At an amusement park, there are 200-kg bumper cars A, B, and...

At an amusement park, there are $200-\mathrm{kg}$ bumper cars $A, B,$ and $C$ that have riders with masses of $40 \mathrm{~kg}, 60 \mathrm{~kg}$, and $35 \mathrm{~kg}$, respectively. Car $A$ is moving to the right with a velocity $\mathbf{v}_{A}=2 \mathrm{~m} / \mathrm{s}$ and $\operatorname{car} C$ has a velocity $v_{B}=1.5 \mathrm{~m} / \mathrm{s}$ to the left, but car $B$ is initially at rest. The coefficient of restitution between each car is $0.8 .$ Determine the final velocity of each car, after all impacts, assuming ( $a$ ) cars $A$ and $C$ hit car $B$ at the same time, $(b)$ car $A$ hits car $B$ before car $C$ does.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Collision Sequencing (Simultaneous vs. Sequential Impacts)

When multiple bodies collide, the order in which impacts occur (simultaneously versus sequentially) can significantly alter the final outcome. Analyzing sequential collisions requires solving the interactions in steps, using the result of one collision as the initial condition for the next, whereas simultaneous collisions require a combined analysis of momentum and restitution effects from all bodies involved.

Coefficient of Restitution

This is a measure of the elasticity of a collision, defined as the ratio of the relative speed of separation to the relative speed of approach. The coefficient quantifies how much kinetic energy is retained or lost during the impact, and it is key to determining the post-collision velocities.

Conservation of Linear Momentum

In all collision problems involving isolated systems, the total linear momentum remains constant before and after the collision. This principle is used to relate the masses and velocities of objects involved in collisions, regardless of the sequence or simultaneity of impacts.

Transcript

Please give Ace some feedback