Textbook Question
Complete the motion diagram by adding acceleration vectors.
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Ch 04: Kinematics in Two Dimensions
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 4, Problem 4a
At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?
Verified step by step guidance1
Analyze the motion of the particle: The particle is curving upward, which indicates that it is undergoing circular motion or a curved trajectory. The velocity vector is tangent to the curve at any given point.
Understand the components of acceleration: Acceleration can have two components in this scenario: (1) a tangential component that changes the magnitude of the velocity (speeding up or slowing down), and (2) a centripetal component that changes the direction of the velocity (curving motion).
Determine the tangential acceleration: Since the particle is speeding up, the tangential acceleration is in the same direction as the velocity vector, which is along the tangent to the curve.
Determine the centripetal acceleration: The centripetal acceleration always points toward the center of the curvature of the path. In this case, it points upward and slightly to the left, perpendicular to the velocity vector.
Combine the components: The net acceleration is the vector sum of the tangential and centripetal accelerations. It will point in a direction that is slightly upward and to the left, combining the effects of speeding up and curving upward.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Acceleration
Acceleration is the rate of change of velocity of an object. It is a vector quantity, meaning it has both magnitude and direction. When a particle is speeding up, its acceleration is in the same direction as its velocity. In the context of circular or curved motion, acceleration can also change direction even if the speed remains constant.
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Guided course
05:47
Intro to Acceleration
Centripetal Acceleration
Centripetal acceleration occurs when an object moves along a curved path, directed towards the center of the curvature. This type of acceleration is essential for maintaining circular motion and is always perpendicular to the object's velocity vector. In the case of a particle curving upward, the centripetal acceleration points inward toward the center of the curve.
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06:48Intro to Centripetal Forces
Net Force and Direction of Acceleration
According to Newton's second law, the net force acting on an object determines its acceleration. The direction of the net force is the same as the direction of the acceleration. In the scenario described, if the particle is curving upward and speeding up, the net force must have a component acting in the upward direction, indicating that the acceleration is also directed upward.
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07:32Weight Force & Gravitational Acceleration
Related Practice
Textbook Question
A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of vx and vy, the x- and y-components of the puck's velocity. The puck starts at the origin. How far from the origin is the puck at t = 5s?
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Textbook Question
Is this particle curving upward, curving downward, or moving in a straight line?
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Textbook Question
A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of vx and vy, the x- and y-components of the puck's velocity. The puck starts at the origin. In which direction is the puck moving at t = 2s? Give your answer as an angle from the x-axis.
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