A 50g bullet strikes a stationary 1.50kg block of wood paced on a horizontal surface just in front of the gun. The bullet becomes embedded in the block and the impact drives them a distance of 10m before they come to rest. If the coefficient of kinetic friction between the block and the surface is .520, what was the speed of the bullet?
Momentum is conserved during collision
use that to find v of total mass after collision in terms of initial Vi of bullet
(.050+1.5) v = .050 Vi
work done by friction = (1/2) m v^2 = u m g*10
where m is .050+1.5
To find the speed of the bullet, we need to use the principle of conservation of momentum. This principle states that the total momentum of a system before an event is equal to the total momentum after the event, assuming no external forces act on the system.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Let's first find the initial momentum of the system. The bullet is initially moving, while the block is stationary. Therefore, the initial momentum will be the momentum of the bullet, and we can calculate it using the given mass of the bullet (50g = 0.05kg) and the unknown initial velocity (v).
Initial momentum = Momentum of the bullet = (mass of the bullet) * (initial velocity of the bullet) = 0.05kg * v
After the impact, the bullet becomes embedded in the block and both objects move together. They come to rest after covering a distance of 10m, which means their final velocity is 0.
Final momentum = Momentum of the block and bullet = (mass of the block + mass of the bullet) * (final velocity)
Now, let's set up the conservation of momentum equation:
Initial momentum = Final momentum
0.05kg * v = (1.50kg + 0.05kg) * 0
Since the final velocity is zero, the right side of the equation becomes zero. The equation then simplifies to:
0.05kg * v = 0
To solve for v, divide both sides of the equation by 0.05kg:
v = 0 / 0.05kg
v = 0
Therefore, the speed of the bullet (initial velocity) is 0. The bullet was not moving before it struck the block of wood.