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Questions and Answers
What does Hooke's Law describe about the force exerted by a spring?
What does Hooke's Law describe about the force exerted by a spring?
In calculating the work done by a spring, how is work defined?
In calculating the work done by a spring, how is work defined?
What is the unit of work in the International System of Units (SI)?
What is the unit of work in the International System of Units (SI)?
What happens to the work done by a spring when it stretches a mass downward?
What happens to the work done by a spring when it stretches a mass downward?
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How do you find the spring constant using the mass and force due to gravity?
How do you find the spring constant using the mass and force due to gravity?
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What does the spring constant 'k' represent in Hooke's Law?
What does the spring constant 'k' represent in Hooke's Law?
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If the spring is compressed, what will be the sign of the force exerted by the spring according to Hooke's Law?
If the spring is compressed, what will be the sign of the force exerted by the spring according to Hooke's Law?
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How is the extension of a spring defined?
How is the extension of a spring defined?
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What happens to the force exerted by the spring when the position x is at the equilibrium position?
What happens to the force exerted by the spring when the position x is at the equilibrium position?
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Which formula represents the relationship between force and displacement for a spring?
Which formula represents the relationship between force and displacement for a spring?
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A weight of 8 N is attached to a spring with a spring constant of 160 N/m. How much will the spring stretch?
A weight of 8 N is attached to a spring with a spring constant of 160 N/m. How much will the spring stretch?
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What does Fs represent in the context of Hooke's Law?
What does Fs represent in the context of Hooke's Law?
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Which statement about Hooke's Law is correct?
Which statement about Hooke's Law is correct?
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What is the relationship between energy and work in physics?
What is the relationship between energy and work in physics?
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Which unit is used to measure work in physics?
Which unit is used to measure work in physics?
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What does the scalar product of two vectors involve?
What does the scalar product of two vectors involve?
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How is work calculated when a force is applied at an angle to the direction of displacement?
How is work calculated when a force is applied at an angle to the direction of displacement?
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What is the primary characteristic of work in physics?
What is the primary characteristic of work in physics?
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What does the notation A·B represent in vector mathematics?
What does the notation A·B represent in vector mathematics?
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Which of the following statements about work is incorrect?
Which of the following statements about work is incorrect?
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Which formula correctly indicates the work done by a constant force acting on an object?
Which formula correctly indicates the work done by a constant force acting on an object?
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Study Notes
Lecture 2: Energy
- Lecture focused on energy, specifically the concept of work and energy transfer.
- Energy is the capacity to do work.
- Energy exists in forms like potential, kinetic, thermal, electrical, chemical, nuclear, and others.
Introduction to Energy
- The more energy, the more work done.
- Energy, in physics, is the capacity for doing work.
- Energy can exist in various forms (potential, kinetic, thermal, electrical, chemical, nuclear, or others).
What is Work?
- Work is a measure of energy transfer/change.
- Work is done when force acting gives energy to an object as it is moved.
Work, Math Formula
- Work (W) = Force (F) • displacement (Δr)
- The formula applies when force is constant.
- Force and displacement are vectors.
Work, Math Formula
- Work is calculated when displacement is along a straight line.
- The force causes an angle with displacement, which is factored into the work calculation.
- The formula is W = F •Δr•cos θ, where θ is the angle between force and displacement vectors.
Units of Work
- Work is a scalar quantity.
- The unit of work is a joule (J).
- 1 joule = 1 newton • 1 meter = kg•m²/s²
Problem
- Determine which of two men consuming less energy to perform work.
- Given forces and angles, calculate the energy expended.
Solution
- Calculations showed the work done by A is 130 J and work done by B is 115 J.
Scalar Product of Two Vectors
- The scalar product (dot product) of two vectors is written as A • B = AB cos θ, where θ is the angle between vectors A and B.
- Scalar product is commutative (A • B = B • A).
Scalar Product, cont
- The scalar product obeys the distributive law of multiplication (A • (B + C) = A • B + A • C).
What is the Work done by other forces?
- Normal force (n) and gravitational force (mg) do not work on an object if the object is moving along the surface.
- The angle between normal force and displacement, and gravitational force is 90 degrees. Hence cos θ = 0.
Concept of Differentiation and Integration
- Concept introduced using a graphic showing two spheres representing constant and variable aspects.
- Deals with the concept of finding unknowns that lead to determining integrals and derivatives.
Work Done by a Varying Force
- When force varies during displacement, the work is calculated by summing the areas under the force-displacement curve.
- Work (W) ≈ Σ F•Δx, where the sum is for all intervals.
Work Done by a Varying Force, cont
- Work done by a varying force can be expressed as W = ∫xixf Fx dx, where the integral is taken from initial position to final position.
Problem: Calculate the work done according to the graph
- Calculate the work done by a variable force on a particle.
- Work is the area under the curve in the force-displacement graph between points x = 0 and x = 6 m.
Solution
- The work is calculated by the following method and total work is 25 J.
- Calculating the area of the rectangle and the triangle under the graph.
Hooke's Law
- Robert Hooke discovered a law for elastic materials in 1676.
- Named after the 17th-century physicist, Robert Hooke.
- Hooke's law states that the extension of an elastic object is directly proportional to the force applied to it, as long as the elastic limit is not exceeded.
Hooke's Law
- Elastic behavior - Materials return to original shape after removal of deforming forces (reversible deformation).
- Inelastic behavior - Materials stay deformed after force removal (irreversible deformation).
- Relationship between force and extension is proportional, like doubling the force to double the extension.
Hooke's Law Data
- Relationship displayed graphically in graphs of force versus extension, consistent with the linear relationship stated in Hooke's Law.
- Data points confirm the relationship as force increases linearly with extension.
Hooke's Law Equation
The force (F) is equal to the spring constant (k) times the extension (x). Formula written as F=-kx
Problem
- Find the extension of a spring with a given weight and spring constant.
Solution
- The extension is 0.05 m, calculated using Hooke's Law formula.
Hooke's Law, final
- The spring's force is opposite to displacement; the force is known as the restoring force.
- If released, the spring oscillates between the maximum displacement in either direction.
Calculate the Work Done by the Spring?
- Calculate the work done by a spring on a block.
- Work done by a spring is the area under the force-extension graph.
Work Done by a Spring
- Work done by a spring is calculated using integration of the area under the force-displacement graph.
Problem
- (a) Calculate the force constant of a spring that stretches 2 cm by a 0.55 kg object.
- (b) Work done by the spring as the object stretches through 2 cm.
- (c) Calculate the work done by gravity.
Solution
- Spring constant (k) calculation: (0.55kg)(9.8 m/s2)/(2x10-2 m) = 270N/m
- Work done by spring: (1/2)(270 N/m)(2x10-2m)^2= 0.054 J
- Work done by gravity: −(0.55kg)(9.8 m/s^2)(2x10^-2 m) = −0.1078 J
Continue
- Calculate further work done by gravity on object.
- Additional exploration is needed with kinetic energy and work to explore more concepts.
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Description
This quiz covers the fundamental concepts of energy and work as discussed in Physics Lecture 2. It explores different forms of energy, the definition of work, and the mathematical formulas used to calculate work done when force is applied. This is essential knowledge for understanding basic physics principles regarding energy transfer and its applications.
