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?

Question

(1 point)
A. • 1.0 m/s
B. • 2.3 m/s
C. • 3.0 m/s
D. • 2.7 m/s

Answer 1

To prove the conservation of momentum, we need to equate the total momentum before the collision to the total momentum after the collision.

Given:

• Mass of first bumper car (m1) = 120 kg
• Initial velocity of first bumper car (u1) = 4.0 m/s
• Final velocity of first bumper car (v1) = -2.0 m/s
• Mass of second bumper car (m2) = 90 kg
• Initial velocity of second bumper car (u2) = -5.0 m/s
• Final velocity of second bumper car (v2) = ? (we need to find this)

Before the collision: Total momentum before = m1 * u1 + m2 * u2

Calculating the initial momentum:

• \( m1 * u1 = 120 , \text{kg} * 4.0 , \text{m/s} = 480 , \text{kg m/s} \)
• \( m2 * u2 = 90 , \text{kg} * -5.0 , \text{m/s} = -450 , \text{kg m/s} \)

So, Total momentum before = \( 480 , \text{kg m/s} - 450 , \text{kg m/s} = 30 , \text{kg m/s} \)

After the collision: Total momentum after = m1 * v1 + m2 * v2

Calculating the momentum after:

• \( m1 * v1 = 120 , \text{kg} * -2.0 , \text{m/s} = -240 , \text{kg m/s} \)
• \( m2 * v2 = 90 , \text{kg} * v2 \)

Setting the total momentum before equal to the total momentum after gives us the equation: \[ 30 , \text{kg m/s} = -240 , \text{kg m/s} + 90 , \text{kg} * v2 \]

Solving for \( v2 \): \[ 30 + 240 = 90 * v2 \] \[ 270 = 90 * v2 \] \[ v2 = \frac{270}{90} = 3.0 , \text{m/s} \]

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

The correct answer is: C. 3.0 m/s