Domanda del libro di testo
FIGURE EX6.10 shows the force acting on a 2.0 kg object as it moves along the x-axis. The object is at rest at the origin at t = 0 s. What are its acceleration and velocity at t = 6 s?
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Ch 06: Dynamics I: Motion Along a Line
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 5
A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000 N, the players have equal pulls, and the angle between the two ropes is 20°. How hard must each player pull to drag the coach at a steady 2.0 m/s?
Guida verificata passo dopo passo1
Step 1: Analyze the forces acting on the sled. The sled is being pulled by two players with equal forces (T₁ and T₂) at an angle of 20° between the ropes. The friction force opposing the motion is 1000 N. Since the sled is moving at a steady speed, the net force in the horizontal direction is zero (Newton's First Law).
Step 2: Break down the tension forces into their horizontal and vertical components. Each player's pull contributes a horizontal component (T₁cosθ and T₂cosθ) and a vertical component (T₁sinθ and T₂sinθ). Here, θ is half the angle between the ropes, which is 10° (since the total angle is 20°).
Step 3: Write the equation for the horizontal force balance. The sum of the horizontal components of the tension forces must equal the friction force: 2Tcosθ = 1000 N. Solve for T, the tension in each rope.
Step 4: Consider the vertical components of the tension forces. These components do not affect the horizontal motion but may contribute to lifting the sled slightly, reducing the normal force and friction. However, since the problem specifies steady motion, we focus only on the horizontal forces.
Step 5: Substitute θ = 10° into the equation from Step 3 and solve for T. Use trigonometric values for cosθ to find the magnitude of the pull required by each player.
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Friction Force
Friction force is the resistance that one surface or object encounters when moving over another. In this scenario, the friction force acting on the sled is 1000 N, which must be overcome by the players' pulling forces to maintain a constant velocity. The frictional force depends on the nature of the surfaces in contact and the normal force acting between them.
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Percorso guidato
08:11
Static Friction & Equilibrium
Tension in Ropes
Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends. In this problem, two players are pulling the sled with equal tension forces (T1 and T2) at an angle of 20 degrees between them. The resultant tension must be calculated to determine how hard each player must pull to overcome the friction and maintain a steady speed.
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Percorso guidato
06:34Calculating Tension in a Pendulum with Energy Conservation
Equilibrium of Forces
An object is in equilibrium when the net force acting on it is zero, meaning it does not accelerate. In this case, the sled is being pulled at a constant speed of 2.0 m/s, indicating that the total horizontal forces (the horizontal components of T1 and T2) must equal the friction force. This principle allows us to set up equations to solve for the tension in the ropes.
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Percorso guidato
05:10Equilibrium
Pratica correlata
Domanda del libro di testo
In an electricity experiment, a 1.0 g plastic ball is suspended on a 60-cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force Felectric on it, causing the ball to swing out to a 20° angle and remain there. What is the magnitude of Felectric?
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Domanda del libro di testo
The forces in FIGURE EX6.9 act on a 2.0 kg object. What are the values of ax and ay, the x- and y-components of the object's acceleration?
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Domanda del libro di testo
The three ropes in FIGURE EX6.1 are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What are the magnitude and direction of the tension T3 in the third rope?
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