What's More Analyze the case given below and answer the guide questions that follow. Situation: A car with a mass of 1 524kg was heading towards a wall. It applied 140N of force in its brakes until it slows down. v₁ 14 m/s time (s) 1 1223 4 5 6 7 8 910 Figure 4. Car moving towards a wall Guide questions: 1. What is the initial momentum of the car? 2. How long did it take for the car to stop after applying brakes? 3. How much impulse was experienced by the car during the application of brakes? What I Have Learned Apply the concepts of momentum and impulse to explain the given applications. 1. Vehicles usually indicate the maximum capacity of passengers. Why do you think it is important not to exceed its maximum capacity? Use the concept of momentum in explaining your answer. 2. Drivers are usually prohibited from over speeding. They are required to follow the prescribed speed limit on different roads. Why do you think the government imposes a speed limit? Defend your answer using the concept of impulse.
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Answer: 1.The initial momentum of the car can be calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity. Therefore, the initial momentum of the car is:
p = 1,524 kg x 14 m/s = 21,336 kg m/s
2.The time it took for the car to stop can be determined from the given data. The car came to a complete stop after 10 seconds. Therefore, the time it took for the car to stop after applying brakes is 10 seconds
3.The impulse experienced by the car during the application of brakes can be calculated using the formula J = FΔt, where J is impulse, F is force, and Δt is the change in time. The force applied by the brakes is 140 N, and the time it took for the car to stop is 10 seconds. Therefore, the impulse experienced by the car is:
J = 140 N x 10 s = 1,400 Ns
What i have learned are:
1.Vehicles usually indicate the maximum capacity of passengers to ensure the safety of passengers and maintain the balance and stability of the vehicle. Exceeding the maximum capacity can affect the momentum of the vehicle. The momentum of a system is conserved unless acted upon by an external force. If the vehicle exceeds its maximum capacity, the mass of the vehicle increases, and the momentum also increases. As a result, the vehicle may be harder to control and can lead to accidents.
2. The government imposes a speed limit to ensure road safety and reduce the risk of accidents. When a vehicle is moving at a high speed, it has a large amount of kinetic energy. When the vehicle suddenly stops, this kinetic energy is converted into other forms of energy, such as heat and sound, which can cause damage to the vehicle and harm the passengers. This sudden change in momentum is referred to as impulse. Therefore, by imposing a speed limit, the government is limiting the impulse experienced by the vehicle and reducing the risk of accidents.
Explanation:
1. Initial momentum of the car can be calculated using the formula p = mv, where p is momentum, m is mass and v is velocity. So, initial momentum of the car = 1,524 kg x 14 m/s = 21,336 kg m/s.
2. To calculate the time taken to stop the car, we need to find the point where the velocity becomes zero. From the given data, we can see that it takes 8 seconds for the car to come to a complete stop.
3. Impulse is given by the formula I = FΔt, where F is force and Δt is time. From the given data, the force applied by the brakes is 140 N, and the time taken for the car to stop is 8 seconds. So, impulse experienced by the car = 140 N x 8 s = 1,120 Ns.
What I Have Learned:
1. It is important not to exceed the maximum capacity of a vehicle as it can lead to an increase in the mass of the vehicle. According to the concept of momentum, momentum is directly proportional to mass. Therefore, if the mass of the vehicle increases, the momentum also increases. This can lead to difficulty in controlling the vehicle and stopping it during emergencies.
2. The government imposes a speed limit on different roads to reduce the impact of the collision during an accident. According to the concept of impulse, impulse is directly proportional to the change in momentum. Therefore, if the speed of the vehicle is high, the change in momentum during a collision is also high, which increases the impulse. As a result, the impact of the collision increases, and it becomes difficult to control the vehicle during emergencies. Therefore, to minimize the impact of a collision and prevent accidents, the government imposes a speed limit on different roads.