Questions and Answers
Which of the following situations satisfy both the first condition for equilibrium (net force = 0) and the second condition for equilibrium (net torque = 0)?
A seagull gliding at a constant angle below the horizontal and at a constant speed
What is the tension in the cable holding a metal advertising sign suspended from the end of a massless rod at an angle θ from the horizontal?
T = w sin θ
Which of these forces is least when a metal advertising sign is suspended from a massless rod at an angle θ from the horizontal?
The tension in the cable
In the example with an automobile engine above an engine compartment, what are the tensions in the supporting cable T1 and the positioning rope T2?
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In the example with a mass of block m as 20.0 kg, what are the tensions on cable 1, cable 2, cable 3, and cable 4?
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In the example with a block resting on an inclined plane at 42 degrees, what are the normal force N and the force due to gravity Fg?
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What is the mass of the block in the example with a block resting on an inclined plane at 42 degrees?
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Study Notes
Mechanical Equilibrium
- Definition of equilibrium: when a body is at rest or moving with constant velocity in an inertial frame of reference
- Types of equilibrium: static equilibrium (at rest) and dynamic equilibrium (in motion)
Forces and Torques
- Forces: pushes or pulls that cause an object to change its motion; units: Newtons (N)
- Categories of forces:
- Contact forces: involve physical contact between two objects
- Field forces: forces that act through empty space
- Newton's laws of motion:
- First law (law of inertia): an object at rest remains at rest, and an object in motion remains in motion with constant velocity, unless acted upon by an external force
- Third law: if two objects interact, the force exerted by one object on the other is equal in magnitude and opposite in direction to the force exerted by the second object on the first
The Equilibrium Model
- Free-body diagram (FBD): a diagram that shows the relative magnitude and direction of all forces acting upon an object in a given situation
- Forces that can be present in an FBD:
- Gravitational force (Fg): attractive force exerted by the Earth on an object, directed towards the center of the Earth
- Normal force (N): force exerted by a surface on an object whenever they are in contact, always perpendicular to the surface
- Tension (T): pulling force exerted by a rope, string, chain, or cable on an object, always lies along the direction of the string
Conditions for Equilibrium
- First condition: the sum of all forces (net force) acting on an object must add up to zero ( translational equilibrium)
- Second condition: the sum of all moments (net moment) acting on an object must add up to zero (rotational equilibrium)
- Conditions for static equilibrium:
- Net force equal to zero
- Net torque equal to zero
Examples and Applications
- Example 1: determining the tension in a cable and the force exerted by a hinge on a rod
- Example 2: determining the weight of an object and the tension in a cable
- Example 3: determining the force exerted by a rope on an object
- Example 4: determining the tension in multiple cables supporting an engine
- Example 5: determining the normal force and force due to gravity on a block resting on an inclined plane
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