Textbook Question
The motor of a 350 g model rocket generates 9.5 N thrust. If air resistance can be neglected, what will be the rocket's speed as it reaches a height of 85 m?
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Ch 06: Dynamics I: Motion Along a Line
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 6, Problem 49b
Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of 200 N and a coefficient of kinetic friction on snow of 0.10. Unfortunately, the skis run out of fuel after only 10 s. How far has Sam traveled when he finally coasts to a stop?
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Determine the net force acting on Sam while the skis are powered. The net force is given by: , where . Substitute the given values to calculate the net force.
Use Newton's second law to find the acceleration while the skis are powered: . Substitute the net force and Sam's mass to calculate the acceleration.
Determine the distance traveled during the powered motion using the kinematic equation: . Here, is the initial velocity (0 m/s), is the time (10 s), and is the acceleration calculated in the previous step.
Find the velocity at the end of the powered motion using the kinematic equation: . This velocity will be the initial velocity for the coasting phase.
Determine the distance traveled during the coasting phase. First, calculate the deceleration due to friction: . Then, use the kinematic equation: . Add the distances from the powered and coasting phases to find the total distance traveled.
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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 principle can be expressed with the formula F = ma, where F is the net force, m is mass, and a is acceleration. In this scenario, understanding how to calculate the net force acting on Sam is crucial for determining his acceleration while the skis are powered.
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Friction
Friction is the force that opposes the relative motion of two surfaces in contact. The coefficient of kinetic friction quantifies this force and is used to calculate the frictional force acting on Sam's skis as he moves across the snow. In this case, the frictional force will affect the deceleration of Sam once the thrust from the skis ceases, ultimately influencing how far he travels before coming to a stop.
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Kinematic Equations
Kinematic equations describe the motion of objects under constant acceleration. These equations relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, after determining the acceleration due to thrust and friction, kinematic equations can be used to calculate the distance Sam travels during the powered phase and the coasting phase until he stops.
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Related Practice
Textbook Question
Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of 200 N and a coefficient of kinetic friction on snow of 0.10. Unfortunately, the skis run out of fuel after only 10 s. What is Sam's top speed?
Textbook Question
A rocket of mass m is launched straight up with thrust Fthrust. Find an expression for the rocket's speed at height h if air resistance is neglected.
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Textbook Question
A baggage handler drops your 10 kg suitcase onto a conveyor belt running at 2.0 m/s. The materials are such that μs = 0.50 and μk = 0.30. How far is your suitcase dragged before it is riding smoothly on the belt?
Textbook Question
A 5.0 kg wooden sled is launched up a 25° snow-covered slope with an initial speed of 10 m/s. What vertical height does the sled reach above its starting point?
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Textbook Question
A large box of mass M is moving on a horizontal surface at speed v₀. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are μs and μk, respectively. Find an expression for the shortest distance dmin in which the large box can stop without the small box slipping.