Domanda del libro di testo
To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E. Find the - and -components of each of the three pulls.
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Ch 04: Newton's Laws of Motion
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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TOC.tableOfContents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Capitolo 4, Problema 1
Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is °. If Rover exerts a force of N and Fido exerts a force of N, find the magnitude of the resultant force and the angle it makes with Rover's rope.
Guida verificata passo dopo passo1
Step 1: Represent the forces exerted by Rover and Fido as vectors. Rover's force vector has a magnitude of 270 N, and Fido's force vector has a magnitude of 300 N. The angle between the two vectors is given as 60.0°.
Step 2: Use the formula for the magnitude of the resultant force when two vectors are at an angle: \( F_{R} = \sqrt{F_{1}^2 + F_{2}^2 + 2F_{1}F_{2}\cos\theta} \), where \( F_{1} \) and \( F_{2} \) are the magnitudes of the forces, and \( \theta \) is the angle between them.
Step 3: Substitute the given values into the formula: \( F_{1} = 270 \, \text{N}, \, F_{2} = 300 \, \text{N}, \text{ and } \theta = 60.0° \). Calculate \( \cos\theta \) using \( \cos(60.0°) = 0.5 \).
Step 4: To find the angle \( \phi \) that the resultant force makes with Rover's rope, use the formula for the direction of the resultant vector: \( \tan\phi = \frac{F_{2}\sin\theta}{F_{1} + F_{2}\cos\theta} \). Substitute the values \( F_{1} = 270 \, \text{N}, \, F_{2} = 300 \, \text{N}, \text{ and } \theta = 60.0° \).
Step 5: Solve the equations step by step to find the magnitude of the resultant force \( F_{R} \) and the angle \( \phi \). Ensure proper handling of trigonometric functions and square roots during calculations.
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Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Vector Addition
Vector addition is the process of combining two or more vectors to determine a resultant vector. In this scenario, the forces exerted by the dogs are vectors with both magnitude and direction. The resultant force can be found using the law of cosines or by breaking the vectors into their components and summing them.
Video consigliato:
Percorso guidato
07:30
Vector Addition By Components
Law of Cosines
The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful in this problem to find the magnitude of the resultant force when two vectors are at an angle to each other. The formula is c² = a² + b² - 2ab*cos(θ), where θ is the angle between the two vectors.
Video consigliato:
Percorso guidato
10:20Gauss' Law
Resultant Force Direction
The direction of the resultant force can be determined using trigonometric functions, specifically the sine and cosine functions. By calculating the angle that the resultant makes with one of the original vectors, we can use the inverse tangent function to find this angle. This is essential for understanding how the combined forces act in relation to the individual forces.
Video consigliato:
Percorso guidato
08:17The Normal Force
Pratica correlata
Domanda del libro di testo
Due to a jaw injury, a patient must wear a strap (Fig. E) that produces a net upward force of N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?
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Domanda del libro di testo
To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E. Use the components to find the magnitude and direction of the resultant of the three pulls.
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