a car of mass 500kg is moving 24 m/s. a lion of mass 100kg drops on to the roof of the car from an overhanging branch. show that the car will slow down to 24m/s.
There is no external horizontal force on the lion/automobile system.
Therefore the total horizontal momentum of the system will not change.
before:
500 * 24 + 100 * 0 = 12,000
after:
(500 + 100) v = 600 v
so
600 v = 12,000
6 v = 120
v = 20 m/s (not 24 of course)
before momentum :-
24*500=12000
after momentum:-
To show that the car will slow down to 24 m/s when the lion drops onto its roof, we need to apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the system consists of the car and the lion, and we need to analyze the system before and after the lion drops onto the car.
Let's denote the original velocity of the car as v1 and the velocity of the lion immediately after it drops onto the car as v2. According to the principle of conservation of momentum:
Initial momentum = Final momentum
The initial momentum is the momentum of the car before the lion drops on it, while the final momentum is the momentum of the combined system (car + lion) after the lion lands on the car.
The momentum of an object is given by the product of its mass and velocity (p = mv). Therefore, the initial momentum of the car is:
Initial momentum of the car = Mass of the car × Initial velocity of the car
Since the mass of the car is 500 kg and the initial velocity is 24 m/s, we have:
Initial momentum of the car = 500 kg × 24 m/s
Now, let's consider the final momentum of the combined system of the car and the lion. The lion has a mass of 100 kg, and its velocity immediately after landing is the velocity of the car (v2) since both will move together after the collision.
Final momentum of the combined system = (Mass of the car + Mass of the lion) × Final velocity of the combined system
Final momentum of the combined system = (500 kg + 100 kg) × 24 m/s
To show that the car will slow down to 24 m/s, we need to demonstrate that the initial momentum is equal to the final momentum.
Therefore, we need to equate the two expressions for momentum and show that they are equal:
500 kg × 24 m/s = (500 kg + 100 kg) × 24 m/s
Now, calculate the expressions on both sides of the equation:
12,000 kg.m/s = 12,000 kg.m/s
Since both sides of the equation are equal, we have shown that the initial momentum is equal to the final momentum. This means that the car will indeed slow down to 24 m/s when the lion drops onto its roof.