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?
Ch 11: Impulse and Momentum
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 11, Problem 8
A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.8. What are the object's speed and direction after the force ends?
Verified step by step guidance1
Identify the given values: The mass of the object is 2.0 kg, the initial velocity is 1.0 m/s to the right, and the force as a function of time is provided in the figure (assume the force-time graph is available). The goal is to find the final speed and direction of the object after the force ends.
Determine the impulse imparted to the object by the force. Impulse is the integral of force over time: \( J = \int F(t) \, dt \). Use the force-time graph to calculate the area under the curve, as this represents the impulse.
Relate impulse to the change in momentum using the impulse-momentum theorem: \( J = \Delta p \), where \( \Delta p = m \cdot \Delta v \). Solve for the change in velocity: \( \Delta v = \frac{J}{m} \).
Determine the final velocity of the object: \( v_f = v_i + \Delta v \), where \( v_i \) is the initial velocity. Use the sign of \( \Delta v \) to determine whether the object is still moving to the right or has reversed direction.
Finally, calculate the magnitude of the final speed (absolute value of \( v_f \)) and specify the direction based on the sign of \( v_f \). If \( v_f > 0 \), the object is moving to the right; if \( v_f < 0 \), it is moving to the left.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Newton's Second Law of Motion
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. Understanding this law is crucial for analyzing how the force affects the object's motion.
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Momentum
Momentum is defined as the product of an object's mass and its velocity, represented by the equation p = mv. It is a vector quantity, meaning it has both magnitude and direction. The conservation of momentum principle states that in a closed system, the total momentum before and after an event remains constant, which is essential for determining the object's speed and direction after the force is applied.
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Kinematics
Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this scenario, kinematic equations can be used to calculate the final speed and direction of the object after the force has acted on it, based on its initial conditions and the effects of the force.
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Related Practice
Textbook Question
FIGURE EX11.6 is an incomplete momentum bar chart for a collision that lasts 10 ms. What are the magnitude and direction of the average collision force exerted on the object?
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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
What is the impulse on a 3.0 kg particle that experiences the force shown in FIGURE EX11.4?
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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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Textbook Question
In FIGURE EX11.5, what value of Fmax gives an impulse of 6.0 N s?
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