Reading Quiz 1. Viscous friction is ___ 1. larger than kinetic friction. ___ 2. equal to kinetic friction. ___ 3. smaller than kinetic friction. ___ 4. resistance to motion in fluids.

2. Torque is ___ 1. the way the British spell talk. ___ 2. related to ability to rotate a body. ___ 3. the product of force and distance. ___ 4. is a force.

3. When a body is in equilibrium ___ 1. it is moving at constant speed. ___ 2. it cannot be rotating. ___ 3. there are no forces acting on it.

Friction Force Always acts in opposition to motion (or tendency towards motion) Experimental facts - proportional to normal force - independent of contact area - independent of relative speed - depends on materials Two types - Static and Kinetic: where are the coefficients of static (kinetic) friction.

Quantitative Questions 1) A 100 kg wooden crate is at rest on a level stone floor. Let .(a) What is the minimum horizontal force needed to start the crate moving? (b) What is the minimum horizontal force needed to keep the crate in motion at constant speed? (c) What will happen if a horizontal force of 500 N is applied to the crate? (d) What is the minimum non-horizontal force (directed at 30° from the horizontal, downwards) needed to start the crate moving?

2) A block slides down an inclined plane 9 2) A block slides down an inclined plane 9.0 meters long that makes an angle of 38° with the horizontal. The coefficient of kinetic friction is 0.25. If the block starts from rest, find the time required for it to reach the foot of the plane. If the block has a mass of 50.0 kg, find the force parallel to the plane required to move it upward at constant speed.

3) The two masses shown below are initially 1 3) The two masses shown below are initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released?

Torque Definition: Interpretation:  = torque F = applied force r = distance between the pivot point and the point of application of the force  = angle between F and r

Center of Mass The center of mass of an object is that point at which the net force can be considered to act for purposes of determining the translational motion of the body as a whole. Center of gravity - point at which the force of gravity can be considered to act. Same point as center of mass in a uniform gravitational field.

Conceptual Problems 1) The center of gravity of an object ____ a) is always at its geometrical center ____ b) is always in the interior of the object ____ c) may be outside the object ____ d) is sometimes arbitrary ____ e) is a real physical point

2) Where is the center of mass of: a) a uniform square b) a uniform cube c) a uniform equilateral triangle d) a bowling ball e) a uniform ring f) a uniform boomerang g) a tank half filled with water and half oil h) a thermometer at very low temperature

Quantitative Problems 1) A person exerts a force of 45 N on the end of a door 84 cm wide. What is the magnitude of the torque if the force is exerted (a) perpendicular to the door, and (b) at a 60 angle to the face of the door? 2) A couple consists of two forces of equal magnitude that act in opposite directions along parallel lines of action a distance d apart. If the magnitude of each force is F what is the torque exerted by a couple?

Static Equilibrium A body is said to be in static equilibrium if it is not in translational or rotational motion. Two conditions must be met: no translational motion - no rotational motion - Stable, Unstable and Neutral Equilibrium

Conceptual Problems 1) In an equilibrium problem the point about which torques are computed ____ a) must pass through one end of the object ____ b) must pass through the object’s center of gravity ____ c) must intersect the line of action of at least one force acting on the object ____ d) may be located anywhere

2) A uniform meter stick supported at the 25 cm mark is in equilibrium when a 1 kg rock is suspended at the 0 cm end (see figure below). The mass of the meter stick is (a) greater than, (b) equal to, or (c) less than, the mass of the rock.

Quantitative Problems 1) Three boys are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and a very light board 3.6 m long. Two boys are already on either end. One has a mass of 50 kg, and the other a mass of 35 kg. Where should the third boy, whose mass is 25 kg, place himself so as to balance the seesaw?

2) The two trees in the figure below are 7. 6 m apart 2) The two trees in the figure below are 7.6 m apart. Calculate the magnitude of the force F a backpacker must exert to hold a 16 kg backpack so that the rope sags at its midpoint by 1.5 m.

3) A shop sign weighing 215 N is supported by a uniform 135 N beam as shown in the figure below. Find the tension in the guy wire and the horizontal and vertical forces exerted by the hinge on the beam.

4) A 5. 0 m long ladder leans against a wall at a point 4 4) A 5.0 m long ladder leans against a wall at a point 4.0 m above the ground. The ladder is uniform and has mass 12.0 kg. A painter of mass 60 kg climbs the ladder and when she is 70 percent of the way up the length of the ladder, it begins to slip. Assume the wall is frictionless but the floor is not. What is the coefficient of static friction between the ladder and the floor? A free-body diagram is included.

5) A 20.0 m long uniform beam weighing 600 N is supported on walls A and B as shown below. (a) Find the maximum weight a person can be to walk to the extreme end D without tipping the beam. Find the forces that the walls A and B exert on the beam when the person is standing: (b) at D; (c) 2.0 m to the right of A.

6) A 36 kg round table is supported by three legs placed equal distances apart on the edge. What minimum mass, placed on the table’s edge, will cause the table to overturn?