Question

Two students in bumper cars want to prove conservation of momentum. They collide their bumper cars. The first bumper car has a mass of 120 kg and was moving with a velocity of 4.0 m/s before the collision and with a velocity of −2.0 m/s after the collision. The second bumper car has a mass of 90 kg and was moving at a velocity of −5.0 m/s before the collision. To prove conservation of momentum, what must the velocity of the second bumper car be after the collision?(1 point) Responses 3.0 m/s 3 point 0 meters per seconds 2.7 m/s 2 point 7 meters per seconds 1.0 m/s 1 point 0 meters per seconds 2.3 m/s

Answer 1

To prove conservation of momentum, we can use the principle that the total momentum before the collision must equal the total momentum after the collision.

Let's denote:
- Mass of the first bumper car \( m_1 = 120 \, \text{kg} \)
- Initial velocity of the first bumper car \( u_1 = 4.0 \, \text{m/s} \)
- Final velocity of the first bumper car \( v_1 = -2.0 \, \text{m/s} \)

- Mass of the second bumper car \( m_2 = 90 \, \text{kg} \)
- Initial velocity of the second bumper car \( u_2 = -5.0 \, \text{m/s} \)
- Final velocity of the second bumper car \( v_2 \) (this is what we need to find)

First, we calculate the total momentum before the collision:

\[
\text{Total momentum before} = m_1 u_1 + m_2 u_2
\]

\[
= (120 \, \text{kg} \times 4.0 \, \text{m/s}) + (90 \, \text{kg} \times -5.0 \, \text{m/s})
\]

\[
= 480 \, \text{kg m/s} - 450 \, \text{kg m/s}
\]

\[
= 30 \, \text{kg m/s}
\]

Next, we calculate the total momentum after the collision:

\[
\text{Total momentum after} = m_1 v_1 + m_2 v_2
\]

\[
= (120 \, \text{kg} \times -2.0 \, \text{m/s}) + (90 \, \text{kg} \times v_2)
\]

\[
= -240 \, \text{kg m/s} + 90 v_2
\]

Now, we set the total momentum before equal to the total momentum after:

\[
30 \, \text{kg m/s} = -240 \, \text{kg m/s} + 90 v_2
\]

Solving for \( v_2 \):

\[
30 + 240 = 90 v_2
\]

\[
270 = 90 v_2
\]

\[
v_2 = \frac{270}{90} = 3.0 \, \text{m/s}
\]

Therefore, the velocity of the second bumper car after the collision must be **3.0 m/s**.