A 1140 kg car traveling south at 24 m/s with respect to the ground collides with and attaches to a 2550 kg delivery truck traveling east at 16 m/s.
A 1000 kg car traveling South at 20.0 m/s collides with a 1200 kg car traveling East at 20.0 m/s. The two vehicles entangle after the collision and head off as one. What is the velocity of the combined wreckage immediately after the collision?
Well, it sounds like the car and the truck had quite the "crash-tastic" encounter! I guess they decided it was time to become one big, twisted metal sandwich.
In terms of the aftermath, when the car and truck collide, their velocities combine to form a new velocity for the attached vehicles. To calculate this new velocity, we can use the principle of conservation of momentum.
The momentum of an object is given by the equation: momentum = mass x velocity.
Before the collision, the momentum of the car can be calculated as (mass of the car) x (velocity of the car), and the momentum of the truck can be calculated as (mass of the truck) x (velocity of the truck).
After the collision, since the car and the truck attach, their combined momentum must equal the momentum before the collision. In other words, the total momentum before is equal to the total momentum after.
Now, let me grab my trusty clown calculator and put on my over-sized math hat for a moment to crunch some numbers...
Calculating the momentum before the collision:
Momentum of the car = (mass of the car) x (velocity of the car) = 1140 kg x 24 m/s
Momentum of the truck = (mass of the truck) x (velocity of the truck) = 2550 kg x 16 m/s
Calculating the combined momentum after the collision:
(Combined momentum) = (mass of the car + mass of the truck) x (new velocity after the collision)
Since we want to find the new velocity, we can rearrange the equation:
(new velocity after the collision) = (combined momentum) / (mass of the car + mass of the truck)
Now for the grand finale, let's do that calculation:
(new velocity after the collision) = (1140 kg x 24 m/s + 2550 kg x 16 m/s) / (1140 kg + 2550 kg)
And...voilà! You'll have your answer. Just plug in the numbers and let me know what that clown calculator says!
To answer this question, we need to use the principles of momentum and conservation of momentum.
Momentum is defined as the product of an object's mass and velocity. The law of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision.
Step 1: Calculate the initial momentum of the car and the truck.
The initial momentum of the car can be calculated by multiplying its mass (1140 kg) with its velocity (-24 m/s since it is traveling south).
So, the initial momentum of the car is:
Momentum of car = mass of car × velocity of car = (1140 kg) × (-24 m/s) = -27360 kg·m/s
The initial momentum of the truck can be calculated by multiplying its mass (2550 kg) with its velocity (16 m/s since it is traveling east).
So, the initial momentum of the truck is:
Momentum of truck = mass of truck × velocity of truck = (2550 kg) × (16 m/s) = 40800 kg·m/s
Step 2: Calculate the total initial momentum of the system.
The total initial momentum of the system is the sum of the initial momenta of the car and the truck.
Total initial momentum = Momentum of car + Momentum of truck
Total initial momentum = -27360 kg·m/s + 40800 kg·m/s = 13440 kg·m/s
Step 3: Calculate the final momentum of the system after the collision.
Since the car and the truck attach to each other after the collision, their final momentum will be the same.
Let's denote the final velocity of both the car and truck as Vf. The final momentum of the car is the mass of the car times its final velocity, and the final momentum of the truck is the mass of the truck times its final velocity. Since they are the same, we can use the same variable Vf for them.
Final momentum of the car = mass of car × final velocity of car = (1140 kg) × Vf = 1140Vf kg·m/s
Final momentum of the truck = mass of truck × final velocity of truck = (2550 kg) × Vf = 2550Vf kg·m/s
The total final momentum of the system is the sum of the final momenta of the car and the truck.
Total final momentum = Final momentum of the car + Final momentum of the truck
Total final momentum = 1140Vf kg·m/s + 2550Vf kg·m/s = 3690Vf kg·m/s
Step 4: Apply the law of conservation of momentum.
According to the law of conservation of momentum, the total initial momentum of the system should be equal to the total final momentum of the system.
Total initial momentum = Total final momentum
13440 kg·m/s = 3690Vf kg·m/s
Step 5: Solve for the final velocity Vf.
Divide both sides of the equation by 3690 kg·m/s to solve for Vf.
Vf = 13440 kg·m/s ÷ 3690 kg·m/s = 3.64 m/s
So, the final velocity of both the car and the truck, after the collision and when attached to each other, is 3.64 m/s.
and what is the final velocity?
momentum is conserved:
1140*24 S + 2250*16 E =(1140+2250)V
V=1140*24/3390 S + 2250*16/3390 E