Download Chapter 6

Physics 4A
Chapter 6: Force and Motion - II
“What we see depends mainly on what we look for.” – John Lubbock
“Your thoughts are the architects of your destiny.” – David O. McKay
Reading: pages 116 – 130
Outline:
⇒ friction
static friction
kinetic friction
example problems
⇒ drag force (read on your own)
⇒ uniform circular motion
Problem Solving
Many problems from Chapter 6 deal with frictional forces. Proceed as before: draw a free-body
diagram and write down Newton's second law in component form, just as for any other secondlaw problem. Use an algebraic symbol, f say, for the magnitude of the frictional force. You must
now decide if the frictional force is static or kinetic. If static friction is involved, f is probably an
unknown but the acceleration is known or is related to other known quantities in the problem. If
the object is at rest on a stationary surface, for example, its acceleration is zero. If it is at rest
relative to an accelerating surface, its acceleration is the same as that of the surface. Kinetic
friction is involved if one surface is sliding on the other. Then, the magnitude of the frictional
force is given by μkN.
To decide on the direction of a force of static friction, first decide which way the object would
move if the frictional force were absent. The frictional force is in the opposite direction.
Consider an object on an inclined plane that is tilted so the object will slide down if you do not
exert a force on it. Suppose, however, you pull on it with a force F that is parallel to the plane
and directed up the plane. You will find that you can apply a fairly wide range of forces without
having the object move. If F is small, the force of friction is up the plane; if F is large, the force
of friction is down the plane. The static frictional force can have any value from μsN down the
plane to μsN up the plane (including 0), depending on the value of F.
Uniform circular motion problems are solved in much the same way as any other second-law
problem. Carry out the set of instructions given in Chapter 5. Draw a free-body diagram. Place
the coordinate system so one of the axes is in the direction of the acceleration, pointing from the
object toward the center of its orbit. For most problems you will want to substitute v2/R for the
magnitude of the acceleration. Here v is the speed of the object and R is the radius of its orbit. To
see how it is done, you should carefully study the sample problems discussed in the text. Always
identify the source of the centripetal force that pulls the object around the circle.
Questions and Example Problems from Chapter 6
Question 1
If you press an apple crate against a wall so hard that the crate cannot slide down the wall, what
is the direction of (a) the static frictional force fs on the crate from the wall and (b) the normal
force FN on the crate from the wall. If you increase your push, what happens to (c) fs, (d) FN, and
(e) fs,max?
Problem 1
A person pushes horizontally with a force of 220 N on a 55 kg crate to move it across a level
floor. The coefficient of kinetic friction is 0.35. What is the magnitude of (a) the frictional force
and (b) the crate’s acceleration?
Problem 2
A 2.5 kg block is initially at rest on a horizontal surface. A 6.0 N horizontal force and a vertical
G
force P are applied to the block as shown in the figure below. The coefficients of friction for the
block and surface are μs = 0.40 and μk = 0.25. Determine the magnitude and direction of the
G
frictional force acting on the block if the magnitude of P is (a) 8.0 N, (b) 10 N, and (c) 12 N.
Problem 3
A loaded penguin sled weighing 80 N rests on a plane inclined at 20° to the horizontal (see the
figure below). Between the sled and the plane, the coefficient of static friction is 0.25, and the
G
coefficient of kinetic friction is 0.15. (a) What is the minimum magnitude of the force F ,
parallel to the plane, that will prevent the sled from slipping down the plane? (b) What is the
minimum magnitude F that will start the sled moving up the plane? (c) What value of F is
required to move the sled up the plane at constant velocity?
Problem 4 (Problem from Exam 1 – Spring 2002)
In the figure below, two blocks are connected over a frictionless, massless pulley. The weight of
block A is 50 N and the coefficient of static friction between block A and the incline is 0.20. The
angle θ of the incline is 30.0o. What is the maximum and minimum mass that block B can have
such that both blocks remain stationary?
Problem 5
Block B in the figure below weighs 711 N. The coefficient of static friction between block and
table is 0.25; assume that the cord between B and the knot is horizontal. Find the maximum
weight of block A for which the system will be stationary.
Problem 6
Suppose the coefficient of static friction between the road and the tires on a car is 0.60 and the
car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level
curve of 30.5 m radius?
Problem 7
As shown in the figure below, a 1.34 kg ball is connected by means of two massless strings to a
vertical, rotating rod. The strings are tied to the rod and are taut. The tension in the upper string
is 35 N. (a) Draw the free-body diagram for the ball. What are (b) the tension in the lower string,
(c) the net force on the ball, and (d) the speed of the ball?