A 2 gram bullet traveling at 1500 m/s [East] hits a 200 g block of wood at rest, and becomes embedded in it. If the block is suspended by long ropes, how high will it travel before it comes to rest?
calculate the velocity of the bullet/block combined mass with the conservation of momentum equation. Now, knowing the velocity, you can set
finalPotentailEnergy=initialKineticenergy
mgh=1/2 m v^2
and solve for height h.
To determine how high the block of wood will travel before coming to rest, we can apply the principle of conservation of mechanical energy.
1. First, let's calculate the initial kinetic energy (KE_initial) of the bullet before it hits the block of wood.
The formula for kinetic energy is:
KE = 0.5 * m * v^2
Where:
KE is the kinetic energy
m is the mass of the object
v is the velocity
The mass of the bullet is given as 2 grams, which is 0.002 kg (since 1 gram = 0.001 kg).
The velocity of the bullet is given as 1500 m/s [East].
Using the formula, we can calculate the initial kinetic energy:
KE_initial = 0.5 * 0.002 kg * (1500 m/s)^2
2. Next, let's determine the potential energy (PE) at the highest point of the block's trajectory. At this point, all the initial kinetic energy of the bullet is converted into potential energy.
The formula for potential energy is:
PE = m * g * h
Where:
PE is the potential energy
m is the mass of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height
Since the block is at rest when the bullet hits it, the mass of the block (200 grams) is used to calculate the potential energy.
3. Equating the initial kinetic energy to the potential energy, we have:
KE_initial = PE
0.5 * 0.002 kg * (1500 m/s)^2 = 0.200 kg * 9.8 m/s^2 * h
Simplifying the equation:
0.5 * 0.002 kg * 2250000 m^2/s^2 = 0.200 kg * 9.8 m/s^2 * h
1125 J = 1.96 J/kg * h
4. Finally, solve for the height (h):
h = 1125 J / 1.96 J/kg
h ≈ 573.98 meters
Therefore, the block of wood will travel approximately 573.98 meters high before it comes to rest.