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