Object 1 has a velocity of 3m/s and a mass of 5kg. Object 2 also has a mass of 5kg but isn't moving. Object 1 collides with Object 2 and they move off together. Work out their speed using the principle of conservation of momentum.
The answer is 1.5m/s
Thank you very much
Well, this scenario sounds like a classic case of a "tandem-turtle" collision. Let's find the speed at which they move off together, shall we?
First, we need to calculate the momentum of each object before the collision. Momentum is calculated by multiplying mass and velocity.
For Object 1, momentum = mass × velocity = 5 kg × 3 m/s = 15 kg·m/s.
Since Object 2 is not moving initially, its momentum is 0 kg·m/s.
Now, according to the conservation of momentum, the total momentum before the collision must equal the total momentum after the collision. So the momentum of the two objects after the collision will also be 15 kg·m/s.
Let's assume the final speed of both objects after the collision is v m/s.
The total mass after the collision is the sum of the masses of Object 1 and Object 2, which is 5 kg + 5 kg = 10 kg.
Using the formula momentum = mass × velocity, we get: 15 kg·m/s = 10 kg × v.
Now, let's solve for v: v = 15 kg·m/s ÷ 10 kg = 1.5 m/s.
So, the speed at which they move off together after the collision is 1.5 m/s.
That's it! The two objects joined forces and rolled away with a speed of 1.5 m/s, like two synchronized turtles on a mission.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it.
The momentum of an object is calculated by multiplying its mass by its velocity:
Momentum = mass * velocity
Let's call the final velocity of the objects together as Vf.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
Object 1 momentum = mass of object 1 * velocity of object 1
= 5 kg * 3 m/s
= 15 kg*m/s
Object 2 momentum = mass of object 2 * velocity of object 2
= 5 kg * 0 m/s
= 0 kg*m/s
Total momentum before the collision = momentum of object 1 + momentum of object 2
= 15 kg*m/s + 0 kg*m/s
= 15 kg*m/s
After the collision:
The objects move off together, so their total mass is the sum of their individual masses (5 kg + 5 kg = 10 kg).
Total momentum after the collision = total mass * final velocity (Vf)
= 10 kg * Vf
According to the principle of conservation of momentum, the total momentum before the collision (15 kg*m/s) is equal to the total momentum after the collision (10 kg * Vf). Therefore, we can set up an equation:
15 kg*m/s = 10 kg * Vf
Solving for Vf, we find:
Vf = (15 kg*m/s) / (10 kg)
Vf = 1.5 m/s
Therefore, the speed of the objects together after the collision is 1.5 m/s.
M1*V1 + M2*V2 = M1*V + M2*V
5*3 + 5*0 = 5*V + 5*V
Solve for v.