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Answer :
To solve this problem, we need to calculate the total momentum of the system before the collision. Momentum is a measure of motion that is calculated as the product of an object's mass and its velocity. It is a vector quantity, which means it has both magnitude and direction. When dealing with momentum in a collision, it is important to pay attention to the direction of motion and assign correct signs to velocities.
Here is the step-by-step solution:
1. Identify the Masses and Velocities:
- The first bumper car has a mass of 222 kg and is moving to the right at a velocity of 3.10 m/s.
- The second bumper car has a mass of 165 kg and is moving to the left at a velocity of 1.88 m/s.
2. Assign Directions:
- We will consider the right direction as positive and the left direction as negative.
3. Calculate Momentum for Each Bumper Car:
- Momentum of the first bumper car (moving right):
[tex]\[
\text{Momentum}_1 = \text{mass}_1 \times \text{velocity}_1 = 222 \, \text{kg} \times 3.10 \, \text{m/s} = 688.2 \, \text{kg} \cdot \text{m/s}
\][/tex]
- Momentum of the second bumper car (moving left):
[tex]\[
\text{Momentum}_2 = \text{mass}_2 \times \text{velocity}_2 = 165 \, \text{kg} \times (-1.88) \, \text{m/s} = -310.2 \, \text{kg} \cdot \text{m/s}
\][/tex]
(Here the velocity is negative because the car is moving in the opposite direction.)
4. Calculate the Total Momentum of the System:
- The total momentum is the sum of the individual momenta:
[tex]\[
\text{Total Momentum} = \text{Momentum}_1 + \text{Momentum}_2 = 688.2 \, \text{kg} \cdot \text{m/s} + (-310.2) \, \text{kg} \cdot \text{m/s} = 378.0 \, \text{kg} \cdot \text{m/s}
\][/tex]
Therefore, the total momentum of the system before the collision is 378.0 kg·m/s.
Here is the step-by-step solution:
1. Identify the Masses and Velocities:
- The first bumper car has a mass of 222 kg and is moving to the right at a velocity of 3.10 m/s.
- The second bumper car has a mass of 165 kg and is moving to the left at a velocity of 1.88 m/s.
2. Assign Directions:
- We will consider the right direction as positive and the left direction as negative.
3. Calculate Momentum for Each Bumper Car:
- Momentum of the first bumper car (moving right):
[tex]\[
\text{Momentum}_1 = \text{mass}_1 \times \text{velocity}_1 = 222 \, \text{kg} \times 3.10 \, \text{m/s} = 688.2 \, \text{kg} \cdot \text{m/s}
\][/tex]
- Momentum of the second bumper car (moving left):
[tex]\[
\text{Momentum}_2 = \text{mass}_2 \times \text{velocity}_2 = 165 \, \text{kg} \times (-1.88) \, \text{m/s} = -310.2 \, \text{kg} \cdot \text{m/s}
\][/tex]
(Here the velocity is negative because the car is moving in the opposite direction.)
4. Calculate the Total Momentum of the System:
- The total momentum is the sum of the individual momenta:
[tex]\[
\text{Total Momentum} = \text{Momentum}_1 + \text{Momentum}_2 = 688.2 \, \text{kg} \cdot \text{m/s} + (-310.2) \, \text{kg} \cdot \text{m/s} = 378.0 \, \text{kg} \cdot \text{m/s}
\][/tex]
Therefore, the total momentum of the system before the collision is 378.0 kg·m/s.
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