Textbook Question
Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E). The pull is of magnitude N. Find the acceleration of the system.
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Ch 05: Applying Newton's Laws
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 5, Problem 16b
An -kg block of ice, released from rest at the top of a -m-long frictionless ramp, slides downhill, reaching a speed of m/s at the bottom. What would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of N parallel to the surface of the ramp?
Verified step by step guidance1
Identify the forces acting on the block: The block is subject to gravity, the normal force from the ramp, and a constant friction force of 10.0 N parallel to the ramp surface. The normal force does no work since it is perpendicular to the motion.
Calculate the work done by friction: The work done by friction is given by \( W_{\text{friction}} = -f \cdot d \), where \( f \) is the friction force (10.0 N) and \( d \) is the length of the ramp (1.50 m). The negative sign indicates that friction opposes the motion.
Determine the initial potential energy: The block starts at a height \( h \) above the bottom of the ramp. Using the geometry of the ramp, \( h \) can be found as \( h = d \cdot \sin(\theta) \), where \( \theta \) is the angle of the ramp. The potential energy is \( U = m \cdot g \cdot h \), where \( m = 8.00 \ \text{kg} \) and \( g = 9.8 \ \text{m/s}^2 \).
Apply the work-energy principle: The total work done on the block is equal to the change in its kinetic energy. The total work includes the work done by gravity and the work done by friction. Set up the equation: \( W_{\text{gravity}} + W_{\text{friction}} = \Delta K \), where \( \Delta K = \frac{1}{2} m v^2 - 0 \) (since the block starts from rest).
Solve for the final speed \( v \): Substitute the expressions for \( W_{\text{gravity}} \), \( W_{\text{friction}} \), and \( \Delta K \) into the work-energy equation. Rearrange to isolate \( v \), and solve for the final speed of the block at the bottom of the ramp.
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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 is crucial for analyzing the forces acting on the block of ice as it slides down the ramp, allowing us to calculate the net force when friction is present.
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Intro to Forces & Newton's Second Law
Conservation of Energy
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the gravitational potential energy of the ice at the top of the ramp is converted into kinetic energy as it slides down, with some energy lost to friction when it is present.
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Frictional Force
Frictional force is the resistance that one surface or object encounters when moving over another. In this problem, the constant friction force of 10.0 N opposes the motion of the ice block, reducing its acceleration and, consequently, its final speed at the bottom of the ramp compared to a frictionless scenario.
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Related Practice
Textbook Question
A light rope is attached to a block with mass kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass is suspended from the other end. When the blocks are released, the tension in the rope is N. What is the acceleration of either block?
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Textbook Question
An -kg block of ice, released from rest at the top of a -m-long frictionless ramp, slides downhill, reaching a speed of m/s at the bottom. What is the angle between the ramp and the horizontal?
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Textbook Question
A light rope is attached to a block with mass kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is N. Find .
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Textbook Question
Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E). The pull is of magnitude N. Find the tension in ropes and .
2
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Textbook Question
A light rope is attached to a block with mass kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass is suspended from the other end. When the blocks are released, the tension in the rope is N. Draw two free-body diagrams: one for each block.
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