A 75-kg crash test dummy in a car traveling at 30 m/s slams into a brick wall. If the time elapsed during the crash was 0.03 seconds without a seatbelt and 0.3 seconds with a seatbelt, calculate the difference in force.
Can you pls show all the steps in your calculations cuz I don’t understand anything
😭I hope so
i do not know but maybe @mathhelper can help you soon
Sure, I can help you with that! To calculate the difference in force with and without a seatbelt, we will use the equation:
Force = (mass * change in velocity) / time
Let's calculate the force without a seatbelt first:
Step 1: Calculate the change in velocity
Change in velocity = final velocity - initial velocity
Given:
Initial velocity (u) = 30 m/s (the speed of the car)
Final velocity (v) = 0 m/s (the car comes to a stop)
Change in velocity = 0 - 30 = -30 m/s
Step 2: Calculate the force without a seatbelt
Force = (mass * change in velocity) / time
Given:
Mass (m) = 75 kg
Time (t) = 0.03 s
Force = (75 kg * -30 m/s) / 0.03 s
Force = -7500 N
The force without a seatbelt is -7500 Newtons (N). The negative sign indicates that the force is acting in the opposite direction of motion.
Now, let's calculate the force with a seatbelt:
Step 1: Calculate the change in velocity (same as before)
Change in velocity = final velocity - initial velocity
Given:
Initial velocity (u) = 30 m/s (the speed of the car)
Final velocity (v) = 0 m/s (the car comes to a stop)
Change in velocity = 0 - 30 = -30 m/s
Step 2: Calculate the force with a seatbelt
Force = (mass * change in velocity) / time
Given:
Mass (m) = 75 kg
Time (t) = 0.3 s
Force = (75 kg * -30 m/s) / 0.3 s
Force = -750 N
The force with a seatbelt is -750 Newtons (N).
Finally, let's calculate the difference in force:
Difference in force = Force without seatbelt - Force with seatbelt
Difference in force = (-7500 N) - (-750 N)
Difference in force = -6750 N
The difference in force between not wearing a seatbelt and wearing a seatbelt is 6750 Newtons (N).
To calculate the difference in force, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a). In this case, the acceleration is caused by the change in velocity during the crash.
Let's calculate the force without a seatbelt first:
1. Calculate the change in velocity (Δv):
Δv = final velocity - initial velocity
The initial velocity of the car is 30 m/s, but we need to find the final velocity. Since the car crashes into a wall, it comes to a stop, so the final velocity is 0 m/s.
Thus, Δv = 0 m/s - 30 m/s = -30 m/s
2. Calculate the acceleration (a):
We know that acceleration is the change in velocity divided by the time taken, so:
a = Δv / t
The time elapsed during the crash without a seatbelt is 0.03 seconds.
Therefore, a = -30 m/s / 0.03 seconds = -1000 m/s²
3. Calculate the force (F):
F = m * a
The mass of the crash test dummy is given as 75 kg.
Therefore, F = 75 kg * -1000 m/s² = -75,000 N
Now, let's calculate the force with a seatbelt:
1. Calculate the change in velocity (Δv):
As before, Δv = 0 m/s - 30 m/s = -30 m/s
2. Calculate the acceleration (a):
The time elapsed during the crash with a seatbelt is 0.3 seconds.
Thus, a = -30 m/s / 0.3 seconds = -100 m/s²
3. Calculate the force (F):
F = m * a
Using the same mass of 75 kg,
F = 75 kg * -100 m/s² = -7,500 N
Finally, to calculate the difference in force, subtract the force with a seatbelt from the force without a seatbelt:
Difference in force = Force without seatbelt - Force with seatbelt
= -75,000 N - (-7,500 N)
= -75,000 N + 7,500 N
= -67,500 N
Therefore, the difference in force between crashing without a seatbelt and with a seatbelt is 67,500 Newtons.