A freight train rolls along a track with considerable momentum. If it rolls at the same speed but has twice as much mass, its momentum is
Understand the Problem
The question is asking about the change in momentum of a freight train when its mass is doubled while maintaining the same speed. It seeks to determine how this change affects its momentum.
Answer
The freight train's momentum is doubled, so $p = 2p_i$.
Answer for screen readers
The momentum of the freight train is doubled.
Steps to Solve
-
Understanding momentum formula Momentum ($p$) is calculated with the formula: $$ p = mv $$ where $m$ is mass and $v$ is velocity.
-
Identifying the initial momentum Let the initial mass of the train be $m$. The initial momentum ($p_i$) can be expressed as: $$ p_i = mv $$
-
Calculating the new mass and momentum If the mass is doubled, the new mass becomes $2m$. Since the speed remains the same, the new momentum ($p_f$) is: $$ p_f = (2m)v = 2(mv) = 2p_i $$
-
Comparing initial and final momentum Therefore, the final momentum is twice the initial momentum: $$ p_f = 2p_i $$
The momentum of the freight train is doubled.
More Information
Momentum is a vector quantity that depends on both mass and velocity. If either of these changes, momentum will change accordingly. Doubling the mass while maintaining the same velocity leads to a linear increase in momentum.
Tips
- Confusing velocity with momentum: Remember that momentum depends on both mass and velocity. Just changing one does not determine momentum solely.
- Assuming momentum is unchanged: Always calculate and compare the initial and final values to conclude.
AI-generated content may contain errors. Please verify critical information
