A body of mass 10 kg with a velocity of 20 meters per second collides with another mass of 8 kg moving in the same direction with a velocity of 5 meters per second. After the colli... A body of mass 10 kg with a velocity of 20 meters per second collides with another mass of 8 kg moving in the same direction with a velocity of 5 meters per second. After the collision, if the velocity of the former is reduced to 16 meters per second, calculate the velocity of the latter.
Understand the Problem
The question is asking us to calculate the final velocity of a mass after a collision, given the masses and initial velocities of both bodies involved. We will use the principle of conservation of momentum to solve this problem.
Answer
To find the final velocities, use the conservation of momentum: $m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$.
Answer for screen readers
The answer will depend on the specific values of masses and initial velocities provided.
Steps to Solve
- Identify the given values
Let:
- Mass of object 1, ( m_1 )
- Initial velocity of object 1, ( v_{1i} )
- Mass of object 2, ( m_2 )
- Initial velocity of object 2, ( v_{2i} )
- Apply conservation of momentum
According to the principle of conservation of momentum, the total momentum before the collision equals the total momentum after the collision. The formula is:
$$ m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} $$
Where ( v_{1f} ) and ( v_{2f} ) are the final velocities of objects 1 and 2 after the collision.
- Rearrange the equation for final velocities
If we need the final velocities:
$$ m_1 v_{1i} + m_2 v_{2i} - m_1 v_{1f} = m_2 v_{2f} $$
We can rearrange this to solve for one of the final velocities depending on the scenario (elastic or inelastic collision).
- Insert known values and solve for the unknown
Substitute the known values into the momentum equation and solve for the unknown final velocity.
The answer will depend on the specific values of masses and initial velocities provided.
More Information
In an elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision, only momentum is conserved. This means the method of approach for calculating final velocities might differ based on the type of collision considered.
Tips
- Forgetting to consider the direction of velocities (it is important to keep track of whether velocities are positive or negative).
- Not applying the conservation of momentum correctly for inelastic collisions.
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