Ch 13: Rotational EquilibriumSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
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Ch 25: Resistors & DC Circuits
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Ch 27: Sources of Magnetic Field
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Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Solution: A horizontal, nonuniform beam of mass M and length ℓ is hinged to a vertical wall at one side, and attached to a wire on the other end. The bar is motionless and a wire exerts a force T at an angle of φ with respect to the vertical. If the mass of the beam is 7 kg, the tension in the wire is 35 N, sin φ = 3/5 and cos φ = 4/5, how far is the center of mass of the beam from the hinge? The acceleration due to gravity is 10 m/s2. 1. 0.32 ℓ 2. 0.5 ℓ, of course 3. 0.4 ℓ  4. Not enough information is given. 5. 0.18 ℓ 6. 0.16 ℓ 7. 0.375 ℓ 8. 0.666667 ℓ 9. 0.3 ℓ 10. 0.625 ℓ

Problem

A horizontal, nonuniform beam of mass M and length ℓ is hinged to a vertical wall at one side, and attached to a wire on the other end. The bar is motionless and a wire exerts a force T at an angle of φ with respect to the vertical. If the mass of the beam is 7 kg, the tension in the wire is 35 N, sin φ = 3/5 and cos φ = 4/5, how far is the center of mass of the beam from the hinge? The acceleration due to gravity is 10 m/s2.

1. 0.32 ℓ

2. 0.5 ℓ, of course

3. 0.4 ℓ 

4. Not enough information is given.

5. 0.18 ℓ

6. 0.16 ℓ

7. 0.375 ℓ

8. 0.666667 ℓ

9. 0.3 ℓ

10. 0.625 ℓ