Answer :
To find the speed of the bullet before impact, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
Let's break down the problem step by step:
Step 1: Calculate the momentum of the bullet before impact.
Momentum = mass x velocity
The mass of the bullet is given as 9 g, which is equivalent to 0.009 kg.
Let's assume the velocity of the bullet before impact is v m/s.
So, the momentum of the bullet before impact is 0.009v kg·m/s.
Step 2: Calculate the momentum of the block after impact.
Since the bullet stays inside the block, the mass of the block with the bullet is 98.2 g + 9 g, which is equal to 0.1072 kg.
Let's assume the final velocity of the block (after impact) is u m/s.
So, the momentum of the block after impact is 0.1072u kg·m/s.
Step 3: Apply the principle of conservation of momentum.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Therefore, we have the equation: 0.009v = 0.1072u.
Step 4: Calculate the distance traveled by the block before it comes to rest.
The block slides a distance of 15 m before coming to rest. This means that the work done against friction is equal to the kinetic energy of the block. We can use this information to find the frictional force and then calculate the deceleration of the block.
The work done against friction is given by the equation: Work = force x distance
The force of friction is equal to the coefficient of friction multiplied by the normal force. The normal force is equal to the weight of the block, which is given by the equation: Normal force = mass x gravity.
So, the force of friction is: Frictional force = coefficient of friction x mass x gravity.
The work done against friction is equal to the kinetic energy of the block, which is given by the equation: Work = 0.5 x mass x final velocity^2.
Since the block comes to rest, the final velocity is 0 m/s.
By equating the work done against friction to the kinetic energy, we can solve for the force of friction and then find the deceleration of the block using the equation: Force = mass x acceleration.
Finally, we can use the equation: Distance = initial velocity^2 / (2 x acceleration) to find the distance traveled by the block.
Step 5: Solve the equations simultaneously.
We have two equations:
0.009v = 0.1072u (from Step 3)
Distance = (u^2) / (2 x acceleration) (from Step 4)
Substitute the known values into these equations and solve them simultaneously to find the value of v, which represents the speed of the bullet before impact.
To learn more about conservation of momentum
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