Understanding the Concepts
* Impulse: Impulse is the change in momentum of an object. It's calculated as: Impulse = Force × Time
* Momentum: Momentum is the mass of an object multiplied by its velocity. Momentum = Mass × Velocity
Calculations
1. Calculate the initial momentum of the car:
* Momentum (car) = 100 kg * 5 m/s = 500 kg·m/s
2. Calculate the initial momentum of the truck:
* Momentum (truck) = 10000 kg * 5 m/s = 50000 kg·m/s
3. Calculate the change in momentum (impulse) for the car:
* Since the car is brought to a stop, its final momentum is 0 kg·m/s.
* Change in momentum (car) = 500 kg·m/s - 0 kg·m/s = 500 kg·m/s
4. Calculate the change in momentum (impulse) for the truck:
* Change in momentum (truck) = 50000 kg·m/s - 0 kg·m/s = 50000 kg·m/s
5. Calculate the force required to stop the car:
* Force (car) = Impulse (car) / Time = 500 kg·m/s / 2 s = 250 N
6. Calculate the force required to stop the truck:
* Force (truck) = Impulse (truck) / Time = 50000 kg·m/s / 2 s = 25000 N
Conclusion
* The force required to stop the car in 2 seconds is 250 Newtons.
* The force required to stop the truck in 2 seconds is 25,000 Newtons.
Key Point: Notice how the truck, with its much larger mass, requires a significantly larger force to stop in the same amount of time, even though it's moving at the same velocity as the car.
