Question

I've been working on this question for a bit now. Please help me if you can!!

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Bug vs. Car:  A car with a mass of 1000kg is traveling west at 15m/s and hits a bug with a mass of 0.0001kg moving east with a velocity of 20m/s.  A.) Is this an elastic or inelastic collision? B.) What is the new velocity of the car?

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Answer 1

A) Inelastic

There are two types of collisions:

- Elastic collision: an elastic collision occurs when the two objects bounces on each other; in this type of collision, both the total momentum and the total kinetic energy of the system are conserved

- Inelastic collision: in such a collision, only the total momentum is conserved, while the total kinetic energy is not conserved (some is converted into heat and other forms of energy due to the presence of frictions). In particular, we call the collision "perfectly inelastic collision" when the two object stick together after the collision.

In the bug vs. car collision in the problem, the car and the bug stick together after the collision, so this is an example of inelastic collision.

B) +14.999997 m/s, west

We can use the law of conservation of total momentum to find the new velocity of the car+bug together:

`m_c u_c + m_b u_B = (m_c+m_B)v`

where

`m_c = 1000 kg` is the mass of the car

`u_c =+15 m/s` is the initial velocity of the car (we have taken west as positive direction)

`m_B = 0.0001 kg` is the mass of the bug

`u_B = -20 m/s` is the initial velocity of the bug (negative since it is opposite to the direction of the car)

v is the final velocity of the car+bug

Solving for v, we find

`v=(m_cu_c+m_B u_B)/(m_c+m_B)=((1000 kg)(+15 m/s)+(0.0001 kg)(-20 m/s))/(1000 kg+0.0001 kg)=+14.999997 m/s`

and the direction is still west.