A car has a momentum of [tex]$20,000 kg \cdot m / s$[/tex]. What would the car's momentum be if its velocity doubles?
Answer (1)
Define momentum as p = m v .
Given initial momentum p 1 = 20 , 000 k g c d o t m / s and final velocity v 2 = 2 v 1 .
Calculate final momentum p 2 = m v 2 = 2 m v 1 = 2 p 1 .
Find p 2 = 2 ( 20 , 000 k g c d o t m / s ) = 40 , 000 k g c d o t m / s .
Explanation
Understanding the Problem We are given that a car has a momentum of 20 , 000 k g c d o t m / s . We need to find the car's momentum if its velocity doubles.
Defining Momentum Momentum is defined as the product of mass and velocity, i.e., p = m v , where p is momentum, m is mass, and v is velocity.
Initial Momentum Let the initial momentum be p 1 and the initial velocity be v 1 . Then, p 1 = m v 1 . We are given that p 1 = 20 , 000 k g c d o t m / s .
Final Velocity Let the final momentum be p 2 and the final velocity be v 2 . We are given that the final velocity is twice the initial velocity, i.e., v 2 = 2 v 1 .
Calculating Final Momentum We want to find the final momentum p 2 . We have p 2 = m v 2 = m ( 2 v 1 ) = 2 ( m v 1 ) = 2 p 1 .
Final Answer Since p 1 = 20 , 000 k g c d o t m / s , we have p 2 = 2 ( 20 , 000 k g c d o t m / s ) = 40 , 000 k g c d o t m / s .
Examples
Understanding momentum is crucial in many real-world scenarios, such as car crashes. If a car's velocity doubles, its momentum also doubles, meaning it would have twice the impact in a collision. This concept is also important in sports, like understanding how a baseball bat transfers momentum to a ball, affecting its speed and distance. By understanding momentum, we can better analyze and predict the outcomes of various physical interactions.
