A stationary bomb of 10kg mass explodes into 3 fragments. two of these parts having mass 4kg and 2kg,fly apart perpendicular to each other with a velocity of 2ms-1 and 3ms-1.find magnitude and direction of 3rd part.
45mls
To find the magnitude and direction of the third fragment, we will use the principle of conservation of momentum. According to this principle, the total momentum before the explosion should be equal to the total momentum after the explosion.
Let's define the directions of the fragments as follows:
- Fragment with mass 4kg: To the right (positive x-axis direction)
- Fragment with mass 2kg: Upwards (positive y-axis direction)
- Fragment with unknown mass: We need to find the magnitude and direction
Step 1: Calculate the initial total momentum.
Before the explosion, the bomb was stationary, which means its momentum was zero since momentum (p) is given by the product of mass (m) and velocity (v): p = mv.
Initial momentum = 0 kg * 0 m/s = 0 kgm/s
Step 2: Calculate the final total momentum.
After the explosion, the fragments fly apart. Let's denote the unknown mass by 'm'. Since the two fragments are flying off perpendicular to each other, we can calculate their momenta separately using their respective masses and velocities.
Fragment with mass 4kg: momentum = mass * velocity = 4kg * 2m/s = 8 kgm/s
Fragment with mass 2kg: momentum = mass * velocity = 2kg * 3m/s = 6 kgm/s
Now, we can calculate the total momentum after the explosion:
Final total momentum = 8 kgm/s (in the x-direction) + 6 kgm/s (in the y-direction)
= √(8² + 6²) kgm/s (magnitude of the resultant momentum)
= √(64 + 36) kgm/s
= √100 kgm/s
= 10 kgm/s
Step 3: Calculate the momentum of the unknown mass.
Since the total momentum after the explosion must be equal to the initial total momentum, we can find the momentum of the unknown mass:
Total momentum before explosion = Total momentum after explosion
0 kgm/s = 10 kgm/s + momentum of the unknown mass
Therefore, momentum of the unknown mass = -10 kgm/s
Step 4: Determine the magnitude and direction of the momentum of the unknown mass.
The magnitude of the momentum of the unknown mass is 10 kgm/s. The negative sign indicates that it is moving in the opposite direction to the total momentum after the explosion. However, since we don't have any information about the direction of the unknown mass fragment, we cannot determine its direction without additional data.
Therefore, the magnitude of the momentum of the third fragment is 10 kgm/s, but the direction remains unknown without further information.