I'm driving my car of mass 1000 kg at 100 km/hr when I accidentally hit the rear end of a truck of mass 5000 kg traveling in the same direction at 90 km/hr. My car and the truck lock together and move as a single object. Let F1 be the force the truck exerts on my car and let F2 be the force my car exerts on the truck. What is F1/F2 during the collision?

324

answer is not 324

1452

To find the ratio of the forces F1 and F2, we need to first understand the principle of conservation of momentum.

According to the principle of conservation of momentum, the total momentum of a system remains constant if no external forces act on it. Momentum is defined as the product of an object's mass and velocity. Mathematically, it can be represented as:

Momentum = mass × velocity

In this case, the car and the truck lock together and move as a single object after the collision. Therefore, the total momentum before the collision will be equal to the total momentum after the collision.

Let's calculate the initial momentum of the system before the collision:

Initial momentum = (mass of car × velocity of car) + (mass of truck × velocity of truck)

Mass of car = 1000 kg
Velocity of car = 100 km/hr = (100 ÷ 3.6) m/s (converting km/hr to m/s)
Mass of truck = 5000 kg
Velocity of truck = 90 km/hr = (90 ÷ 3.6) m/s (converting km/hr to m/s)

Initial momentum = (1000 kg × (100/3.6) m/s) + (5000 kg × (90/3.6) m/s)

Now, let's calculate the final momentum of the system after the collision:

Final momentum = (mass of car + mass of truck) × velocity of the combined object

Mass of the combined object = mass of car + mass of truck = (1000 kg + 5000 kg)
Velocity of the combined object = (velocity of car × mass of car + velocity of truck × mass of truck) / (mass of car + mass of truck)

Plugging in the known values:

Final momentum = [(1000 kg × (100/3.6) m/s) + (5000 kg × (90/3.6) m/s)] / (1000 kg + 5000 kg)

Now, we can find the ratio of the forces F1 and F2 during the collision:

F1/F2 = (force exerted by the truck on the car) / (force exerted by the car on the truck)

According to Newton's third law of motion, where forces come in pairs, F1 and F2 will be equal in magnitude but opposite in direction. Therefore, their ratio will be equal to 1.

So, F1/F2 = 1