a bomb of 5 kg explodes into two equal fragments. At what angle, these fragments fly apart?
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To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the explosion is equal to the total momentum after the explosion.
Let's assume that after the explosion, each fragment has a mass of m kg and they fly off in opposite directions, making an angle θ with respect to the original direction of the bomb's momentum.
1. Before the explosion:
The bomb's momentum is given by P = mv, where m is the mass of the bomb and v is its velocity.
Therefore, the initial momentum is P_initial = 5 kg * v.
2. After the explosion:
After the explosion, the fragments fly off in opposite directions.
The momentum of the first fragment is given by P1 = mv1, where m is the mass of each fragment and v1 is the velocity of the first fragment.
The momentum of the second fragment is given by P2 = mv2, where v2 is the velocity of the second fragment.
Since the fragments have equal masses and opposite velocities, we have v1 = -v2.
Therefore, the total momentum after the explosion is P_total = P1 + P2 = mv1 + mv2 = mv1 - mv1 = 0.
3. Conservation of momentum:
According to the principle of conservation of momentum, the initial and total momentums should be equal.
Therefore, P_initial = P_total.
So, 5 kg * v = 0.
Since the initial momentum is zero, it means the bomb was at rest before the explosion. Therefore, both fragments will move off in opposite directions with equal magnitudes of velocity, and the angle between them will be 180 degrees or π radians.
To find the angle at which two fragments fly apart after a bomb explosion, we can make use of the concept of conservation of momentum.
Here's how to approach it:
Step 1: Understand the conservation of momentum.
When no external forces are acting on a system, the total momentum before an event is equal to the total momentum after the event. This principle is known as the conservation of momentum.
Step 2: Determine the initial momentum.
In this case, the bomb is at rest before the explosion, so the initial momentum is zero.
Step 3: Calculate the momentum after the explosion.
Since the bomb fragments into two equal fragments, each fragment will have half the mass of the bomb (5 kg) and will fly in opposite directions. Let's call the mass of each fragment "m." Hence, each fragment will have a mass of 2.5 kg.
The momentum of the first fragment can be represented as p1 = m * v1, where "v1" is the velocity of the first fragment after the explosion.
The momentum of the second fragment can be represented as p2 = m * v2, where "v2" is the velocity of the second fragment after the explosion.
Since the fragments fly in opposite directions, the magnitude of their velocities will be the same. Therefore, v1 = -v2.
So, p1 = m * (-v2) = -m * v2.
Step 4: Apply the conservation of momentum.
According to the conservation of momentum, the total momentum after the explosion should be zero because the bomb was initially at rest. Therefore, p1 + p2 = 0.
Substituting the values, we have:
-m * v2 + m * v2 = 0
The two terms cancel each other out, resulting in 0 = 0.
Step 5: Determine the angle.
Since both terms of the equation cancel each other out, there is no specific angle at which the fragments fly apart. In this scenario, the fragments will move in opposite directions, along a straight line.
To summarize, when a bomb of 5 kg explodes into two equal fragments, the fragments will fly apart in opposite directions along a straight line, rather than at a specific angle.