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

Knight Calc 5th Edition

Ch 11: Impulse and Momentum

Problem 13

Chapter 11, Problem 13

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?

Verified step by step guidance

Convert the mass of the glider from grams to kilograms, as SI units are required for calculations. Use the conversion: \( 1 \ \text{g} = 0.001 \ \text{kg} \). Thus, \( m = 600 \ \text{g} = 0.6 \ \text{kg} \).

Understand that the force exerted by the spring on the glider is related to the glider's acceleration through Newton's second law: \( F = m \cdot a \). Rearrange this to find acceleration: \( a = \frac{F}{m} \).

From the graph provided (FIGURE EX11.13), determine the force \( F \) as a function of time \( t \). Use this to calculate the acceleration \( a(t) \) at different points in time.

Recognize that the glider's velocity changes due to the spring's force. The relationship between velocity and acceleration is given by \( v(t) = v_0 + \int a(t) \cdot dt \), where \( v_0 \) is the initial velocity. Use this to find when the velocity becomes zero, as this marks the end of contact with the spring.

Integrate the force (or acceleration) over time to determine the total time of contact. This involves solving \( \int F(t) \cdot dt = m \cdot \Delta v \), where \( \Delta v \) is the change in velocity (from initial velocity to zero).

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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 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 the context of the glider and spring collision, understanding how momentum is transferred during the interaction is crucial for analyzing the motion of the glider.

Hooke's Law

Hooke's Law describes the relationship between the force exerted by a spring and the displacement of the spring from its equilibrium position. It states that the force exerted by the spring is proportional to the distance it is compressed or stretched, which is essential for determining the force acting on the glider during its contact with the spring.

Impulse and Momentum

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. The relationship between impulse and momentum is key to solving the problem, as it allows us to calculate the duration of contact between the glider and the spring by analyzing the force exerted and the resulting change in the glider's velocity.

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Related Practice

Textbook Question

Three identical train cars, coupled together, are rolling east at speed v₀. A fourth car traveling east at 2v₀ catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

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Textbook Question

A 2.0 kg object is moving to the right with a speed of when it experiences the force shown in FIGURE EX11.9. What are the object's speed and direction after the force ends?

Textbook Question

A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the glider's velocity just after the skydiver lets go?

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Textbook Question

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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Textbook Question

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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Textbook Question

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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