chapter 5 outline applying newton’s laws statics dynamics friction kinetic friction static...
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Chapter 5 OutlineApplying Newton’s Laws
• Statics
• Dynamics
• Friction
• Kinetic friction
• Static friction
• Fluid resistance
• Circular Motion
• Fundamental forces
Statics
• When a body is not accelerating, we say that it is in equilibrium.
• Statics is the study of bodies in equilibrium.
• Since the acceleration is zero, we use Newton’s first law to solve these problems.
; ;
• Carefully draw a free body diagram that shows all forces acting on the body.
• Choose an appropriate coordinate system.
Normal Force
• When an object is resting on a surface, the surface is exerting a force on the object, called the normal force.
• The normal force is always perpendicular to the surface.
• The textbook uses the letter for the normal force. It is also common to use .
Statics Example
Dynamics
• Now we consider a body that is accelerating.
• Dynamics is the study of bodies not in equilibrium.
• Since the acceleration is not zero, we use Newton’s second law to solve these problems.
; ;
• Carefully draw a free body diagram that shows all forces acting on the body.
• Choose an appropriate coordinate system.
Apparent Weight
• Consider the case of a person standing on a scale in an elevator.
• If the elevator is still or moving at a constant velocity, the scale will read the person’s actual weight, .
• If the elevator is acceleration, the scale will read the apparent weight.
• If the body is accelerating downward at the acceleration due to gravity, that is , it experiences apparent weightlessness.
• This is the case during free fall, or while in orbit.
Dynamics Example
Frictional Forces
• So far, we have ignored one of the most important types of force: the force of friction.
• Contact force
• Parallel to surface
Kinetic Friction
• When the surfaces are moving relative to each other, we have kinetic friction.
• The force of kinetic friction is proportional to the normal force, , and the coefficient of kinetic friction, .
• depends on both surfaces.
• Does not depend on contact area!
Static Friction
• When the surfaces are still with respect to each other, we have static friction.
• The force of static friction is proportional to the normal force, , and the coefficient of static friction, .
• depends on both surfaces.
• Generally, for a given pair of surfaces.
Static and Kinetic Friction
Coefficient of Rolling Friction
• In practice, we often use wheels to reduce the frictional forces involved in moving objects.
• Still, we have to consider the frictional force involved.
• The coefficient of rolling friction, :
• The frictional force takes into account the deformation of the wheels.
• For steel on steel (trains), values of are typically to .
Friction Example
Fluid Resistance
• In the case of the contact between solid surfaces, we find that the frictional force is roughly independent of the relative speed or contact area.
• For motion through fluids, the resistive force is quite sensitive to the speed.
• For small objects moving at very low speeds, the fluid resistance force, , is approximately proportional to the speed.
• At higher speeds, the fluid resistance force, , is approximately proportional to the square of the speed.
Terminal Speed
• Since the fluid resistance force is speed dependent, there will be some speed at which the weight of a falling body is balanced by the drag force.
• At this point, the acceleration is zero, and the body has reached its terminal speed.
• From , the terminal speed is:
Fluid Resistance Example
Circular Motion
• Recall from Chapter 3 that circular motion is produced by a centripetal acceleration towards the center of curvature.
• The period, , is the time for one full circle.
• The acceleration towards the center must be provided by some force.
• Planet in orbit: Gravity
• Ball on a string: Tension
• Car going around turn?
Circular Motion Example
Consider a racecar going around a turn with a radius of curvature of . The static and kinetic coefficients of friction between the track and the tires are and , respectively.
• What is the maximum speed at which the car can take the corner without skidding if the track is (a) flat or (b) banked at ?
Fundamental Forces
• We have talked about a lot of different kinds of forces.
• Gravitational, friction, normal, fluid resistance, tension…
• Are these all actually different in nature?
• Four fundamental forces (we think):
• Gravitational
• Electromagnetic
• Strong
• Weak
• All interactions arise through one of these fundamental forces.
• All of the interactions we have dealt with so far were electromagnetic or gravitational.
Chapter 5 OutlineApplying Newton’s Laws
• Statics:
• Dynamics:
• Friction
• Kinetic friction:
• Static friction:
• Rolling resistance:
• Fluid resistance: or
• Terminal velocity:
• Circular Motion
• Fundamental forces