Two carts with masses of 4.82 kg and 2.72 kg move toward each other on a frictionless track with speeds of 5.03 m/s and 3.52 m/s respectively. The carts stick together after colliding head-on. Find the final speed.
m1*V1-m2*V2 = 4.82*5.03-2.72*3.52=14.7
m*V = 14.7
V = 14.7/m = 14.7/(4.82+2.72) = 1.95 m/s
To find the final speed of the carts after collision, we can use the concept of conservation of linear momentum.
The linear momentum of an object is given by the product of its mass and velocity. Mathematically, it can be represented as:
Linear momentum (p) = mass (m) * velocity (v)
According to the law of conservation of linear momentum, the total linear momentum before the collision is equal to the total linear momentum after the collision for a system of objects.
Before the collision, the total linear momentum of the system is given by:
Initial momentum = (mass of cart 1 * velocity of cart 1) + (mass of cart 2 * velocity of cart 2)
= (4.82 kg * 5.03 m/s) + (2.72 kg * -3.52 m/s) [since the carts move towards each other, we take the velocity of the second cart as negative]
= 24.3266 kg·m/s - 9.5744 kg·m/s
= 14.7522 kg·m/s
After the collision, the carts stick together, so their masses combine, and we need to find their common velocity.
Let's assume the final velocity of the carts after the collision is v (m/s).
The combined mass of the carts after the collision is the sum of their individual masses, i.e., 4.82 kg + 2.72 kg = 7.54 kg.
Therefore, the total linear momentum after the collision is given by:
Final momentum = (combined mass * final velocity)
= (7.54 kg * v)
According to the conservation of linear momentum, the initial momentum (14.7522 kg·m/s) is equal to the final momentum (7.54 kg * v).
14.7522 kg·m/s = 7.54 kg * v
Now we can solve for v:
v = 14.7522 kg·m/s / 7.54 kg
v ≈ 1.9544 m/s
Therefore, the final speed of the carts after the collision is approximately 1.9544 m/s.