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Ch 11: Impulse and Momentum
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 11: Impulse and MomentumProblem 14
Chapter 11, Problem 14

A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?

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Identify the principle involved: This is a conservation of momentum problem. The total momentum of the system (railroad car + gravel) before the gravel is dropped must equal the total momentum of the system after the gravel is dropped, assuming no external forces act on the system.
Write the equation for conservation of momentum: \( m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f \), where \( m_1 \) is the mass of the railroad car, \( v_1 \) is its initial velocity, \( m_2 \) is the mass of the gravel, \( v_2 \) is the initial velocity of the gravel (which is 0 since it is dropped vertically), and \( v_f \) is the final velocity of the system.
Substitute the known values into the equation: \( (10,000 \text{ kg})(2.0 \text{ m/s}) + (4,000 \text{ kg})(0 \text{ m/s}) = (10,000 \text{ kg} + 4,000 \text{ kg}) v_f \).
Simplify the equation: Calculate the total momentum on the left-hand side and the total mass on the right-hand side. This will leave you with an equation in terms of \( v_f \), the final velocity.
Solve for \( v_f \): Divide the total momentum by the total mass to find the final velocity of the railroad car and gravel system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event, provided no external forces act on it. In this scenario, the momentum of the railroad car and the gravel must be calculated before and after the gravel is dropped to find the new speed of the car.
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Momentum Calculation

Momentum is defined as the product of an object's mass and its velocity (p = mv). To solve the problem, we need to calculate the initial momentum of the railroad car and the gravel separately, and then combine them to find the final momentum of the system after the gravel is added.
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Final Velocity Determination

After applying the conservation of momentum, the final velocity of the railroad car can be determined using the formula for momentum. By setting the total initial momentum equal to the total final momentum, we can solve for the final speed of the railroad car after the gravel is added, ensuring that we account for the combined mass of the car and the gravel.
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A force in the +x-direction increases linearly from 0 N to 9000 N in 5.0 s, then suddenly ends. What impulse does this force provide?

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Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s in the +x-direction fires its engines. FIGURE EX11.10 shows the thrust force as a function of time. The mass lost by the rocket during these 30 s is negligible. At what time does the rocket reach its maximum speed? What is the maximum speed?

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A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.13 shows the glider's velocity and the force exerted on the glider by the spring. How long is the glider in contact with the spring?

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