A 45.0g bullet is fired on a 2.0kg wooden block which is resting on a horizontal surface with a coefficient friction of 0.4 . If the speed of the bullet is 165m/s when it hits the block. Determine the maximum horizontal distance of the block will reach
oh yea the bullet was embedded to the block after it hits
momentum before = momentum just after
.045 * 165 = 2.045 * Vi
solve for Vi, the inital velocity fater collision
Ke = (1/2)(2.045)(Vi^2) initial kinetice energy of bullet-block system
That Ke will be the work done by friction:
Ke = F * d = mu m g * d
m cancels so
so
0.4 (9.81) d = 0.5 Vi^2
To determine the maximum horizontal distance the block will reach when the bullet hits it, we need to apply the principles of momentum and friction.
First, let's calculate the momentum of the bullet before it hits the block. Momentum is calculated by multiplying an object's mass by its velocity.
Momentum (bullet) = mass (bullet) x velocity (bullet)
= 45.0g x 165m/s (convert grams to kilograms by dividing by 1000)
= 0.045kg x 165m/s
= 7.425 kg·m/s
According to the principle of conservation of momentum, the total momentum of the system (bullet + block) before and after the collision remains constant. Therefore, the momentum of the bullet before it hits the block is equal to the combined momentum of the bullet and the block after the collision.
Now, let's consider what happens after the bullet hits the block. The bullet comes to a stop and transfers its momentum to the block, causing it to move. The block will start moving due to the frictional force acting on it.
The frictional force can be calculated using the coefficient of friction and the normal force. The normal force is equal to the weight of the block, which can be calculated by multiplying the mass of the block by the acceleration due to gravity.
Weight (block) = mass (block) x acceleration due to gravity
= 2.0kg x 9.8m/s²
= 19.6N
Frictional force = coefficient of friction x normal force
= 0.4 x 19.6N
= 7.84N
The frictional force opposes the motion of the block, so we need to apply the concept of work to determine how much work is done by the frictional force. The work done by a force can be calculated by multiplying the force by the displacement.
Work (friction) = frictional force x displacement
The work done by friction will be equal to the change in kinetic energy of the block (ΔKEblock) since the bullet transfers all its momentum to the block. This can be expressed as:
ΔKEblock = Work (friction)
The work done by friction can also be represented as the product of the frictional force and the distance traveled by the block. Therefore:
Work (friction) = frictional force x displacement
Now, the displacement of the block is what we want to determine, which is the maximum horizontal distance it reaches. We can rearrange the equation to solve for the displacement:
displacement = Work (friction) / frictional force
By substituting the values, we get:
displacement = (0.4 x 19.6N) / 7.84N
= 0.4 x 19.6 / 7.84
= 1.0m
Therefore, the maximum horizontal distance the block will reach is 1.0 meter.