A 5kg bullet fired from a gun at 725m/s becomes embedded in a .50kg block of wood that is free to move along a surface and the coefficient of friction .355 between the surface and block of wood. find the distance it slides acroos the table
To find the distance the block slides across the table, we need to consider the conservation of momentum and the work done by friction.
First, let's calculate the initial momentum of the bullet before it hits the block. The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v):
Momentum of bullet = mass of bullet x velocity of bullet
= 5 kg x 725 m/s
= 3625 kg·m/s
Since the bullet becomes embedded in the block, the final momentum of the bullet and the block together is equal to the initial momentum of the bullet.
Now, let's calculate the final velocity of the bullet and block together after the collision. The total mass after the collision is the sum of the masses of the bullet and the wood block.
Mass after collision = mass of bullet + mass of block
= 5 kg + 0.50 kg
= 5.50 kg
Using the principle of conservation of momentum, we can calculate the final velocity (v_f) of the bullet and block using the equation:
Initial momentum = Final momentum
Initial momentum of bullet = Final momentum of bullet + block
(5 kg x 725 m/s) = (5.50 kg) x v_f
Simplifying the equation:
3625 kg·m/s = 5.50 kg x v_f
v_f = 3625 kg·m/s / 5.50 kg
≈ 659.1 m/s
The final velocity of the bullet and block together after the collision is approximately 659.1 m/s.
Next, we need to find the distance the block slides across the table. The work done by friction can be calculated using the equation:
Work = force x distance
The force of friction can be calculated using the equation:
Force of friction = coefficient of friction x normal force
The normal force is equal to the weight of the block. The weight (W) is calculated by multiplying the mass (m) by the acceleration due to gravity (g).
Weight of block = mass of block x acceleration due to gravity
= 0.50 kg x 9.8 m/s^2
= 4.9 N
Now, we can calculate the force of friction:
Force of friction = coefficient of friction x normal force
= 0.355 x 4.9 N
≈ 1.7395 N
The force of friction acting on the block is approximately 1.7395 N.
The work done by friction is equal to the force of friction multiplied by the distance (d) the block slides:
Work = force of friction x distance
Since work is equal to force multiplied by distance, we can rearrange the equation to calculate the distance:
Distance = Work / force of friction
To find the work done by friction, we need to consider that the work done by friction opposing the motion is equal to the initial kinetic energy (KE) of the bullet and block before the collision, which is equal to:
Initial KE = 0.5 x mass x velocity^2
Initial KE = 0.5 x 5.50 kg x (725 m/s)^2
≈ 1362812.5 J
Now we can calculate the distance:
Distance = Work / force of friction
= Initial KE / force of friction
= 1362812.5 J / 1.7395 N
≈ 783782.57 m
The block slides approximately 783782.57 meters across the table.