two carts with masses of 10.0kg and 2.5kg move in opposite directions on a frictionless track, with speeds of 6.0m/s and 3.0m/s respectively. The carts stick together after colliding head on. Find the final speed of the two cars
4.2
Well, when two carts collide and stick together, it's bound to be a sticky situation! Let's crunch some numbers to find the final speed.
To find the final speed, we can use the law of conservation of momentum. According to it, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum, p, of an object is given by the equation p = mv, where m is the mass of the object and v is its velocity.
Now, let's calculate the initial momentum:
For the first cart of mass 10.0 kg traveling at 6.0 m/s, the initial momentum is: p1 = (10.0 kg) * (6.0 m/s) = 60.0 kg·m/s.
For the second cart of mass 2.5 kg traveling at 3.0 m/s, the initial momentum is: p2 = (2.5 kg) * (3.0 m/s) = 7.5 kg·m/s.
Since the carts stick together, we can consider them as a single system with a combined mass of 10.0 kg + 2.5 kg = 12.5 kg.
To find the final speed, we divide the total momentum by the combined mass:
Total final momentum = p1 + p2 = 60.0 kg·m/s + 7.5 kg·m/s = 67.5 kg·m/s.
Final velocity = momentum / total mass = (67.5 kg·m/s) / (12.5 kg) = 5.4 m/s.
So, after the head-on collision, the two carts will have a final combined speed of 5.4 m/s. They might not be Olympic sprinters (or should I say "sprint carts"?), but they definitely stick together and keep moving forward!
To find the final speed of the two cars after they collide and stick together, we can apply the law of conservation of momentum.
The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming there are no external forces acting on the system.
The formula to calculate momentum is:
Momentum = mass x velocity
Before the collision, the total momentum is the sum of the momenta of the two cars:
Total momentum before = (mass of first car x velocity of first car) + (mass of second car x velocity of second car)
Total momentum before = (10.0 kg x 6.0 m/s) + (2.5 kg x (-3.0 m/s)) [Note: the direction of the velocity for the second car is opposite to the direction of motion]
Total momentum before = 60.0 kgm/s - 7.5 kgm/s [Note: kgm/s is the unit of momentum]
Total momentum before = 52.5 kgm/s
After the collision, the two cars stick together and move with a common final velocity (let's call it "v").
The mass of the combined system is the sum of the masses of the two cars:
Total mass after = mass of first car + mass of second car
Total mass after = 10.0 kg + 2.5 kg
Total mass after = 12.5 kg
Now, using the law of conservation of momentum, we can equate the total momentum before the collision to the total momentum after the collision:
Total momentum before = Total momentum after
52.5 kgm/s = 12.5 kg x v
Simplifying the equation, we can solve for the final velocity "v":
v = 52.5 kgm/s / 12.5 kg
v = 4.2 m/s
Therefore, the final speed of the two cars, after they collide and stick together, is 4.2 m/s.
To find the final speed of the two carts after they stick together, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, it can be represented as:
Momentum = mass × velocity
Before the collision, the momentum of the first cart, denoted as Cart 1, is given by:
Momentum of Cart 1 before collision = mass of Cart 1 × velocity of Cart 1
= 10.0 kg × 6.0 m/s
= 60.0 kg·m/s
Similarly, the momentum of the second cart, Cart 2, before the collision is:
Momentum of Cart 2 before collision = mass of Cart 2 × velocity of Cart 2
= 2.5 kg × (-3.0 m/s) (Note: The direction of velocity should be considered when calculating momentum in this case, as the carts are moving in opposite directions.)
= -7.5 kg·m/s
To find the total momentum before the collision, we can sum the momenta of Cart 1 and Cart 2:
Total momentum before collision = Momentum of Cart 1 before collision + Momentum of Cart 2 before collision
= 60.0 kg·m/s + (-7.5 kg·m/s)
= 52.5 kg·m/s
Now, after the collision, the two carts stick together and move as one. Let's assign the final velocity of the combined carts as V.
The total mass of the combined system is the sum of the masses of Cart 1 and Cart 2:
Total mass = mass of Cart 1 + mass of Cart 2
= 10.0 kg + 2.5 kg
= 12.5 kg
Applying the principle of conservation of momentum, we can write:
Total momentum after collision = Total momentum before collision
(mass of the combined system) × (final velocity of the combined system) = 52.5 kg·m/s
(12.5 kg) × (final velocity) = 52.5 kg·m/s
Dividing both sides of the equation by 12.5 kg, we can solve for the final velocity:
final velocity = 52.5 kg·m/s ÷ 12.5 kg
final velocity = 4.2 m/s
Therefore, the final speed of the two cars, after colliding and sticking together, is 4.2 m/s.
Momentum conservation applies.
10*6-2.5*3= 12.5(V)
solve for V