a 2kg block of wood rests on a long table top. a 5 gram bullet moving horizontally with speed of 150m/s is shoot into the block and stricks in it then block slides 270cm along the table and stops. find
a)speed of block after impact
b)friction force between block and table.
To find the solutions to these questions, we need to apply the principle of conservation of momentum and use the concept of work done by friction. Here's how we can calculate the solutions step by step:
Step 1: Calculate the initial momentum of the bullet-block system.
The initial momentum of the bullet-block system is calculated as the product of the mass and velocity of the bullet. The bullet's mass is given as 5 grams, which is 0.005 kg, and its velocity is given as 150 m/s.
Initial momentum of the bullet-block system = mass of bullet * velocity of bullet
= 0.005 kg * 150 m/s
Step 2: Calculate the final momentum of the bullet-block system.
Since the bullet gets embedded in the block, the final momentum of the system can be calculated using the mass and velocity of the block after the impact. The mass of the block is given as 2 kg.
Final momentum of the bullet-block system = mass of block * velocity of block
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.
Initial momentum of the bullet-block system = Final momentum of the bullet-block system
Using this equation, we can find the velocity of the block after the impact.
Step 4: Calculate the speed of the block after the impact.
To determine the speed of the block after the impact, we need to divide the final momentum of the system by the mass of the block.
Velocity of block = Final momentum of the bullet-block system / mass of block
Step 5: Convert the velocity of the block into speed.
Since the velocity is a vector quantity, to find the speed, we need to take its magnitude (absolute value).
Speed of block after impact = |Velocity of block|
Step 6: Calculate the friction force between the block and the table.
To find the friction force, we need to apply the concept of work done by friction. The work is given by the product of the friction force and the displacement of the block.
Work done by friction = friction force * displacement
Using this equation, we can rearrange it to solve for the friction force.
Friction force = Work done by friction / displacement
Now, let's calculate the solutions:
Step 1:
Initial momentum of the bullet-block system = 0.005 kg * 150 m/s
Step 2:
Final momentum of the bullet-block system = 2 kg * velocity of the block
Step 3:
0.005 kg * 150 m/s = 2 kg * velocity of the block
Step 4:
velocity of the block = (0.005 kg * 150 m/s) / 2 kg
Step 5:
Speed of block after impact = |velocity of the block|
Step 6:
Friction force = Work done by friction / 270 cm
Please note that in Step 5, I mention taking the magnitude (absolute value) of the velocity because we are only interested in the magnitude of the speed, not the direction.
Let me know if you need any further assistance with the calculations!