unit area exerted on the two passengers, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
For the passenger not wearing a seat belt:
1. Calculate the acceleration using the formula v = u + at, where u is the initial velocity (15 m/s), v is the final velocity (0 m/s), and t is the time taken to come to rest (0.03 s). Rearranging the formula, we get:
a = (v - u) / t
a = (0 - 15) / 0.03
a = -500 m/s^2 (negative sign indicates deceleration)
2. Use the formula F = ma, substituting the mass of the head (5.4 kg) and the acceleration (-500 m/s^2) to find the average force:
F = 5.4 kg * (-500 m/s^2)
F = -2700 N (negative sign indicates the force is in the opposite direction of motion)
3. Since the area of contact between the head and the windshield is given as 5 x 10^-4 m^2, we can calculate the force per unit area:
Force per unit area = Force / Area of contact
Force per unit area = (-2700 N) / (5 x 10^-4 m^2)
Force per unit area ≈ -5.4 x 10^6 N/m^2
For the passenger wearing a seat belt:
1. Calculate the acceleration using the formula v = u + at, where u is the initial velocity (15 m/s), v is the final velocity (0 m/s), and t is the time taken to come to rest (0.50 s). Rearranging the formula, we get:
a = (v - u) / t
a = (0 - 15) / 0.50
a = -30 m/s^2 (negative sign indicates deceleration)
2. Use the formula F = ma, substituting the mass of the passenger (75 kg) and the acceleration (-30 m/s^2) to find the average force:
F = 75 kg * (-30 m/s^2)
F = -2250 N (negative sign indicates the force is in the opposite direction of motion)
3. Since the area of contact between the passenger and the seat belt is given as 0.12 m^2, we can calculate the force per unit area:
Force per unit area = Force / Area of contact
Force per unit area = (-2250 N) / (0.12 m^2)
Force per unit area ≈ -18,750 N/m^2
Therefore, the average force exerted on the passenger not wearing a seat belt is approximately -2700 N, and the force per unit area is approximately -5.4 x 10^6 N/m^2. The average force exerted on the passenger wearing a seat belt is approximately -2250 N, and the force per unit area is approximately -18,750 N/m^2.