Question

name: brian puya date: 10/12/23 period: 5 segment 1 summative exam: forces & motion - version b engineers are testing three bumper - car designs while collecting the data below.

car	force	time	impulse	rank
car 2	20,000 n	0.3 s	6000 kg·m/s
car 3	30,000 n	0.2 s	6000 kg·m/s

1. in the

ank\ column, identify which bumper car is the safest (1), second - safest (2), and least safe (3).

1. using the impulse - momentum theorem (j = fδt), explain which bumper car would be the safest. use the data above to support your reasoning. (l.t. 1.3)

□ what is the relationship shown in the data? discuss the arrow math.
□ what variable(s) affects the safety of the bumper car? how/why does this connect to safety?
□ make connections with classroom observations and activities to support your response.

Explanation:

Step1: Understand impulse - momentum theorem

The impulse - momentum theorem is $J = F\Delta t$, where $J$ is impulse, $F$ is force and $\Delta t$ is time. A safer bumper car is one that can spread out the force over a longer time for a given impulse.

Step2: Analyze the data

All three cars have the same impulse $J = 6000\ kg\cdot m/s$. For Car 1, $F_1=15000\ N$ and $\Delta t_1 = 0.4\ s$. For Car 2, $F_2 = 20000\ N$ and $\Delta t_2=0.3\ s$. For Car 3, $F_3 = 30000\ N$ and $\Delta t_3 = 0.2\ s$.

Step3: Determine the safety ranking

Since a lower force is better for safety when the impulse is the same, the car with the longest time of impact (lowest force) is the safest. So, Car 1 is the safest (1), Car 2 is the second - safest (2) and Car 3 is the least safe (3).

Step4: Explain using the theorem

According to $J = F\Delta t$, when $J$ is constant, $F$ and $\Delta t$ are inversely proportional. So, the car with the longest time of impact has the lowest force exerted on the passengers during a collision, which is safer. In the data, Car 1 has the longest time of impact among the three cars for the same impulse, so it exerts the least force on the passengers.

Step5: Variables affecting safety

The variables that affect the safety of the bumper car are force and time of impact. A longer time of impact for a given impulse means a lower force on the passengers, which is safer because it reduces the chance of injury. For example, in classroom observations, we might have seen that objects that stop more gradually (longer time of impact) experience less damage and exert less force on other objects.

Answer:

1. Car 1: 1, Car 2: 2, Car 3: 3
2. According to the impulse - momentum theorem $J = F\Delta t$, when the impulse $J$ is the same for all three cars, the car with the longest time of impact ($\Delta t$) has the lowest force ($F$) exerted on the passengers. Car 1 has the longest time of impact ($0.4\ s$) among the three cars, so it is the safest as it exerts the least force on the passengers during a collision. The variables that affect safety are force and time of impact. A longer time of impact reduces the force on passengers, reducing the chance of injury, as seen in classroom activities where gradual stops are safer.