A 1,59 block of wood is placed on the edge of a table 1,2m above the floor.the block is stuck by a bullet,mass 0,01kg,moving @an unknown,horizontal velocity.After the impact,the bullet is embedded in the block,which falls to the floor.the block strikes the floor with a speed of 5m.s-1.ignore all types of triction.calculate the velocity with which the bullet strikes the block
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To calculate the velocity with which the bullet strikes the block, we can use the principle of conservation of momentum.
The momentum before the impact is equal to the momentum after the impact.
The momentum of an object is calculated by multiplying its mass by its velocity.
Given:
Mass of the bullet (m1) = 0.01 kg
Velocity of the bullet (v1) = unknown
Mass of the block (m2) = 1.59 kg
Velocity of the block before the impact (v2) = 0 (since it is at rest)
Velocity of the block after the impact (v3) = 5 m/s
Using the principle of conservation of momentum, we can write the equation:
m1 * v1 + m2 * v2 = m1 * v1 + m2 * v3
We know that the bullet is embedded in the block, so the final velocity of the block after the impact (v3) will be the same as the velocity of the bullet before the impact (v1).
Substituting the known values into the equation, we get:
0.01 kg * v1 + 1.59 kg * 0 = 0.01 kg * v1 + 1.59 kg * 5
0.01 kg * v1 = 1.59 kg * 5
0.01 kg * v1 = 7.95 kg m/s
Dividing both sides of the equation by 0.01 kg, we find:
v1 = 7.95 kg m/s / 0.01 kg
v1 = 795 m/s
Therefore, the velocity with which the bullet strikes the block is 795 m/s.
To calculate the velocity with which the bullet strikes the block, we can use the principle of conservation of momentum. The momentum before the impact is equal to the momentum after the impact.
1. First, we need to determine the initial momentum before the impact. The block is initially at rest, so its momentum is zero.
2. The bullet's momentum before the impact can be calculated using the formula p = m * v, where p is the momentum, m is the mass, and v is the velocity. Since the bullet's mass is given as 0.01 kg, we need to find its velocity.
3. To find the bullet's velocity, we can use the principle of conservation of energy. The potential energy of the block, just before it falls, is equal to the bullet's kinetic energy just before the impact. We can express these energies using the formulas:
Potential Energy of the block = m * g * h, where m is the mass of the block (1.59 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the table (1.2 m).
Kinetic Energy of the bullet = (1/2) * m * v^2, where m is the mass of the bullet (0.01 kg), and v is its velocity.
Set these two equations equal to each other:
m * g * h = (1/2) * m * v^2
Now we can solve for v:
1.59 kg * 9.8 m/s^2 * 1.2 m = (1/2) * 0.01 kg * v^2
Simplify:
18.666 kg m^2/s^2 = 0.005 kg * v^2
Divide both sides by 0.005 kg:
v^2 = 18.666 kg m^2/s^2 / 0.005 kg
v^2 ≈ 3733.2 m^2/s^2
v ≈ √(3733.2 m^2/s^2)
v ≈ 61 m/s
So, the velocity with which the bullet strikes the block is approximately 61 m/s.
Note: It's important to remember that this calculation assumes there are no external forces acting on the system, such as air resistance or friction.