Physics Chapter 3: Work and Kinetic Energy

Chapter Contents

• Chapter 1: Physical Quantities and Measurement
• Chapter 2: Work and Kinetic Energy
• Chapter 3: Mechanical Properties of Materials
• Chapter 4: Fluid Mechanics
• Chapter 5: The Law of Universal Gravitation
• Chapter 6: Sound Waves in Elastic Media

Lecture 3: Work and Kinetic Energy

• Work Done by a Constant Force
• Work Done by a Varying Force
• Work Done by a Spring
• Kinetic Energy and the Work-Kinetic Energy Theorem
• Situations Involving Kinetic Friction
• Power
• Conservation and Non-conservation Forces
• Conservation of Mechanical Energy
• Relationship Between Conservative Forces and Potential Energy

Situations Involving Kinetic Friction

• A book moving on a horizontal surface with initial and final velocities
• The external force (kinetic friction) acts in the opposite direction of motion.
• Initial kinetic energy = 1/2mv₁²; Final kinetic energy = 1/2mv₂²
• Newton's second law relates forces, mass, and acceleration.
• Friction is the only force acting on the book in the x-direction.

Situations Involving Kinetic Friction- (continued)

• Kinematics equation for motion under constant acceleration: v₂² - v₁² = 2axd
• Multiplying the equation by m: maxd = 1/2m(v₂² - v₁²)
• Force due to friction * distance = change in kinetic energy
• Part of lost kinetic energy warms up book and surface.
• Work-Kinetic theorem: K₁ + ΣW₀ther - fkd = K₂

Friction Force (fk)

• The force resisting motion when two surfaces are in contact.
• fk = μn, where μ is the coefficient of friction and n is the normal force.
• N = mg

Exercise: A Block Pulled on a Rough Surface

• A 6.0-kg block pulled horizontally by 12 N force.
• Coefficient of kinetic friction is 0.15
• Find the final speed after moving 3.0 m.
• Normal force balances gravity.
• Friction force = 0.15 * (6.0 kg) * (9.8 m/s²)
• Final speed: v = 1.8 m/s by applying Newton's second law and kinematics equation

Power

• Work done in a time interval Δt is W; average power expended is P = ΔW/Δt
• Power is the time rate of energy transfer.
• Instantaneous power = lim (ΔW/Δt) as Δt approaches 0, is P = dW/dt
• P = F.v, where v is instantaneous speed

Power (continued)

• SI unit of Power = Joules/sec = Watt (W).
• In British engineering system, 1 hp = 746 W.
• 1 kWh = 3.6 x 10⁶ J
• Electrical energy = power * time.

Conservative Forces

• Work done by a conservative force between two points is independent of the path.
• Work done by conservative forces is the same for any path joining two points.
• Examples include gravitational force and spring force.

Conservative Forces (continued)

• Example of throwing a ball
• Work by gravity is independent of path.

Non-Conservative Forces

• Work done by a non-conservative force depends on the path.
• Example of friction.

Non-Conservative Forces (continued)

• Work done against friction is path-dependent.

Conservation of Mechanical Energy

• Total mechanical energy in an isolated system remains constant when only conservative forces act.
• Total mechanical energy = kinetic energy + potential energy.
• E₁ = E₂, where E₁ and E₂ are the initial and final total mechanical energies.

Change in Mechanical Energy for Non-conservative Forces

• If a non-conservative force (like friction) acts, then ΔK + ΔU = –fkd

Relationship between Conservative Forces and Potential Energy

• Change in potential energy = - work done by the force along x axis
• Conservative force = - rate of change of potential energy with respect to position (x)
• Gravitational potential energy = mgh

Relationship between Conservative Forces and Potential Energy (continued)

• Spring potential energy = 1/2kx²

Motion on a Curved Track

• Child slides down a curved track (no friction)
• Initial KE + Initial PE = Final KE + Final PE

Motion on a Curved Track (continued)

• Initial KE (zero) + Initial PE = Final KE + zero PE

Example Ball in Free Fall

• Ball dropped from height h. Calculate speed at height y (neglecting air resistance).
• Initial KE + Initial PE = Final KE + Final PE (using gravitational potential energy)
• Final velocity = √2g(h-y)

Ch. 3: Mechanical Properties of Materials

• Introduction
• Young's Modulus: Elasticity in Length
• Shear Modulus: Elasticity of Shape
• Bulk Modulus: Volume Elasticity
• Prestressed concrete

Introduction to Mechanical Properties of Materials

• All objects can be deformed.
• Internal forces resist deformation.
• Stress = external force / area
• Strain = change in dimension / initial dimension
• Stress proportional to strain (within elastic limit)

Young's Modulus: Elasticity in Length

• Stress: force / area
• Strain: change in length / initial length
• Young's Modulus = stress / strain = (F/A) / (ΔL/L₀)

Shear Modulus: Elasticity of Shape

• Shear stress: tangential force / area
• Shear strain: horizontal displacement / height
• Shear Modulus = shear stress / shear strain

Bulk Modulus: Volume Elasticity

• Bulk stress: change in pressure
• Bulk strain: change in volume / initial volume
• Bulk Modulus = bulk stress / bulk strain

Additional Information

• Table of Young's, Shear and Bulk Moduli for various substances
• Explanation of Ductile and Brittle materials

This quiz focuses on Chapter 3 covering Work and Kinetic Energy in Physics. It explores concepts such as work done by various forces, the kinetic energy theorem, and situations involving kinetic friction. Test your understanding of these key physical principles and their applications.