You are the designer of a school bus and would like to know what the maximum stopping distance is that will ensure the students to remain in their seats. The coefficient of static friction for the passenger and the bus seat is .5, and the coefficient of kinetic friction for the passenger and the bus seat is .3. The typical velocity of the bus while it makes its round is 16 m/s. In order to find a safe stopping distance, you must first determine the maximum stopping acceleration where the children remain in their seats. Then, determine the maximum stopping distance for the school bus. Then, describe what would happen if during a head on collision, the bus comes to a stop in a much shorter distance then the maximum stopping distance calculated. Lastly, describe what would happen to the passengers and how you could prevent this from happening?

Question

You are the designer of a school bus and would like to know what the maximum stopping distance is that will ensure the students to remain in their seats. The coefficient of static friction for the passenger and the bus seat is .5, and the coefficient of kinetic friction for the passenger and the bus seat is .3. The typical velocity of the bus while it makes its round is 16 m/s. In order to find a safe stopping distance, you must first determine the maximum stopping acceleration where the children remain in their seats. Then, determine the maximum stopping distance for the school bus. Then, describe what would happen if during a head on collision, the bus comes to a stop in a much shorter distance then the maximum stopping distance calculated. Lastly, describe what would happen to the passengers and how you could prevent this from happening?

Answer 1

To determine the maximum stopping acceleration where the children remain in their seats, we should consider the forces acting on them. When the bus stops, the only force acting on the children is the force of static friction. The maximum static friction force can be calculated using the coefficient of static friction (0.5) and the normal force (which is equal to the weight of the children).

To find the normal force, we need to determine the weight of the children. Let's assume there are 50 children on the bus, each weighing an average of 40 kg. The total weight of the children is:

Weight = 50 children * 40 kg/child = 2000 kg

Now, we can calculate the maximum static friction force:

Maximum Static Friction Force = coefficient of static friction * Weight
= 0.5 * 2000 kg * 9.8 m/s^2 (acceleration due to gravity)
= 9800 N

Since the maximum static friction force is equal to the mass of the children multiplied by the maximum acceleration, we can rearrange the equation to solve for the maximum stopping acceleration:

Maximum Stopping Acceleration = Maximum Static Friction Force / Weight
= 9800 N / 2000 kg
= 4.9 m/s^2

Therefore, the maximum stopping acceleration to ensure the children remain in their seats is 4.9 m/s^2.

Now, to determine the maximum stopping distance for the school bus, we can use the kinematic equation:

v^2 = u^2 + 2as

where:
v = final velocity (0 m/s as the bus stops)
u = initial velocity (16 m/s as given)
a = acceleration (-4.9 m/s^2 as calculated)
s = stopping distance (unknown)

Rearranging the equation to solve for s:

s = (v^2 - u^2) / (2a)
= (0^2 - 16^2) / (2 * -4.9)
= 128 / 9.8
= 13.1 meters

Therefore, the maximum stopping distance for the school bus is approximately 13.1 meters.

In a head-on collision, if the bus comes to a stop in a much shorter distance than the maximum stopping distance calculated, the passengers will experience a sudden and abrupt deceleration. This can lead to injuries, especially if they are not properly restrained.

To prevent this from happening and to ensure the safety of the passengers, it is essential to have appropriate safety measures in place. One of the most effective measures is the use of seat belts. By wearing seat belts properly, passengers can be securely restrained and protected during sudden decelerations or collisions. Additionally, having properly designed and maintained vehicle structures, such as reinforced frames and energy-absorbing materials, can also help mitigate the impact forces and minimize potential injuries.