A bullet of mass m= 2.50×10-2kg is fired along an incline and imbeds itself quickly into a block of wood of mass M= 1.60kg. The block and bullet then slide up the incline, assumed frictionless, and rise a height H= 1.45m before stopping. Calculate the speed of the bullet just before it hits the wood.
Use conservation of momentum to get initial speed of bullet/block system
(m+M)V = m v so V =mv/(m+M)
calculate (1/2) (m+M) V^2
then (m+M) g h = (1/2) (m+M)V^2
calculate V then go back to v = (m+M)V/m
To calculate the speed of the bullet just before it hits the wood, we can use the principle of conservation of mechanical energy. Here's how you can solve it step by step:
Step 1: Identify the initial and final positions of the bullet and block.
The initial position is when the bullet and block are at the bottom of the incline, and the final position is when they reach a height of H=1.45m.
Step 2: Calculate the gravitational potential energy at the initial and final positions.
At the initial position, the gravitational potential energy is zero, as both the bullet and block are at the bottom.
At the final position, the gravitational potential energy is given by: U = mgh, where m is the total mass of the bullet and block, g is the acceleration due to gravity, and h is the height H.
Step 3: Calculate the initial kinetic energy of the bullet.
The initial kinetic energy of the bullet is given by: K = (1/2)mv^2, where m is the mass of the bullet and v is its velocity.
Step 4: Apply the conservation of mechanical energy.
According to the principle of conservation of mechanical energy, the total mechanical energy at the initial position is equal to the total mechanical energy at the final position. This can be expressed as:
K(initial) = K(final) + U(final)
Step 5: Use the conservation equation to solve for the initial velocity.
Substitute the values into the conservation equation and solve for v:
(1/2)mv^2 = mgh
Simplify the equation:
v^2 = 2gh
Take the square root of both sides:
v = √(2gh)
Now, plug in the known values:
v = √(2 * 9.8 * 1.45)
Calculate the value:
v ≈ 5.29 m/s
Therefore, the speed of the bullet just before it hits the wood is approximately 5.29 m/s.