Select the best answer for the question.
15. A car with two people traveling down the road has a mass of 100 kg and a velocity of 5 m/s. The car pulls over and picks up two people. The mass of the car is now 150 kg. What's the new momentum if the velocity stays the same?
A. 500 kg-m/s
B. 750 kg-m/s
C. 250 kg-m/s
D. 1,250 kg-m/s
Answer (2)
Define momentum as the product of mass and velocity.
State the formula: $momentum = mass
\times velocity$.
Substitute the new mass (150 kg) and the constant velocity (5 m/s) into the formula.
Calculate the new momentum: 150 × 5 = 750 k g ⋅ m / s . The final answer is 750 kg-m/s .
Explanation
Understanding the Problem We are given a scenario where a car's momentum changes due to a change in mass. Momentum is defined as the product of mass and velocity. The car initially has a mass of 100 kg and a velocity of 5 m/s. After picking up two people, the mass increases to 150 kg, while the velocity remains constant at 5 m/s. We need to calculate the new momentum of the car.
Stating the Formula To find the new momentum, we use the formula: m o m e n t u m = ma ss × v e l oc i t y
Substituting the Values The new mass is 150 kg, and the velocity is 5 m/s. Substituting these values into the formula, we get: N e w M o m e n t u m = 150 k g × 5 m / s
Calculating the New Momentum Performing the multiplication, we find: N e w M o m e n t u m = 750 k g ⋅ m / s
Final Answer Therefore, the new momentum of the car is 750 kg-m/s.
Examples
Understanding momentum is crucial in many real-world scenarios, such as designing safer vehicles. For example, when engineers design cars, they consider how the momentum of the car changes during a collision. By understanding momentum, they can design safety features like airbags and crumple zones that help to reduce the force of impact on the occupants, potentially saving lives. Similarly, in sports, understanding momentum helps athletes to improve their performance, such as in baseball where the momentum of the bat and ball determines the distance the ball travels.
The new momentum of the car after picking up additional passengers is calculated using the formula for momentum, which is mass times velocity. Since the mass becomes 150 kg and the velocity remains 5 m/s, the new momentum is 750 kg-m/s. Therefore, the correct option is B. 750 kg-m/s.
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