Two Chapter 5

• The gravitational force on one object may indirectly produce motion in another.

• For the above illustrated situation, the gravitational force on the mass hanging from the side of the table can cause motion in the object resting on the table.
• To understand the physics of problems like the one illustrated above, we make the following assumptions.
  • Strings have negligible mass and only pull (never push)
    • Remember that pulling forces are tension forces.
  • Strings transmit forces which are undiminished (There is the same tension throughout the string's length.).
  • A frictionless pulley changes the direction of a tension (string), gut not the magnitude of the tension.
  • Strings do not stretch.
• For the following diagram, calculate the acceleration of the 2.0 kg mass and the tension in the string.

• With the above example, notice how in step 2 the total mass of the system is used in the calculation of the acceleration. In step 3, we considered the 5.0 kg object to calculate the tension. We could have used the 2 kg object as well to come up with the same answer. Also notice the sign of the acceleration in step 3. This acceleration must be negative since it is down.

• Friction - The force that opposes motion.
  • Friction is caused by the nature of the surfaces.
    • Projections in each surface catch onto one another to produce friction.
    • Cohesion and adhesion between molecules prevents free movement.
• Friction is proportional to the normal force acting between surfaces

• Normal force - The force that one body exerts on another perpendicular to the common surface.

• The coefficient of friction depends upon the nature of the two surfaces and is experimentally determined. It also does not have any units.
• Friction and the coefficient of friction do not depend upon
  • speed
  • area of contact
• The coefficient of friction does depend upon whether the object is moving or not.
• Coefficient of Static Friction - The coefficient of friction used to describe the maximum frictional force to be overcome just to start an object sliding on a surface.
  • Coefficient of static friction determines the friction when an object is not moving.

• Static friction exists only when there is an outside force. Otherwise F_s = 0.
• Coefficient of Kinetic friction - the coefficient of friction used to describe the friction present when movement occurs.

• Static friction (starting friction) is always larger than kinetic friction. This occurs because the coefficient of static friction is larger than the coefficient of kinetic friction. For these reasons, you do not spin your tires when stuck in snow. Once the tires spin, the friction between the snow and the tires is less than when they are not spinning.
• Consider a person of mass 50 kg sliding down a hill in a toboggan. The snow has a coefficient of kinetic friction of 0.15. What is the acceleration of the person down the hill?

• When considering the x-direction, it is important to realize that friction opposes motion. Since the motion is down the hill, the frictional force must be up the hill. When substitution is made into the formula, the frictional force must work out to be a positive number, because it is in the +x direction. Similarly, F_gx must work out to be a negative number, since it is directed in the -x direction.

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November 5, 2013