how do i go about in solving this?
A helium atom (mass 4.0 u) moving at 596 m/s to the right collides with an oxygen molecule (mass 32 u) moving in the same direction at 402 m/s. After the collision, the oxygen molecule moves at 445 m/s to the right. What is the velocity of the helium atom after the collision?
total momentum before collision to the right=
4*596 + 32*402
total momentum to the right after collision=
4*v + 32*445
total momentum after = total momentum before so solve for v
To solve this problem, you can use the concept of conservation of momentum. According to this principle, in the absence of external forces, the total momentum of a system before a collision is equal to the total momentum after the collision.
Here's how you can go about solving the problem step by step:
1. Define the variables:
- Let the velocity of the helium atom after the collision be denoted by v1 (in m/s).
- Let the velocity of the oxygen molecule after the collision be denoted by v2 (in m/s).
2. Apply conservation of momentum:
- Before the collision, the total momentum is the sum of the momenta of the helium atom and the oxygen molecule. It is given by:
Momentum_before = (mass_helium * velocity_helium) + (mass_oxygen * velocity_oxygen)
- After the collision, the total momentum is the sum of the momenta of the helium atom and the oxygen molecule. It is given by:
Momentum_after = (mass_helium * v1) + (mass_oxygen * v2)
Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision:
Momentum_before = Momentum_after
3. Substitute the given information:
- Mass of helium atom (m_helium) = 4.0 u
- Velocity of helium atom before collision (v_helium) = 596 m/s
- Mass of oxygen molecule (m_oxygen) = 32 u
- Velocity of oxygen molecule before collision (v_oxygen) = 402 m/s
- Velocity of oxygen molecule after collision (v2) = 445 m/s
Substituting these values into the conservation of momentum equation, we get:
(4.0 * 596) + (32 * 402) = (4.0 * v1) + (32 * 445)
4. Solve for v1:
Rearrange the equation to solve for v1:
(4.0 * v1) = (4.0 * 596) + (32 * 402) - (32 * 445)
v1 = [(4.0 * 596) + (32 * 402) - (32 * 445)] / 4.0
Evaluating this expression will give you the velocity of the helium atom after the collision (v1).
5. Calculate the value of v1:
Plug in the values and evaluate the expression:
v1 = [(4.0 * 596) + (32 * 402) - (32 * 445)] / 4.0
Therefore, by plugging in the values and evaluating the expression, you will find the final velocity of the helium atom after the collision.