A box of mass m = 6kg slides with speed v = 4 m/s across a frictionless floor. It suddenly explodes into two pieces. One piece, with mass m1 = 2kg moves in the same direction with speed v1 = 8m/s. Find the velocity of the second piece.
Its answer is 2 m/s , but I don't know how to solve it, my answer was 4 m/s, see how I solved it.
Solution: Mass 6 kg, splits into m1=2kg and m2=4kg, v1= 8m/s, v2=?
m1 v1 = m2 v2
(2) (8) = (4) (v2)
16/4 = V2
v2= 4 m/s
BUT THE ANSWER IS 2 m/s , so what was my mistake that cost me wrong answer , please help me.
original momentum = 6 * 4 = 24
final momentum = 2 * 8 + V * 4
16 + 4 v = 24
4 v = 8
v = 2 m/s
@damon , thanks sir
I was also searching this . It helped me
Well, it seems like you got your calculation right, but you forgot one crucial detail - the conservation of momentum. When an object explodes into two pieces, the total momentum of the system must remain the same.
In this case, the momentum before the explosion is given by:
momentum before = (mass of box) x (velocity of box) = (6 kg) x (4 m/s) = 24 kg·m/s
After the explosion, the total momentum is divided between the two pieces. We know the mass and velocity of one piece, so we can calculate its momentum:
momentum of piece 1 = (mass of piece 1) x (velocity of piece 1) = (2 kg) x (8 m/s) = 16 kg·m/s
To find the momentum of the second piece, we can subtract the momentum of the first piece from the total momentum before the explosion:
momentum of piece 2 = momentum before - momentum of piece 1 = 24 kg·m/s - 16 kg·m/s = 8 kg·m/s
Now, we can find the velocity of the second piece by dividing its momentum by its mass:
velocity of piece 2 = (momentum of piece 2) / (mass of piece 2) = (8 kg·m/s) / (4 kg) = 2 m/s
So, the correct answer is indeed 2 m/s. Keep in mind the importance of considering the conservation of momentum in physics problems. And don't worry, even clowns sometimes forget things.
To find the velocity of the second piece, let's analyze the situation using the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before and after an event remains constant, as long as there are no external forces acting on the system.
Before the explosion, the box is sliding with a velocity of 4 m/s, and the total mass is 6 kg.
After the explosion, the box splits into two pieces, one with a mass of 2 kg (m1) and a velocity of 8 m/s (v1), and the other with a mass of 4 kg (m2) and an unknown velocity (v2).
Let's now apply the conservation of momentum equation:
Initial momentum = Final momentum
(mass of box) * (initial velocity of box) = (mass of piece 1) * (final velocity of piece 1) + (mass of piece 2) * (final velocity of piece 2)
(6 kg) * (4 m/s) = (2 kg) * (8 m/s) + (4 kg) * (v2)
Simplifying the equation:
24 kg·m/s = 16 kg·m/s + 4 kg·v2
Subtracting 16 kg·m/s from both sides:
8 kg·m/s = 4 kg·v2
Dividing both sides by 4 kg:
2 m/s = v2
Therefore, the velocity of the second piece is indeed 2 m/s.
Your mistake in the calculation was a simple arithmetic error. Instead of dividing 16/4, you accidentally wrote it as 16/4 = v2, resulting in v2 = 4 m/s. However, the correct calculation should have been 16/4 = 4, and then dividing both sides by 4 kg gives v2 = 2 m/s.